127K.C.S.E. GEOGRAPHY P22012 QUESTIONSSECTION AAnswer all the questions in this section.1 a What is mining? 2 marks b State four benefits of Soda Ash mining to the economy of Kenya. 4 marks 2. A Name two methods used in deep sea fishing. 2marks b State three ways in which the government of Kenya is promotingthe fishing industry. 3 marks 3 a Apart from the sun, name three other sources of electricity. 3marks b Give three advantages of using solar energy. 3marks 4. Give three reasons why it is necessary for the government of Kenya tocarry out a national census. 3marks a Identify two methods used to control tsetse flies in Kenya. 2 marks b State three negative effects of uncollected garbage on the environment. 3 marks For More Free KCSE past papers visit www.freekcsepastpapers.com128SECTION BAnswer questions 6 and any other two questions in this section.6. Study the photograph below and answer question Source: Internet a i Identify the type of photograph shown above. 1mark ii Draw a rectangle measuring 15 cm by 10 cm to represent the area coveredby the photograph. 1 mark For More Free KCSE past papers visit www.freekcsepastpapers.com129 iii On the rectangle, sketch and label four main features shown on thephotograph. 4 marks iv Using evidence from the photograph, identify two indicators which showthatthe area receives high rainfall. 2 marks b i Name three exotic types of dairy cattle reared in Kenya. 3 marks ii Explain three human factors that favour dairy farming in theKenya Highlands. 6 marks C Explain four ways in which dairy farming in Kenya is different fromdairy farming in Denmark. 8 marks 7. A i What is agro-forestry? 2 marks ii Give four reasons why agro-forestry is encouraged in Kenya. 4 marks b Use the map of Kenya below to answer questions b i and ii .For More Free KCSE past papers visit www.freekcsepastpapers.com130 i Name the forest reserves marked H, J and K. 3marks ii Explain four factors that favour the growth of natural forest in the areamarked L.


Study the photograph below and answer question Source: Internet a i Identify the type of photograph shown above. 1mark ii Draw a rectangle measuring 15 cm by 10 cm to represent the area coveredby the photograph. 1 mark For More Free KCSE past papers visit www.freekcsepastpapers.com129 iii On the rectangle, sketch and label four main features shown on thephotograph. 4 marks iv Using evidence from the photograph, identify two indicators which showthatthe area receives high rainfall. 2 marks b i Name three exotic types of dairy cattle reared in Kenya. 3 marks ii Explain three human factors that favour dairy farming in theKenya Highlands. 6 marks C Explain four ways in which dairy farming in Kenya is different fromdairy farming in Denmark. 8 marks 7. A i What is agro-forestry? 2 marks ii Give four reasons why agro-forestry is encouraged in Kenya. 4 marks b Use the map of Kenya below to answer questions b i and ii .For More Free KCSE past papers visit www.freekcsepastpapers.com130 i Name the forest reserves marked H, J and K. 3marks ii Explain four factors that favour the growth of natural forest in the areamarked L. 8 marks c Explain four problems facing forestry in Kenya. 8 marks 8. I Name two provinces in Canada where wheat is grown on a largescale. 2 marks For More Free KCSE past papers visit www.freekcsepastpapers.com131 a ii State three physical conditions that favour wheat farming inCanada. 3 marks b Compare wheat farming in Kenya and Canada under the followingsubheadings: i research; 2 marks ii government policy; 2 marks ii transport. 2 marks b Explain four problems that affect wheat farming in Canada. 8 marks c Your Geography class intends to carry out a field study on wheatharvesting in a farm. I State two reasons for preparing a working schedule. 2 marks ii Outline two problems that face wheat harvesting you are likely to findout. 2 marks iii Suppose during the field study you used the interview method to collectdata,state two limitations of the method.


3 marks b Compare wheat farming in Kenya and Canada under the followingsubheadings: i research; 2 marks ii government policy; 2 marks ii transport. 2 marks b Explain four problems that affect wheat farming in Canada. 8 marks c Your Geography class intends to carry out a field study on wheatharvesting in a farm. I State two reasons for preparing a working schedule. 2 marks ii Outline two problems that face wheat harvesting you are likely to findout. 2 marks iii Suppose during the field study you used the interview method to collectdata,state two limitations of the method. 2 marks 9. A i Identify the three types of inland waterways used for transportin Africa. 3 marks ii Give four reasons why the government of Kenya is expanding pipelinetransport. 4 marks For More Free KCSE past papers visit www.freekcsepastpapers.com132 b i State three advantages of railway transport. 3 marks ii State four conditions of roads in Kenya that may lead to motor vehicleaccidents. 4 marks c The sketch map below shows the Great Lakes and St.Lawrence Seaway. Use it to answer question C.KEY:xxxxxx - International Boundary. Name:For More Free KCSE past papers visit www.freekcsepastpapers.com133 i the ports marked M and P. ii the Lake marked N.For More Free KCSE past papers visit www.freekcsepastpapers.com134 d Explain four benefits of the Great Lakes and St.Lawrence Seaway to theeconomies ofU.S.A.and Canada. 8 marks 10 . A i Name two settlement patterns. 2 marks ii Explain four physical factors that influence settlement. 8marks b i Explain how the following factors have led to the growth of Thika town. Eocation; 2 marks Transport; 2 marks Eand. 2 marks ii Apart from being a transport and communication centre, give three otherfunctions of Thika town. 3 marks c Explain three positive effects of urbanization to a country. 6 marks For More Free KCSE past papers visit www.freekcsepastpapers.com.


SECTION A 25 marks Answer all the questions in this section n the spaces provided, A drug manufacturer gives the mass of the active ingredient in a tablet as 5 mg. Express this quantity in kilogramme and in standard form, 1 mark The masses of equal volumes of certain liquid and of water were found to be my andrespectively. Given that the density of water is Igem , express the density. P, ofthe liquid in terms of my and my. Show your work 2 marks Fig. 1 shows a brick placed on a plane inclined at an angle to the horizontal. The weight. W. of the brick is shownFigure a Onthe same diagram show with arrows the other two forces acting on the brick andname them, 1 mark b State how each of the two forces named in a above is affected when the angle isreduced. 1 mark Water is known to boil at 100 C. A student heated some water and noticed that it boiled atwore. State two possible reasons for this observation 2 marks Fig. 2 shows a flask filled with water, The Mask i ited witha cork through which a tubeis inserted. When the flask is cooled, the water level rises slightly, then falls stealThe Figure?Explain this observation. Marks Fig. 3 shows a hot water bath with metal rods inserted through one of its sides. Some waxis fixed at the end of each rod. Use this information to answer questions 6 and 7.Meta rodHoe water 7 Figure3What property of metals could be tested using this set-up? 1 mark Besides the len comparing theath of the rods that is kept constant, what else should be kept constant whenroperty forthe different metal rods? 1 mark Fig. 4 shows a conical flask 1Sem high, filled with aliquid of density 1200kgm". Theatmospheric pressure of the surrounding is 8.4 x 10 Pa FiguresDetermine the pressure atthe point marked X, atthe bottom of the flask marks Explain the difference between a liquid and a gas in terms of intermolecular distances andforces. 2 tnarks Fig. 5 shows a toy resting on top ofa closed bottle.


Theatmospheric pressure of the surrounding is 8.4 x 10 Pa FiguresDetermine the pressure atthe point marked X, atthe bottom of the flask marks Explain the difference between a liquid and a gas in terms of intermolecular distances andforces. 2 tnarks Fig. 5 shows a toy resting on top ofa closed bottle. Use the information on the figure toanswer questions 10 and 11 Light hollow plasticsatelThin ctl odHeavy Lead Heavy Leadbar aFigures 10 Mark on the diagram, point Q. the approximate centre of gravity of the toy.ing a reason, name the state of equilibrium of the toy. Un12 Fig. 6 showsa sheet of paper rolled into a tube. Figures When a fast stream of ar is blown into the tube as shown in the diagram the paper tubecollapses. Explain the observation. Mark 2 marks 2 marks 13. The graphs in Fig. 7 represent the relations between extension e and mass m added on twosprings x andy. HH iu ieatr Rae SRTGiven that the two springs are made of same material, give a reason why the graphs aredifferent. Mark 14 The system in Fig. 8 is in equilibrium. Metrele, Figures When the temperature of the water is raised the system is observed to tlt to the right, statethe reason for tis observation, marks SECTION B 55 marks Answer all the questions in this section in the spaces provided.15 a State Newton s second law of motion. Mark b A matatu starts from rest and accelerates to cover a distance of 49m in 7seconds. Determine: i itsacceleration; 3 marks Gi its velocity after 7seconds. 2 marks Atrolley moving on a horizontal bench of height 1.2m, strikes a barrie atthe edgeof the bench. The brass mass on the top ofthe toley flies off on impact and lands on the ground 2.5m from the edge of the bench,Determine: 3 the time taken by the brass mass to reach the ground; 2 marks iy the speed at which the tolley struck the barrier 2 marks 16 a Define the term heat capacity 0 mark b You are provided with the apparatus shown in Fig.


Mark b A matatu starts from rest and accelerates to cover a distance of 49m in 7seconds. Determine: i itsacceleration; 3 marks Gi its velocity after 7seconds. 2 marks Atrolley moving on a horizontal bench of height 1.2m, strikes a barrie atthe edgeof the bench. The brass mass on the top ofthe toley flies off on impact and lands on the ground 2.5m from the edge of the bench,Determine: 3 the time taken by the brass mass to reach the ground; 2 marks iy the speed at which the tolley struck the barrier 2 marks 16 a Define the term heat capacity 0 mark b You are provided with the apparatus shown in Fig. 9 and a stop watch, Lappe stciter Describe an experiment to determine the specific latent heat of steam, , using the setup. In your answer clearly explain the measurements to be made and how these measurements could be used to determine 6 marks A block of metal of mass 150g at 100 C is dropped into a lagged calorimeter of heat capacity 40JK" contaming 100g of water at 25 C. The temperature ofthe resulting,mixture is 34 C. specific heat capacity of water 42005KgK" Determine: i heat gained by calorimeter; 2 marks Gi heat gained by water; mark ii heat lost by the metal block: 1 mark ix specific heat capacity of the metal block. 3 marks a What is meant by absolute zero temperature? Mark Fig. 10 shows a set up to investigate the relationship between temperature andvolume fora certain gas, Beaker Figure 10 b State two factors that are kept constant, in order to determine the relationship. 2 marks Thegraph in Fig. 11 shows the relationship between volume and temperature for theexperiment. Graph of Volume against Temperature...a te; What was the volume of the gas at 0 C? 1 markGi At what temperature would the volume ofthe gas be zero?


Co b State two conditions necessary forthe process to take place marks o State what happens othe end-products ofthe process. S marks Give thee reason in ach case why support i necessary i plans 5 marks Gi animals 6 marks Whyismovement necessary in animals? Marks 'A freshly obtained dandelion stem measuring Sem long was split enginwise to optain twosimilar pieces. The pieces were placed in solutions of different concentrations in petri dishes for 20 minutes. The appearance after 20 minutes is as shown. Epidernis. EpidermisPiece in L, Piece in Ly Account for the appearance of the pieces in solutions Land Le 6 marks State the significance of the biological proces involved in the experiment 2 marks SECTION B 40 marks Answer question 6 compulsory and either question 7 or 8 in the spaces provided after question 86 Anexperiment was carried out to investigate transpiration and absorption of water insunflower plants in their natural environment with adequate supply of water. The amount of water was determined in two hour intervals. The results are shown in the table below. Amounts of water in grammesTime of dayTranspiration Absorption 1100-13 00 3 013.0015 00 45 30 1500-1700 32 a21700-19 00 46 61900-21 00 25 32 2190-2300 e2300-01 00 oe is01.00 -03 00 on u a Using the same axes, plot graphs to show transpiration and absorption of water ingrammes against time ofthe day. Marks b At what time ofthe day was the amount of ws the same for transpiration andabsorption? Mark Account for the shape of the graphs of transpiration; marks Gi absorption, G marks 4 What would happen to transpiration and absorption of water ifthe experiment wascontinued till 05 00 hours? 2 marks Name two factors that may affect transpiration and absorption at any given time. 2 marks Explain how the factors you named in e above affect transpiration. 2 marks Describe the nitrogen cycle, 20 marks a State four characteristics of gaseous exchange surfaces.


Marks b At what time ofthe day was the amount of ws the same for transpiration andabsorption? Mark Account for the shape of the graphs of transpiration; marks Gi absorption, G marks 4 What would happen to transpiration and absorption of water ifthe experiment wascontinued till 05 00 hours? 2 marks Name two factors that may affect transpiration and absorption at any given time. 2 marks Explain how the factors you named in e above affect transpiration. 2 marks Describe the nitrogen cycle, 20 marks a State four characteristics of gaseous exchange surfaces. 4 marks b Describe the mechanism of gaseous exchange in a mammal. 16 marks.


KCSE 2011 HISTORY PAPER 1QUESTIONSSECTION A 25marks Answer all the question in this section in the answer booklet provided.1Give two unwritten sources of information on History and Government. 2marks 2What was the main reason for the migration of the Eastern Bantu fromShungwaya during the pre-colonial period? 1 mark 3Give two reasons why Kenyan communities fought against each other during thepre Colonial period. 2 marks 4Identify the two main items of trade from the interior of Kenya during the longdistance trade. 2 marks 5Identify two contributions made by the early Christian missionaries in the fieldof education in Kenya. 2 marks 6Give the meaning of the term national integration. 1 mark 7What constitutional amendment made Kenya return to a multi-party state? 1mark 8Name the document which contains the rights of the child in Kenya. 1mark 9Identify two economic benefits of the Kenya-Uganda railway during the colonialPeriod. 2 marks 10Give two ways through which the white settlers acquired land in Kenya duringthe colonial period. 2 marks 11State two problems faced by trade union movement during the colonial period inKenya. 2 marks 12State one change introduced by the Littleton Constitution of 1954 that benefitedthe Africans in the struggle for independence. 1mark 13What was the main contribution of Thomas Joseph Mboya to the history ofKenya? 1 mark 14State the main function of parliament in Kenya. 1 mark 15Give one member of the AEMO at its inception in 1957. 1mark 16Name the education commission that recommended the introduction of the 8.4.4system of education in Kenya. 1 mark 17Give two external sources of Government revenue in Kenya. 2 marks SECTION B 45 marks Answer any three questions from this section in the answer booklet provided.18 a State Five economic activities of the Borana during the pre-colonialperiod. For More Free KCSE past papers visit www.freekcsepastpapers.com 5 marks b Describe the social organization of the Maasai during the pre-colonialperiod. 10 marks 19 a State three reasons for the coming of the Portuguese to the Kenyan Coastin the 15th Century.


KCSE 2011 HISTORY PAPER 1QUESTIONSSECTION A 25marks Answer all the question in this section in the answer booklet provided.1Give two unwritten sources of information on History and Government. 2marks 2What was the main reason for the migration of the Eastern Bantu fromShungwaya during the pre-colonial period? 1 mark 3Give two reasons why Kenyan communities fought against each other during thepre Colonial period. 2 marks 4Identify the two main items of trade from the interior of Kenya during the longdistance trade. 2 marks 5Identify two contributions made by the early Christian missionaries in the fieldof education in Kenya. 2 marks 6Give the meaning of the term national integration. 1 mark 7What constitutional amendment made Kenya return to a multi-party state? 1mark 8Name the document which contains the rights of the child in Kenya. 1mark 9Identify two economic benefits of the Kenya-Uganda railway during the colonialPeriod. 2 marks 10Give two ways through which the white settlers acquired land in Kenya duringthe colonial period. 2 marks 11State two problems faced by trade union movement during the colonial period inKenya. 2 marks 12State one change introduced by the Littleton Constitution of 1954 that benefitedthe Africans in the struggle for independence. 1mark 13What was the main contribution of Thomas Joseph Mboya to the history ofKenya? 1 mark 14State the main function of parliament in Kenya. 1 mark 15Give one member of the AEMO at its inception in 1957. 1mark 16Name the education commission that recommended the introduction of the 8.4.4system of education in Kenya. 1 mark 17Give two external sources of Government revenue in Kenya. 2 marks SECTION B 45 marks Answer any three questions from this section in the answer booklet provided.18 a State Five economic activities of the Borana during the pre-colonialperiod. For More Free KCSE past papers visit www.freekcsepastpapers.com 5 marks b Describe the social organization of the Maasai during the pre-colonialperiod. 10 marks 19 a State three reasons for the coming of the Portuguese to the Kenyan Coastin the 15th Century. 3 marks b Explain six effects of the Portuguese rule on the East African Coast. 12 marks 20 a Identify three methods used by the British to establish their rule in Kenya.


2marks 2What was the main reason for the migration of the Eastern Bantu fromShungwaya during the pre-colonial period? 1 mark 3Give two reasons why Kenyan communities fought against each other during thepre Colonial period. 2 marks 4Identify the two main items of trade from the interior of Kenya during the longdistance trade. 2 marks 5Identify two contributions made by the early Christian missionaries in the fieldof education in Kenya. 2 marks 6Give the meaning of the term national integration. 1 mark 7What constitutional amendment made Kenya return to a multi-party state? 1mark 8Name the document which contains the rights of the child in Kenya. 1mark 9Identify two economic benefits of the Kenya-Uganda railway during the colonialPeriod. 2 marks 10Give two ways through which the white settlers acquired land in Kenya duringthe colonial period. 2 marks 11State two problems faced by trade union movement during the colonial period inKenya. 2 marks 12State one change introduced by the Littleton Constitution of 1954 that benefitedthe Africans in the struggle for independence. 1mark 13What was the main contribution of Thomas Joseph Mboya to the history ofKenya? 1 mark 14State the main function of parliament in Kenya. 1 mark 15Give one member of the AEMO at its inception in 1957. 1mark 16Name the education commission that recommended the introduction of the 8.4.4system of education in Kenya. 1 mark 17Give two external sources of Government revenue in Kenya. 2 marks SECTION B 45 marks Answer any three questions from this section in the answer booklet provided.18 a State Five economic activities of the Borana during the pre-colonialperiod. For More Free KCSE past papers visit www.freekcsepastpapers.com 5 marks b Describe the social organization of the Maasai during the pre-colonialperiod. 10 marks 19 a State three reasons for the coming of the Portuguese to the Kenyan Coastin the 15th Century. 3 marks b Explain six effects of the Portuguese rule on the East African Coast. 12 marks 20 a Identify three methods used by the British to establish their rule in Kenya. 3 marks b Explain Six results of the Nandi resistance against British occupation. 12 marks 21 a State five demands made by the East African Association EAA to theBritishColonial government in Kenya. 5 marks b Explain five factors that promoted the rise of African nationalism in Kenyaafter 1945. 10 marks SECTION C 30 marks Answer any two questions from this section in the answer booklet provided.22 a State three circumstances that can make a Kenyan citizen to be deniedthe right to life. 3 marks b Explain six civic responsibilities of a Kenyan citizen. 12 marks 23 a Give three reasons why general elections are important in Kenya. 3marks b Explain six functions of the body in charge of elections in Kenya. 12marks 24 a Identify three social functions of local authorities. 3marks For More Free KCSE past papers visit www.freekcsepastpapers.com.


285 FORM IV MOCK EXAMINATION, 2023 121 1 MATHEMATICS ALT A TERM 2 2023 C TIME: HRS SECTION I 50 marks Answer all questions in this section. 1. All odd numbers from 1 10 are arranged in descending order to form a number. I Write the number 1 mark ii Write the total value of the second digit of the number formed in a i 1 mark iii Express the value of the number in a ii as a product of its prime factors in power form 2 marks 2. A shopkeeper bought a bag of sugar. He intends to repack the sugar in 40 g , 250 g and 750 g . Determine the least mass in grams of sugar that was in the bag. 3 marks 3. Given that 0.3010 and 0.4771 without using tables or calculator find log0.036 correct to 4 significant figures. 3 marks 4. Evaluate 2ofof 3 marks 5. Using the grid provided below, solve the simultaneous equation 3 marks xyxy 6. Given that a chord of length 10 cm subtends an angle of c1.2 at the circumference of the circle. Calculate the radius of the circle. 3 marks 7. When a shopkeeper sells articles at Ksh 24.05, he makes a 30 profit on the cost price. During a sale, he reduced the price of each article to Ksh 22.95 . Calculate the percentage profit on an article sold at the sale price. 3 marks 8. The size of one interior angle of an irregular polygon is 080 . Each of the other interior angles is 0128 . Find the number of sides of the polygon. 3 marks www.freekcsepastpapers.com286 9. Simplify 275 2 marks 10. Given the inequalities 29xxx a Solve the inequality 3 marks b Represent on a number line 1 mark 11.


3 marks www.freekcsepastpapers.com286 9. Simplify 275 2 marks 10. Given the inequalities 29xxx a Solve the inequality 3 marks b Represent on a number line 1 mark 11. The diagram below represents a right rectangular based pyramid of 5 cm by 4 cm. The slant edge of the pyramid is 6 cm. Draw and label the net of the pyramid. 3 marks 12. Vectors 43ij OA, 2ij OB and 53ij OC. Show that points A, B and C are collinear. 3 marks 13. Find the period , amplitude and phase angle of the function 3sin602yx 3 marks 14. Simplify 2xxxx 3 marks 15. Write the following ratios in ascending order 2:3, 15:16, 7:6 , 13:15 3 marks 16. Under an enlargement, the image of the points A 3,1 and B 1,2 are A 3,7' and B 7,5'. Find the centre and scale factor of enlargement. 4 marks SECTION II 50 marks Answer only five questions in this section. 17. A straight line passes through P1,1 and Q 3,4 . A Find the length of line PQ 2 marks b Find the equation of the perpendicular bisector of line PQ , leaving the equation in the form ymxc 4 marks c Determine the equation of line parallel to line PQ and passes through point 2,3 , leaving your answer in double intercept form. Hence state the y intercept. 4 marks 18. The marks scored by 30 students in test were recorded as follows a Starting with the class 18 22 , make a frequency distribution table for the data.


Hence state the y intercept. 4 marks 18. The marks scored by 30 students in test were recorded as follows a Starting with the class 18 22 , make a frequency distribution table for the data. 2 marks b Using the frequency distribution in a above calculate : i the mean 2 marks ii the median 3 marks c Draw a frequency polygon to represent the data. 3 marks www.freekcsepastpapers.com287 19. The solid below is made up of hemispherical part and a frustum of cone. The top and bottom radius of the frustum are 5 cm and 15 cm respectively. The vertical height of the frustum is 24 cm . A Determine the vertical height of the cone from which the frustum was cut. 2 marks b Calculate i The volume of the solid correct to 2 decimal places 3 marks ii The surface area of the solid correct to 2 decimal places 5 marks 20. A i Draw the graph of the function 5yxx for 23x 5 marks ii Use the graph to solve the equation50xx 1 mark b Use the graph to solve the simultaneous equation 5yxx and 22yx 3 marks c Write down the quadratic equation which the line 22yx is solving. 1 marks 21. The diagram below shows the speed time graph for a bus travelling between two stations, the bus starts from rest and accelerates uniformly for 75 seconds. It then travels at constant speed for 150 seconds and finally decelerates uniformly for 100 seconds. A Given that the distance between the two stations is 5225 m. Calculate i Maximum speed in km h attained by the bus. 3 marks ii The acceleration of the bus 2 marks c A van left Nairobi at 8.30 a.m and travelled towards Mombasa at an average speed of 80 km h . At 8.30 am a car left Nairobi and travelled along the same road at an average speed of 120 km h . I Calculate the distance covered by the car to catch up with the van.


3 marks ii The acceleration of the bus 2 marks c A van left Nairobi at 8.30 a.m and travelled towards Mombasa at an average speed of 80 km h . At 8.30 am a car left Nairobi and travelled along the same road at an average speed of 120 km h . I Calculate the distance covered by the car to catch up with the van. 4 marks ii Find the time of the day when the car caught up with van. 1 mark www.freekcsepastpapers.com288 22. On the Cartesian plane below, triangle PQR has vertices P 2, 3 , Q 1, 2 and R 4, 1 while triangle P Q R has vertices P -2, 3 , Q -1, 2 and R -4, 1 . A Describe fully the transformation which maps triangle PQR onto triangle P Q R . 1 mark b On the same plane, draw triangle P Q R , the image of triangle PQR under a reflection in the line 2 marks c Describe fully a single transformation which maps triangle P Q R onto triangle P Q R . 2 marks d Draw triangle P Q R such that it can be mapped onto triangle PQR by a positive quarter turnabout 0, 0 3 marks e State a pair of triangles that is i oppositely congruent 1 mark ii directly congruent 1 mark 23. The equation of the curve is 1yxx a Determine i the stationary points 4 marks ii the nature of the stationary points in a i above 2 marks b Determine i the equation of the tangent to the curve at 1x 2 marks ii the equation of the normal to the curve at 1x 2 marks 24. The boundaries of ranchAB, BC , CD and DA are straight lines such that B is 0075 from A and a distance of50 km . C is due east of B and a bearing of 0N80 E from A .


Without using tables or calculator, evaluate and simplify 4 marks sin 300 sin 450cos 600 1 4. Given the position vectors 4 8 2 and 3 2 . Point C divides vector AB in the ratio of 3:-1. Find the magnitude of . Give your answer to 2dp 3 marks 5. Given that the values P 8.2 cm, A 4.1cm and B 7.0 cm were measured to 1dp. Find the percentage error in the evaluation of. 3 marks 6. Expand 1 12 10 upto the 4th term in the ascending powers of . Hence evaluate the value of 0.95 10 to 3 decimal places. 3 marks 7. Two types of coffee grade A and B retails at sh.240 and sh.300 respectively. Mohamed sell a mixture of both grades at shs.303 60, making a profit of 10 . Find the ratio in which he mixed the grades 3 marks 8. Juma a form 2 student was told to pick two number x and y from a set of digits 0, 1, 2, 3, 4, 5 and 6. Find the probability that the is at least 3. 3 marks 9. Two quantities are such that y varies partly as the square of and partly inversely as the square root of . Given that when 4, 40 and when 1, 18. Find the value of y when 0.25. 4 marks 10.


The total number of both vaccines should be more than 600 boxes. The number of boxes of Johnson and Johnson should be less than 500 boxes and more or equal to twice the number of Astrazenica. Letting x to represent the number of Johnson and Johnson boxes and y to represent the number of boxes of Astrazenica. A i Form all the in equalities in and to represent the above information. 3 marks ii Represent the inequalities on a graph 4 marks b If the cost of importing 1 box of Johnson and Johnson is sh1000 and astrazenica is shs.800. Find maximum cost of importing the vaccines. 3 marks www.freekcsepastpapers.com285 FORM IV MOCK EXAMINATION, 2023 121 1 MATHEMATICS ALT A TERM 2 2023 C TIME: HRS SECTION I 50 marks Answer all questions in this section. 1. All odd numbers from 1 10 are arranged in descending order to form a number. I Write the number 1 mark ii Write the total value of the second digit of the number formed in a i 1 mark iii Express the value of the number in a ii as a product of its prime factors in power form 2 marks 2. A shopkeeper bought a bag of sugar. He intends to repack the sugar in 40 g , 250 g and 750 g . Determine the least mass in grams of sugar that was in the bag. 3 marks 3. Given that 0.3010 and 0.4771 without using tables or calculator find log0.036 correct to 4 significant figures. 3 marks 4. Evaluate 2ofof 3 marks 5. Using the grid provided below, solve the simultaneous equation 3 marks xyxy 6. Given that a chord of length 10 cm subtends an angle of c1.2 at the circumference of the circle. Calculate the radius of the circle. 3 marks 7. When a shopkeeper sells articles at Ksh 24.05, he makes a 30 profit on the cost price.


Calculate the radius of the circle. 3 marks 7. When a shopkeeper sells articles at Ksh 24.05, he makes a 30 profit on the cost price. During a sale, he reduced the price of each article to Ksh 22.95 . Calculate the percentage profit on an article sold at the sale price. 3 marks 8. The size of one interior angle of an irregular polygon is 080 . Each of the other interior angles is 0128 . Find the number of sides of the polygon. 3 marks www.freekcsepastpapers.com268 NAKURU - FORM FOUR MOCK EXAMINATION, 2023 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS 30 MINUTES SECTION I 50 MARKS Answer ALL Questions in this Section 1. Evaluate the following; 3 marks 7 32of 2. Use square roots, reciprocal and square tables to evaluate to 4 significant figures the expression; 3 marks 0.06458 12 20.4327 2 3. Solve for x in the equation1 3 log2 xx 3marks 4. A farmer has a piece of land measuring 840m by 396m. He divides it into square plots of equal size. Find the maximum area of one plot. 3 marks 5. The following data was obtained from the mass of a certain animal. Complete the table and the histogram below. 3 marks Mass kg 41-50 51-55 56-65 frequency 20 40 6. Solve the following inequalities and state the integral values 3 marks 2x 2 3x 1 x 11 7. The figure below shows a regular polygon A B C D E F with the interior angles indicated. Find the value of the smallest angle in the polygon. 3 marks www.freekcsepastpapers.com269 8. The figure below represents a plot of land ABCD such that AB 85m, BC 75m, CD 60m, DA 50m and angle ACB 900. Not drawn to scale .


3 marks www.freekcsepastpapers.com269 8. The figure below represents a plot of land ABCD such that AB 85m, BC 75m, CD 60m, DA 50m and angle ACB 900. Not drawn to scale . Determine the area of the plot, in hectares, correct to two decimal places. 3marks 9. A rectangular tank has a hole in it such that 11cm3 of water leaks out every 5 seconds. Using as 3.142. Calculate:- i The capacity of the water lost from the tank every hour. 2marks ii The time it takes to fill a cylindrical tank of radius 30cm and height 30cm into which the leaking water drains; in hours to 4 significant figures. 2marks 10. Find the value of x if. 3 marks x3 11. The image of a point K 1,2 after translation is K1 -1,2 . What is the coordinate of the point R whose image is R1 -3,3 after undergoing the same translation. 3 marks 12. Mugo, a fruit vendor obtained a total of Kshs. 6144 from her sales of oranges on Monday at Kshs. 8.00 each. She had bought 560 more oranges to add to what had remained on Sunday where she had sold 240 more oranges than on Saturday. She had sold 750 oranges on Saturday. Calculate the total number of oranges Mugo had bought on Saturday. 4 marks 13. Simplify the following expression by reducing it to a single fraction. 3 marks 2 33 22 1 4 14. Water and ethanol are mixed such that the ratio of the volume of water to that of ethanol is 3: 1. Taking the density of water as 1 g cm3 and that of ethanol as 1.2g cm3, find the mass in grams of 2.5 litres of the mixture. 3 marks 15.


Water and ethanol are mixed such that the ratio of the volume of water to that of ethanol is 3: 1. Taking the density of water as 1 g cm3 and that of ethanol as 1.2g cm3, find the mass in grams of 2.5 litres of the mixture. 3 marks 15. A Kenyan bureau buys and sells foreign currencies as shown below Buying Selling In Kenya shillings In Kenya Shillings 1 Hong Kong dollar 9.74 9.77 100 Japanese Yen 75.08 75.12 A tourists arrived in Kenya with 105 000 Hong Kong dollars and changed the whole amount to Kenyan shillings. While in Kenya, she pent Kshs 403 897 and changed the balance to Japanese Yen before leaving for Tokyo. Calculate the amount, in Japanese Yen that she received. 3 marks 16. Draw triangle ABC such that AB 4.4cm, BC 4cm and angle ABC 1200, construct an orthocenter of the triangle ABC and mark it X. 3 marks www.freekcsepastpapers.com270 SECTION II 50 MARKS Answer FIVE questions ONLY from this section 17. A line L1 passes through the points 2, 3 and 1, 6 and is perpendicular to L2at 1, 6 . A Find the equation of 1. 2 marks b Find the equation of 2 in the form 0 where a, b and c are constants. 2 marks c Given that another line 3 is parallel to 1 and passes through point 1,2 , find the and intercepts of 3 . 3 marks d Find the point of intersection of 2and 3. 3 marks 18. A sector of angle 1080 is cut from a circle of radius 20 cm. It is folded to form a cone. Calculate to 1 decimal place: use a The curved surface area of the cone. 2 marks b The base radius of the cone.


It is folded to form a cone. Calculate to 1 decimal place: use a The curved surface area of the cone. 2 marks b The base radius of the cone. 3 marks c The vertical height of the cone. 2 marks d If 12 cm of the cone is chopped off to form a frustum as shown below. Calculate the volume of the frustum formed. 3 marks 19. A village Q is 7 km from village P on a bearing of 0450. Village R is 5 km from village Q on a bearing of 1200 and village S is 4 km from village R on a bearing of 2700. A Taking a scale of 1 m to represent 1 Km, locate the three villages. 3 marks b Use the scale drawing to find the: i. Distance and bearing of the village R from village P. 2 marks ii. Distance and bearing of village P from village S. 2 marks c Calculate the area enclosed by the three villages 3 marks 20. The floor of a rectangular room can be covered completely by a carpet costing sh. 200 per square metre. The total cost of the carpet would be sh. 5600. Taking the length of the room to be x m; a Express width of the room in terms of x 2marks b If a uniform width of 12 m is left uncovered all round. The cost is sh. 2000 less. Form and solve an equation to determine the value of x. 5marks c Later it was decided that the floor left uncovered in b above should also be covered. However the cost of the carpet had then gone up by sh. 150 per square metre. Determine the cost in covering the previously uncovered region. 3marks 12cmwww.freekcsepastpapers.com271 21. A Given that the matrix 2A , find A-1, the inverse of A. 2 marks b Kariuki bought 400 goats and 600 sheep for a total of Kshs 1,700,000.


3marks 12cmwww.freekcsepastpapers.com271 21. A Given that the matrix 2A , find A-1, the inverse of A. 2 marks b Kariuki bought 400 goats and 600 sheep for a total of Kshs 1,700,000. Maina bought 180 goats and 240 sheep for a total of Kshs 720,000. If the price of a goat is sh. X and that of a sheep is shs y, i Form two equations to represent the above information. 2 marks ii Use the matrix A-1 to find the price of one goat and one sheep. 3 marks c John bought 450 goats and 720 sheep. He was given a total discount of shs 66,600. If the discount on the price of a goat was 2 , calculate the percentage discount on the price of a goat. 3 marks 22. The distance between two towns A and B is 460 km. A minibus left town A at 8.45 am and travelled towards Bat an average speed of 65km hr. A matatu left B at 10.55 am on the same day and travelled towards A at an average speed of 80km hr. A How far from town B did they meet? 4 marks b At what time did the two vehicles meet? 2 marks c A motorist started from his home at 9.15am on the same day and travelled to B at an average speed of 120km hr. He arrived at the same time as the minibus. Calculate the distance from B to his home. 4 marks 23. Three partners Mutua, Muthoka and Mwikali contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000 respectively to start a business of a matatu plying Mbumbuni Machakos route. The matatu carries 14 passengers with each paying Sh. 250. The matatu makes two round trips each day and ever full. Each day Sh. 6000 is used to cover running costs and wages. A Calculate their net profit per day.


Each day Sh. 6000 is used to cover running costs and wages. A Calculate their net profit per day. 2 marks b The matatu works for 25 days per month and is serviced every month at a cost of KSh. 10,000. Calculate their monthly profit in June. 1 mark c The three partners agreed to save 40 of the profit, 24 is shared equally and the rest to be shared in the ratioof their contribution. Calculate Muthoka s share in the month of June. 4 marks d The matatu developed mechanical problems and they decided to sell it through an agent who charged a commission of 5 on selling price. Each partner received KSh. 475,000 from the agent after he had taken his commission. Determine the price at which the agent sold the matatu. 3 marks 24. The displacement S metres of a body moving along a straight line after t seconds is given by S 2t3 32 2 3t a Find its initial acceleration. 3 marks b Calculate:- i The time when the body was momentarily at rest. 3 marks ii Its displacement by the time it comes to rest momentarily 2 marks c Calculate the maximum velocity attained 2 marks www.freekcsepastpapers.com272 NAKURU - FORM FOUR MOCK EXAMINATION, 2023 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS 30 MINUTES SECTION I 50 MARKS Answer all the questions from this section 1. Use Logarithms correct to four significant figures to evaluate. 4marks 24.36 0.0665471.4823 2. Find the value of given that the matrix 74 3 is singular 3 marks 3. In the figure below QT is a tangent to the circle at Q. PXRT and QXS are straight lines. PX 6cm, RT 8cm, QX 4.8cm and XS 5cm. Find the length of QT 3 marks 4.


PXRT and QXS are straight lines. PX 6cm, RT 8cm, QX 4.8cm and XS 5cm. Find the length of QT 3 marks 4. Use the trapezium rule with seven ordinates to find the area bounded by the curve 2 1 lines x -2, x 4 and x axis 3 marks 5. Given that 2 make the subject of the formula 3 marks 6. A Construct triangle PQR such that PQ 7cm, QR 5cm and 30 2 marks b Construct the focus L1 of points equidistant from P and Q to meet the locus L2 of points equidistant from Q and R 2 marks 7. The points 5, 5 and -3, -1 are ends of a diameter of a circle centre A. Determine: a The coordinates of A. 1 mark b The equation of a circle expressing it in form x2 y2 ax by c 0 2 marks 8. A transformation is represented by the matrix 1342 . This transformation maps a triangle ABC of the area 12.5cm2 onto another triangle A B C . Find the area of triangle A B C . 3marks 9. Pipe A can fill a tank in 2 hours, pipes B and C can empty the tank in 5 hours and 6 hours respectively. How long would it take a To fill the tank if A and B are left open and C closed 2 Marks b To fill the tank with all the pipes open 2 Marks 10. I Expand and simplify 1-3x 5 upto the term in x3 2 marks ii Hence use your expansion to estimate 0.97 5 correct to 4d.p. 2 marks 11. Solve for x in the equation: 2 4 1 for 00 x 1800 3 marks 12.


I Expand and simplify 1-3x 5 upto the term in x3 2 marks ii Hence use your expansion to estimate 0.97 5 correct to 4d.p. 2 marks 11. Solve for x in the equation: 2 4 1 for 00 x 1800 3 marks 12. Wanjiku pays for a car on hire purchase in 15 monthly instalments. The cash price of the car is Ksh.300, 000 and the interest rate is 15 p.a. A deposit of Ksh.75, 000 is made. Calculate her monthly repayments. 3 marks 13. The gradient function of a curve is given 3x2 8x 2. If the curve passes through the point, 2, 2 , find its equation. 3 marks www.freekcsepastpapers.com273 14. Simplify the following surds leaving your answer in the form a b 3marks 52 2 5 22 2 5 15. The sum of two numbers is 24. The difference of their squares is 144. What are the two numbers? 3marks 16. The data below represents the marks scored by 9 form 4 students in an exam: 40, 37, 39, 40,41,43,44, 37,44 Calculate the interquartile range of the above data 3 marks SECTION II 50 MARKS Answer five questions only from this section 17. The following table shows the rate at which income tax was charged during the year 2021 Monthly taxable income in Ksh. Tax rate 0 9860 10 9861 19720 15 19721 29580 20 29581 39440 25 39441 49300 30 49301 59160 35 over 59160 40 Maina earns a basic salary of Ksh.42000 and a monthly house allowance of sh.13000. He contributes 7.5 of his basic salary to pension scheme. This contribution is exempted from taxation.


Tax rate 0 9860 10 9861 19720 15 19721 29580 20 29581 39440 25 39441 49300 30 49301 59160 35 over 59160 40 Maina earns a basic salary of Ksh.42000 and a monthly house allowance of sh.13000. He contributes 7.5 of his basic salary to pension scheme. This contribution is exempted from taxation. He is entitled to a personal relief of sh.2400 per month. Calculate: a His monthly Taxable income 2 marks b Calculate his net monthly tax 6 marks c Maina s monthly salary 2 marks 18. The above diagram represents a wooden prism. ABCD is a rectangle. Points E and F are directly below C and B respectively. M is the mid-point of CD. AB 8 cm, BC 10 cm and CE 4.5 cm. A Calculate the size of angle CDE 2 marks b Calculate the i Length of AC 2 marks ii Angle AC makes with the plane ADEF 2 marks c Find the: i Length of MB 2 marks ii Angle CBM 2 marks 19. An aeroplane left town 65 , 15 to another town 65 , 165 at a speed of 200 knots using the shortest route. 227 , 6370 a Find i The shortest distance travelled in nautical miles. 3 marks ii The time taken from P to Q in hours. 2 marks www.freekcsepastpapers.com274 b Another plane left P at 1.30 p.m local time and travelled to T 650N, 60 0E along the parallel of latitude. Find i The distance between P and Q to the nearest kilometres. 3 marks ii The local time of arrival at T if the plane flew at 470km hr. 2 marks 20.


Find i The distance between P and Q to the nearest kilometres. 3 marks ii The local time of arrival at T if the plane flew at 470km hr. 2 marks 20. The probability that a student goes to school by a boda-boda is 23 and by a matatu is 14 . If he uses a bodaboda the probability that he is late is 25 and if he uses matatu the probability of being late is 310. If he uses other means of transport the probability of being late is 320. A Draw a tree diagram to represent this information. 3marks b Find the probability that he will be late for school. 3marks c Find the probability that he will be late for school if he does not use a matatu. 2marks d What is the probability that he will not be late to school? 2marks 21. A farmer has 50 acres of land. He has a capital Shs. 2,400 to grow carrots and potatoes as cash crops. The cost of growing carrots is Shs.40 per acre and that of growing potatoes is Shs.60 per acre. He estimates that the respective profits per acre are Shs.30 on carrots and Shs. 40 on potatoes . By letting x and y to represent the acres of carrots and potatoes respectively:- a Form suitable inequalities to represent this information. 4marks b By representing this information on a graph, determine on how many acres he should grow each crop for maximum profit 4marks c Find the maximum profit. 2marks 22. The 2nd and 5th terms of an arithmetic progression are 8 and 17 respectively. The 2nd, 10th and 42nd terms of the A.P. form the first three terms of a geometric progression. Find a the 1st term and the common difference. 3marks b the first three terms of the G.P and the 10th term of the G.P. 4marks c The sum of the first 10 terms of the G.P. 3marks 23.


3marks b the first three terms of the G.P and the 10th term of the G.P. 4marks c The sum of the first 10 terms of the G.P. 3marks 23. In the triangle PQR below L and M are points on PQ and QR respectively such that PL:LQ 1:3 and QM:MR 1:2, PM and RL intersect at X, given that PQ b and PR c a Express the following vectors in terms of b and c i QR 1mark ii PM 1mark iii RL 1mark b By taking PX hPM and RX kRL where h and k are constants find two expressions of PX in terms of h, k, b and c. Hence determine the values of the constant h and k. 6marks c Determine the ratio LX:XR 1mark 24. Given that y 2sin 2x and y 3cos x 45 o a Complete the table below. 2mks x 00 200 400 600 800 1000 1200 1400 1600 1800 2sin2 x 0 1.97 0.68 -0.68 -1.73 -1.29 0.00 3cos x 450 2.12 1.27 -0.78 -2.46 -2.72 -2.12 b Use the data to draw the graphs of y 2 sin 2x and y 3 cos x 45o for 0o x 180oonthe same axes. 4marks a. State the amplitude and period of each curve. 2marks b. Use the graph to solve the equation 2 sin 2x 3cos x 450 0 for 00 x 1800 2marks www.freekcsepastpapers.com255 MUMIAS WEST FORM 4 JOINT EXAMINATIONS, 2023 121 1 MATHEMATICS PAPER 1 Section I 50 marks Answer all the questions in this section. 1.


2marks b. Use the graph to solve the equation 2 sin 2x 3cos x 450 0 for 00 x 1800 2marks www.freekcsepastpapers.com255 MUMIAS WEST FORM 4 JOINT EXAMINATIONS, 2023 121 1 MATHEMATICS PAPER 1 Section I 50 marks Answer all the questions in this section. 1. Without using calculators evaluate 1 3 of 52 2 marks 2. Use the method of completing the square to solve the quadratic equation 2x2 13x 15 0 3 marks 3. Solve for in the equation 6 cos2 - Sin - 4 0 in the range 0o 180o. 3 marks 4. The sides of a rectangle are x cm and x 1 cm. A circle has radius of x 2 cm. If the sum of the area of the rectangle and the circle is 184 cm2. Using as 722 find the value of x. 4 marks 5. In the figure below ABCD is a cyclic quadrilateral and BD is a diagonal. EADF is a straight line, 680, 450and 980 Calculate the size of a 2 marks b 2 marks 6. A line L1 passes through point 1, 2 and has a gradient of 5. Another line L2 is perpendicular to L1 and meets it at a point where x 4. Find the equation for L2 in the form y mx c. 4 marks 7. Find the value of x in the following equation. 3 marks 9x 32x 1 53 8. The first and the last terms of an AP are 2 and 59 respectively.


Find the value of x in the following equation. 3 marks 9x 32x 1 53 8. The first and the last terms of an AP are 2 and 59 respectively. If the sum of the series is 610, find the number of terms in the series and the common difference. 4 mks 9. All prime numbers less than ten are arranged in descending order to form a number. A Write the number formed 1 mark b State the total value of the second digit in the number formed in a above 1 mk 10. Use reciprocals, square and square roots tables to evaluate, to 4 significant figures. 4 marks 2 0.3446 0.8673 2 11. Solve the inequality 3 2x x 352 x and show the solution on the number line. 4 marks 12. A Kenyan bank buys and sells currencies at the exchange rates below. Currency Buying Ksh Selling Ksh 1Euro 147.87 148.00 1Us dollar 74.22 74.50www.freekcsepastpapers.com256 An American tourist arrived in Kenya with 24,000 Euros He converted all the Euros to Kenya shillings at the bank. He spent a total of Sh. 200,000 while in Kenya and converted the rest to into US dollars at the bank. Find the amount in dollars that he received to the nearest whole number. 3 marks 13. A salesman earns a basic salary of sh. 9,000 per month. In addition, he is also paid a commission of 5 for sales above sh. 15,000. In a certain month he sold goods worth sh. 120,000 at a discount of 2 . Calculate his total earnings that month. 3 marks 14. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm3, find the volume of the frustum. 3 marks 15. Vector OP 6i j and OQ -2i 5j. A point N divides PQ internally in the ratio 3:1. Find PN in terms of i and j. 3 marks 16.


2 marks www.freekcsepastpapers.com257 20. Bujumba Boys Secondary School. Intends to buy a certain number of chairs For Ksh. 16,200. The supplier agreed to offer a discount of Ksh. 60 per chair which will enable the school to get 3 chairs more. Taking y as the originally intended number of chairs: - a Write an expression in terms of y for i Original price per chair. 1mark ii Price per chair after discount. 1mark b Determine i The number of chair the school originally intended to buy. 4marks ii Price per chair after discount. 2marks iii The amount of money the school would have saved per chair of it got the intended number of chairs at a discount of 15 . 2marks 21. A Without using a protractor, construct triangle ABC such that angle ABC 600, BC 8cm and AC 9cm. Measure AB. 3marks b Drop a perpendicular from A to BC and measure its length. 2marks c Hence calculate the area of triangle ABC. 2marks d Locate a point D on BC such that the area of triangle ABC is three times that of triangle ABD. 3marks 22. In triangle ABC, shown below, AB a AC b point M lies on AB such that AM: MB 2:3 and point N lies on AC such that AN: NC 5:1 line BN intersects line MC at X. a Express the following in terms of a and b i BN 1 mark ii CM 1 mark b Given that BX kBN and CX rCM where k and r are scalars i Write two different expressions for AX in term of a, b, k and r 4marks ii Find the values of k and r 4 marks Mwww.freekcsepastpapers.com258 23. A triangle ABC has vertices A 2,1 , B 5,2 and C 0,4 . A On the grid provided plot the triangle ABC. 2 marks b A1B1C1 is the image of ABC under a translation 2 5 . Plot A1B1C1 and state its coordinates.


A On the grid provided plot the triangle ABC. 2 marks b A1B1C1 is the image of ABC under a translation 2 5 . Plot A1B1C1 and state its coordinates. 2 marks c Plot A11B11C11 the image of A1B1C1 after a rotation about the origin through a negative quarter turn. State its coordinates. 3 marks d A111B111C111 is the image of A11B11C11 after a reflection on the line y 0. Plot A111B111C111 and state its coordinates. 3 marks 24. Three business partners Abila, Bwire and Chirchir contributed Ksh 120,000, Ksh 180,000 and Ksh 240,000 respectively to boost their business. They agreed to put 20 of the profit accrued back into the business and to use 35 of the profits for running the business. The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225,000 was realised. A. Calculate the amount. I Put back into the business. 2mks ii Used for official operations. 1mk b. Calculate the amount of profit each partner got. 4mks c If the amount put back into the business was added to individual s shares proportionately of their initial contributions, find the amount of Chirchir s new shares. 3mkswww.freekcsepastpapers.com259 MUMIAS WEST JOINT EVALUATION TEST, 2023 121 2 MATHEMATICS PAPER 2 TIME: 2 HOURS SECTION I: Answer all questions in this section. 1. Find the quadratic equation whose roots are 33 and write it in the form ax2 bx c 0 where a, b and c are integers. 3mks 2. Given that G 2 qn 2 . Express m in terms of n, q and G. 3mks 3. The heights, in centimeters of 7 students were; 143, 139, 145, 154, 159, 147,156. Find the mean absolute deviation of the data.


3mks 3. The heights, in centimeters of 7 students were; 143, 139, 145, 154, 159, 147,156. Find the mean absolute deviation of the data. 3mks 4. Triangle ABC has vertices A 4, 1 , B 6, 1 and C 8, 3 . The image of ABC under a transformation N is A 2, 1 , B 4, 1 and C 2, 3 . Find the matrix N. 3mks 5. State the amplitude, period and phase angle of; y 2 sin 12 x 300 3mks 6. The points P -6, 5 and Q 2, -1 are the ends of a diameter of a circle centre M. Determine: a The coordinates of M 1mk b The equation of the circle in the form x2 y2 ax by c 0 2mks 7. Without using mathematical table or a calculator, express sin 45o in surd form. Hence simplify; 8 leaving your answer in surd form. 3mks 1 Sin 45o 8. Simplify completely; 3mks 9x2 16x 7 162x2 98 9. A sum of Ksh 8000 was partly lent at 10 p.a simple interest and 12.5 p.a simple interest. The total interest after 2 years was Ksh. 1775. How much was lent at 10 simple interest? 3mks 10. The position vectors of points X and Z are 8i 3j 4k and 4i 6j -2k respectively. If Y divides line XZ in the ratio 9: -5, find the coordinates of Y. 3mks 11. In the figure below AB is a tangent to the circle centre O and radius 12cm. The area of the triangle AOB is 120cm2. OXB is a straight line. Calculate XB. 3mks 12. A die and a coin are cast simultaneously. I Draw a table to show all possible outcomes.


3mks 12. A die and a coin are cast simultaneously. I Draw a table to show all possible outcomes. 2mks ii What is the probability of a tail and a number less than 4 showing up. 1mk 13. Calculate the percentage error in the area of the triangle below given the included angle is exactly 50o. 3mks 14. Use binomial expansion to simplify;www.freekcsepastpapers.com260 2 5 4 - 2 - 5 4 4mks 15. Solve the simultaneous equation. 4mks 2x y 3 x2 xy - 4 16. Without using logarithms table or calculator, solve for x in Log 5 2 log 2x 10 log x-4 3mks SECTION II: Answer ANY FIVE questions in this section. 17. In the figure below OP p, OQ q. QX meets OY at R, OX: OP 2:3 and QY: YP 1:3. A Express the following in terms of p and q. i QP 1mk ii OY 2mks iii QX 1mk b Given that OR hOY and QR kQx i Express OR in terms of h, q and p. 1mk ii Express OR in terms of k, q and p. 1mk iii Solve for h and k 4mks 18. The sum of quantities A and B is y. A varies inversely as x and B varies directly as x. When x 4, Y 17 and when x 6, y 13. I Express y in terms of x. 7mks ii Find y when x 10 and x when y 11.5. 3mks 19. The figure below is a right pyramid on a rectangle base. TC TB TA 17cm and TO 15cm. AB is twice BC Calculate; i The length AB 4mks ii The angle between TC and plane ABCD.


The figure below is a right pyramid on a rectangle base. TC TB TA 17cm and TO 15cm. AB is twice BC Calculate; i The length AB 4mks ii The angle between TC and plane ABCD. 2mks iii The angle between TO and plane TAB. 2mks iv The angle between TAD and ABCD. 2mks www.freekcsepastpapers.com261 20. A In mathematics, the scores obtained by 30 students were recorded as shown in the table below. Score x 59 61 65 k 71 72 73 75 No. Of students 2 3 5 6 7 4 2 1 Given that fd -1.2 where d x 69, determine; f i Score k 4mks ii Standard deviation 4mks b The data below represents the ages in months at which 9 babies started walking 9, 11, 12, 11, 10, 8, 10, 13, 9. Find quartile range 2mks 21. Under a transformation represented by the matrix M a b , the image of A -1, 2 , B -1, -1 and c d c 1, -1 are A -3, 2 , B 0,-1 and C x, y a Find the matrix m. 3mks b Find the coordinates of C 1mk c Plot triangles ABC and A B C on the grid provided below. 2mks d Describe fully the transformation M. 2mks e Draw the triangle A B C , the image of A B C under a stretch of scale factor -2 with the y-axis invariant. 2mks 22. A The first term of an arithmetic progression AP is 6. The sum of the first 7 terms of the AP is 126. I Find the common difference of the AP 2mks ii Find the 19th term of the AP.


A The first term of an arithmetic progression AP is 6. The sum of the first 7 terms of the AP is 126. I Find the common difference of the AP 2mks ii Find the 19th term of the AP. 1mk b The 2nd, 3rd and 11th terms of an increasing arithmetic progression AP form the first 3 terms of a geometric progression GP . The first term of the AP is -2. I Find the common difference of the AP and the common ratio r of the GP. 4mks ii Find the sum of the first 5 terms of the geometric progression GP 3mks 23. A Complete the table below. X 0 30 60 90 120 150 180 210 240 270 300 330 360 y Sin x 300 0.50 0.00 -0.50 y 2Cos x 300 1.73 0.00 -1.73 2.00 1.73 b On the same axes, draw the graphs of y sin x 30 o and y 2Cos x 300 5mks c Use your graphs to solve the equation. 2mks 2 Cos x 300 1 Sin x 300 d State the amplitude of Sin x 300 1mk 24. Using a ruler and a pair of compasses only for all constructions in this question. A Construct triangle ABC in which AB 6cm, BC 7cm and angle ABC 750. 3mks b Find the locus x such that Ax 3cm. 1mk c On the same side of BC as , Construct the locus of P such that angle BPC 120o. 3mks d Show by stating the locus of Q inside triangle ABC such that BPC BQC. 1mk e On the side of AB opposite C, construct the locus of T such that the area of triangle ATB is 60cm2.


Two brands of tea costing Sh. 160 and Sh. 140 per kilogram respectively are mixed in the ration 2: 3 by mass. The mixture is sold at Sh. 240 per kilogram. Find the percentage profit made. 3 marks 14. Triangle is the image of triangle ABC under transformation represented by the matrix 3154 . If the area of triangle is 140 2, find the area of triangle ABC 3 marks www.freekcsepastpapers.com242 15. Given that PR 2cm, PN 12cm and PM 3cm. Find the length of: i PS 2 marks ii PQ 1 mark 16. Given that tan 1 3, find the value of cos . 3 marks SECTION II 50 Marks Answer any five questions only in this section. 17. In a science class, 23 of the class are boys and the rest are girls. 80 of the boys and 90 of the girls are right handed. The probability that the right handed student will break a test tube in any session is 110 and that for the left handed student is 310 ,regardless of whether boy or girl. A Draw a tree diagram to represent this information 2 marks b Using the tree diagram drawn, find the probability that: i A student chosen at random from the class is left handed 2 marks ii A test tube is broken by a left handed student. 2 marks iii A test tube is broken by a right handed student. 2 marks iv A test tube is not broken in any session 2 marks 18. In a triangle ABC, E is the midpoint of BC, D is a point on AC such that AD: DC 3: 2 and F is the point of intersection of AE and BD.


2 marks iii A test tube is broken by a right handed student. 2 marks iv A test tube is not broken in any session 2 marks 18. In a triangle ABC, E is the midpoint of BC, D is a point on AC such that AD: DC 3: 2 and F is the point of intersection of AE and BD. Vectors and a Express the following vectors in terms of and only i AE 2 marks ii BD 1 mark b By expressing vectors BF in two ways, find the ratio BF: FD given that BF hBD and AF tAE where h t are constants 5 marks c Hence find vector BF in terms of b and c only 2 marks www.freekcsepastpapers.com243 19. The table below shows the rates at which income tax is charged on annual income. Annual taxable income K Rates Sh per K 1 2800 3 2801 4600 5 4601 7200 6 7201 9000 7 9001 11 800 9 11 801 13 600 10 Over 13 600 12 A company employee earns a basic monthly salary of Ksh. 18 600 and a house allowance of 15 of his basic salary. If the employee is married and claims a monthly family relief of Sh. 250, calculate; a His annual taxable income in Kenya pounds. 2 marks b His net salary per month. 8 marks 20. The marks obtained by 50 students in an examination were recorded in the table below Marks 0 9 10 19 20 29 30 39 40 49 50 59 60 69 70 79 Number of student 3 6 10 12 9 5 3 2 Using 44.5 as the assumed mean, calculate i The actual mean mark 4 marks ii The standard deviation to 2 decimal place 3 marks iii The quartile deviation 3 marks 21.


15 . Calculate to 2 d.p. A Height VO. 3 marks b The inclination of VAB to ABC. 2 marks c The inclination of VB to ABC. 3 marks d The volume of the pyramid. 2 marks www.freekcsepastpapers.com244 23. A small-scale farmer wishes to buy some sheep and goats for rearing. Sheep cost Sh 400 and a goat cost Sh.300.The farmer has enough space for only 20 animals and may spend at most Sh. 6 800. The number of goats should not exceed twice the number of sheep. A By letting x and y to represent the number of sheep and goats he can buy respectively, write down all inequalities from the above information. 4 marks b Represent the inequalities on the grid provided 4 marks c From your graph, find the maximum number of animals he can buy at the lowest cost 2 marks 24. The displacement of a particle S metres, t seconds after passing a fixed-point O is given by 3 2 5 2.


Wasike starts cycling from his home at 8.00a.m toward s Wanjala s house at 16km h. Wanjala stars cycling towards Wasike s house 30 minutes later at 8km h. what time did they meet. 3mks 11. The line which joins the point A 3, K and B -2, 5 is parallel to the line whose equation is 5y 2x-7 0. Find the value of K. 3mks 12. Given that Cos A 513 and angle A is acute, without using tables or calculator, find the value of 2 tan A 3 sin A. 3 mks 13. Find the greatest integral value of x which satisfies. 2x 3 2 8 3x 5 5x 6 3 3mks 14. The figure below not drawn to scale is a right pyramid with slant height of 5cm and square base of 3cm. A Draw its net and label it. 2mks b Calculate the total surface area. 2mks 15. A plane leaves town P to town Q on a bearing of 130 and a distance of 350km. It then flies 500km on a bearing of 060 to town R. Find, by scale drawing the distance between town R and town P. 3 mks 16. The following data was obtained from the mass of a certain animal. Complete the table and the histogram below. 3 marks Mass kg frequency 41-50 20 51-55 56-65 40www.freekcsepastpapers.com222 SECTION II: 50 MARKS Answer only FIVE question from this section. 17. The ends of the roof of a workshop are segment of a circle of radius 10m. The roof is 20m long .The angle at the centre is 1200 as shown in the figure below. A Calculate: i The area of one end of the roof. 4mks ii The area of the curve surface of the roof. 2mks b What would be cost to the nearest shilling of covering the two ends and the curved surface with galvanized iron sheet costing sh.80 per square meter?


A Calculate: i The area of one end of the roof. 4mks ii The area of the curve surface of the roof. 2mks b What would be cost to the nearest shilling of covering the two ends and the curved surface with galvanized iron sheet costing sh.80 per square meter? 4mks 18. A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is three quarters full of milk. A Calculate the volume of milk in litres. 3 marks b The milk is packed in small packets in a shape of a right pyramid with an equilateral base triangle of side 16cn. The height of each packet is 13.6cm. Full packets obtained are sold at ksh.25 per packet. I The volume in cm3 of each packet to the nearest whole number. 3 marks ii The number of full packets of milk. 2 marks iii The amount of money realized from the sale of milk. 2 marks 19. A On the grid provided below, plot the polygon A 3, 7 , B 5, 5 , C 3, 1 , D 1, 5 on a Cartesian plane 2mks b A1B1C1D1 is the image of ABCD under a translational T 6 9 . Plot A1B1C1D1 and state its coordinates. 2mks c Plot A11B11C11D11, the image of A1B1C1D1 after a rotation about -1, 0 through a positive quarter turn. State its coordinates. 3mks d A111B111C111D111 is the image of A11B11C11D11 after a reflection in the line Y x 2. Plot A111B111C111D111and state its coordinates 3mks 20. A straight line passes through the points 8, -2 and 4,-4 . A Write its equation in the form ax by c 0, where a, b and c are integers. 3 Marks b If the line in a above cuts the x-axis at point P, determine the coordinates of P.


A straight line passes through the points 8, -2 and 4,-4 . A Write its equation in the form ax by c 0, where a, b and c are integers. 3 Marks b If the line in a above cuts the x-axis at point P, determine the coordinates of P. 2 Marks c Another line, which is perpendicular to the line in a above passes through point P and cuts the y axis at the point Q. Determine the coordinates of point Q. 3 Marks d Find the length of QP 2 Marks 21. Matrix P is given by 4 a Find p-1 3mks b Two institutes regions and Alphax purchased beans at sh. B per bag and maize at sh. M per bags. Regions purchased 8 bags of beans and 14 bags of maize for sh. 47,600. Alphax purchased 10 bags of beans and 16 bags of maize for sh. 57,400. I Form a matrix equation to represent the information above 2mks ii Use the matrix p-1 to find the prices of one bag of each item 3mks c The price of bean later went up by 5 and that of maize remain constant. Regions bought the same quality of beans but spent the same total amount of money as before on the two items. State the new ratio of beans and maize. 2mks 10m 1200 10mwww.freekcsepastpapers.com223 22. In the diagram below, the coordinates of points A and B are 1, 6 and 15, 6 respectively. Point N is on OB and that 3 ON 2 OB.ne OA is produced to L such that OL 3 OA a Vector LN. 3 marks b Given that a point M is on LN such that LM : MN 3:4, find the coordinate of M. 2 marks c If line OM is produced to T such that OM : MT 6:1 i Find the position vector of T. 1 mark ii Show that points L, T and B are collinear.


3 marks b Given that a point M is on LN such that LM : MN 3:4, find the coordinate of M. 2 marks c If line OM is produced to T such that OM : MT 6:1 i Find the position vector of T. 1 mark ii Show that points L, T and B are collinear. 4 marks 23. A Complete the table below for the functions xforxxy 2 mks x -2 -1 0 1 2 3 y b Draw the graph of 2 xxyfrom the table above. 2 mks c Use your graph to solve the equation 2 xxy 0 1 mk e From your graph, find the value of X which satisfy the simultaneous equations. 1 mk 2 xxy 22 xy d Write down the equation which is satisfied by the values of x in e above in the form ax2 bx c 0 2 mks 24. The diagram below shows a circle ABC with AB 12cm, BC 15cm, and AC 14cm Calculate to 4 significance figures: a The angle ACB 3mks b The radius of the circle. 3mks c The area of the shaded region 4mks www.freekcsepastpapers.com224 MOMALICHE 2 CYCLE 10 Kenya Certificate of Secondary Education 121 2 MATHEMATICS PAPER 2 SECTION 1 50 MARKS Answer all questions in this section. 1. A positive two digit number is such that the product of the digits is 24. When the digits are reversed, the number formed is greater than the original number by 18. Find the number. 3mks 2. Use tables of squares, square roots and reciprocals to evaluate 4mks 218149.01602698.0234 3. The height and radius of a cone are measured as 21 cm and 14.0 cm respectively. Taking 3.142, find the percentage error in the volume of the cone. 3mks 4.


The height and radius of a cone are measured as 21 cm and 14.0 cm respectively. Taking 3.142, find the percentage error in the volume of the cone. 3mks 4. Express the following in surd form and simplify by rationalizing the denominator without using a calculator and leave your answer in the form a 3mks 1 3001 600 5. Solve for x in:Log2 x 7 Log2 x 7 3 3mks 6. A businessman obtained a loan of Ksh 450,000 from a bank to buy a Matatu that was valued at the same amount. The bank charges interest at 24 per annum compounded quarterly per year. Calculate the total amount of money the businessman paid to clear the loan in 412 years to the nearest shilling. 3mks 7. In the diagram below, BT is a tangent to the circle at B. AXCT and BXD are straight lines. AX 6cm, CT 8cm, BX 4.8cm and XD 5cm. Find the length of BT. 3Marks 8. Find the possible values of x given that 886 is a singular matrix. 3mks 9. The cost C of operating an electronic business is partly constant and partly varies as the square of labour input L. If C 25,000 when L 20 and C 45,000 when L 30. Find C when L 8. 3mks 10. The 2nd, 4thand 7th terms of an A.P. are the first 3 consecutive terms of a G.P. Find the common ratio of the G.P if the common difference of the A.P. is 2. 3mks 11. P and Q are two points such that OP i 2j 3k and OQ 4i 5j 3k. M is a point that divides PQ externally in the ratio 3:2. Find the co-ordinates of M, given that O is the origin. 3mks 12.


And a premium relief of 10 on her insurance premium of K 800 p.a. The table of tax rate is as below. Taxable income K p.a. Rate 1 2100 10 2101 4200 15 4201 6300 20 6301 8400 25 Over 8400 30 Calculate; a Calculate the net tax per annum. 7mks b Other deductions includes W.C.P.S Shs 600 per month, NHIF Shs. 500 per month. Calculate her net pay per month. 3mks 18. The Line AB 5cm is a side of a triangle ABC in which angle ABC 90 and angle BAC 60 . A Construct triangle ABC 2mks b Construct the Locus P such that angle APB angle ACB 2mks c Locate by construction points Q1 and Q2 which satisfy the conditions below: i Q1 and Q2 lie on the same side of line AB and C 3mks ii Area of triangle AQ1B Area of triangle AQ2B 3 4 Area of triangle ABC iii Angle AQ1B Angle AQ2B 30 Measure the length of the line Q1Q2 3mks d Calculate the area above the line Q1Q2 bounded by the locus of point P 3mks 19. The diagram below shows a square based pyramid V vertically above the middle of the base. PQ 10cm and VR 13cm. M is the midpoint of VR. Find to 2 decimal places a i the length PR. 2mks ii the height of the pyramid. 2mks b i the angle between VR and the base PQRS. 2mks ii the angle between MR and the base PQRS. 2mks iii the angle between the planes QVR and PQRS. 2mks 20.


O, A, B, C is the image of OABC under transformation matrix. 2 00 2 a Find the coordinates of O1A1B1C1 2mks ii On the grid provided, draw OABC and O1A1B1C1 2mks b Find O11A11B11C11, the image of O1A1B1C1 under transformation matrix 1 00 2 2mks ii On the same grid draw O11A11B11C 11 1mk c Find a single matrix that maps O11A11B11C11 onto OABC 3mks 22. The following table shows the distribution of marks obtained by 50 students in a test. Marks 45-49 50-54 55-59 60-64 65-69 70-74 75-79 No. Of Students 3 9 13 15 5 4 1 By using an assumed mean of 62, calculate a The mean 5mks b The variance 3mks c The standard deviation 2mks 23. A box contains 3 brown, 9 pink and 15 white cloth pegs. The pegs are identical except for the colour. A Find the probability of picking. I A brown peg. 1mark ii A pink or a white peg. 2 marks b Two pegs are picked at random, one at a time without replacement. Find the probability that: i At least one brown peg is picked 4marks ii both pegs are of the same colour. 3marks 24. A wholesaler stocks two types of rice: Refu and Tamu. The wholesale prices of 1 kg of Refu and 1 kg of Tamu are Ksh 80 and Ksh 140 respectively. The wholesaler also stocks blend A rice which is a mixture of Refu and Tamu rice mixed in the ratio 3 : 2. A. i A retailer bought 10 kg of blend A rice. To this blend, the retailer added some Tamu rice to prepare a new mixture blend X. The .ratio of Refu rice to Tamu rice in blend X was 1:2.


I A retailer bought 10 kg of blend A rice. To this blend, the retailer added some Tamu rice to prepare a new mixture blend X. The .ratio of Refu rice to Tamu rice in blend X was 1:2. Determine the amount of Tamu rice that was added. 3marks ii The retailer sold blend X rice making a profit of 20 . Determine the selling price of 1 kg of blend X. 3 marks b. The wholesaler prepared another mixture, blend B, by mixing x kg of blend A rice with y kg of Tamu rice. Blend B has a wholesale price of Ksh130 per kg. Determine the ratio x : y. 4mks www.freekcsepastpapers.com204 KIRINYAGA CENTRAL SUB-COUNTY EFFECTIVE 40 JOINT EXAMINATION 2023 Kenya Certificate of Secondary Education 121 1 MATHEMATICS Paper 1 2 hours SECTION I: 50 Marks Answer all the questions in this section. 1. Evaluate without using a Mathematical table or a calculator 20.2 x 2590. X1122 3marks 2. Using logarithms to evaluate correct to 4 significant figures. 4marks .280.006347 x 152.9 3. The G.C.D of three numbers is 30 and their L.C.M is 900. Two of the numbers are 60 and 150. Find the least possible third number. 3 marks 4. David s clock loses 15 seconds every hour. He gets the correct time on the clock at 0700H on a Monday. Determine the time shown on the clock when the correct time was 1900H on Wednesday the same week. 3 marks 5. Two similar containers have masses of 256 kilograms and 128 kilograms respectively. If the surface of the smaller container has an area of 810cm2, what is the area of the corresponding surface of the larger container to 2 decimal places? 3 marks 6. Find the value of y in the equation 3 marks 21 yy 7. Mwangi spends one-third of his salary on food, one quarter on rent, three-fifth of the remainder on transport and saves the rest. If he spends Ksh.


Find the value of y in the equation 3 marks 21 yy 7. Mwangi spends one-third of his salary on food, one quarter on rent, three-fifth of the remainder on transport and saves the rest. If he spends Ksh. 8400 on transport, find how much money he saves. 3 marks 8. A Kenyan bureau buys and sells foreign currencies as shown below. Buying Selling in Kenya shillings in Kenya shillings 1 Hong Kong dollar 9.74 9.77 100 Japanese Yen 75.08 75.12 A tourist arrived in Kenya with 105,000 Hong Kong dollars and changed the whole amount to Kenya shillings. While in Kenya, she spent Kshs. 403897 and changed the balance to Japanese Yen, before leaving for Tokyo. Calculate the amount in Japanese Yen that she received. 3 marks 9. The coordinates of A, B, C and D are A -3, 6 , B 2, 4 , C 4, -3 and D 3, -5 respectively. If A1 is -6, 7 under a translation T. Find the coordinates of B1, C1 and D1 under T. 3 marks 10. Solve; 4x 3 6x 1 3x 16 hence state the integral values. 3 marks 11. In the figure below AOC is a diameter of a circle centre O. ABDE is a cyclic quadrilateral and angle COD 280. Www.freekcsepastpapers.com205 Determine the size of a Angle AED 2 marks b Angle CAD 2 marks 12. An aircraft left town A and flew eastwards along a latitude to town B 600N, 350E . If it took 51 2 hours at a speed of 910km hr, find the position of A. Take 22 7, R 6370km 3marks 13. Object A of area 10cm2 is mapped onto its image B of area 60cm2 by a transformation whose matrix is given by 4xP.


If it took 51 2 hours at a speed of 910km hr, find the position of A. Take 22 7, R 6370km 3marks 13. Object A of area 10cm2 is mapped onto its image B of area 60cm2 by a transformation whose matrix is given by 4xP. Find the positive values of x. 3marks 14. Simplify 216a4b8a8ab6b 3 Marks 15. Solve the following simultaneous equations. 3 marks ab 16. The base ABCDE of a right pyramid is a regular pentagon of side 3cm. Point V is a vertex of the pyramid and the length of the slanting edge is 4cm. Draw a labeled net of the pyramid. 3 marks SECTION II : 50 Marks Answer only FIVE questions in this section 17. A line passes through P k, -3 and Q 5, k , where k is a positive non zero integer. The magnitude of PQ is 34 units. A Find the value of k. 3 marks b Determine the equation of the perpendicular bisector of PQ in the form of ax by c 0 Where a, b and c are integers. 4 marks c Find the equation of a line parallel to PQ and passing through -1, 3 in the form of y mx c. 3 marks 18. A carpenter constructed a closed wooden box with internal measurements 1.5m long, 0.8m wide and 0.4m high. The wood used in constructing the box was 1.0cm thick and had a density of 0.6g cm3. Determine: a i the volume in cm3 of the wood used. 4 marks ii the mass of the box in kg correct to 1 decimal place. 2 marks b Identical cylindrical tins of diameter 10cm, height 20cm with a mass of 120 grams each were packed in the box. Calculate the: i maximum number of tins that were packed.


4 marks ii the mass of the box in kg correct to 1 decimal place. 2 marks b Identical cylindrical tins of diameter 10cm, height 20cm with a mass of 120 grams each were packed in the box. Calculate the: i maximum number of tins that were packed. 2 marks ii total mass of the box with the tins in kilograms. 2 marks 19. The figure below represents a triangular flower garden ABC in which AB 4m, BC 5m and BCA 300. Point D lies on AC such that BD 4m and BDC is obtuse. Find correct to 2 decimal places. A BDC 3 marks b the length of AD 3 marks c the length of DC 2 marks d the area of the flower garden ABC 2 marks www.freekcsepastpapers.com206 20. A particle moves along a straight line such that its displacement S metres from a given point is; S t3 5t2 3t 4. Where t is time in seconds. Find; a The displacement of the particle at t 5 sec. 2 marks b The velocity of the particle when t 5 sec. 2 marks c The values of t when the particle is momentarily at rest. 3 marks d The acceleration of the particle when t 2 sec. 3 marks 21. A On the graph provided, draw the graph of; y x3 5x2 2x 9 for -2 x 5 using a scale of 1cm for 1 unit on the x-axis and 1 cm for 5 units on the y axis. 5 marks b Use the graph to estimate the roots of the equations. I x3 5x2 2x 9 0 2 marks ii x3 5x2 4x 3 0 3 marks 22. John is a civil servant who earns a basic salary of Ksh. 38,300, house allowance of Ksh. 12,000 and a medical allowance of Ksh.


John is a civil servant who earns a basic salary of Ksh. 38,300, house allowance of Ksh. 12,000 and a medical allowance of Ksh. 3600 every month. He claims a family relief of Ksh. 1172 and insurance relief of 3 of the premium paid. Using tax table below; calculate; Taxable Income Tax rates K p.a Ksh. Per pound 1 8800 2 8801 16800 3 16801 24800 5 24801 36800 7 36801 48800 9 Over 48800 10 a John s annual taxable income in Kenya pounds per annum. 2 marks b Tax due every month from John s to 2 d.p 5 marks c If further deductions are made every month from his salary - WCPS of 2 of basic salary - Life insurance premium of sh 4600 - Sacco Loan repayment of sh 14200 Calculate: i John s total deductions 1 mark ii John s net salary per month 2 marks 23. In a road safety survey, 1000 vehicles were examined. 62 of these were found to have defective tyres, 30 had defective steering wheels and 45 had defective brakes. Assuming that this sample accurately represent all the vehicles in the country, find the probability that a vehicle in the country picked at random has; a i Defective brakes 1 mark ii Defective brakes but neither of the other two defects 3marks iii Has no defects 2 marks b If the owner of a defective vehicle is warned if his car has one or two of these defects, but is fined sh 300 if his car has all three defects, what is the total amount of fined that one would expect to be imposed after 10,000 vehicles had been inspected at random? 4 marks 24. A bus and a Nissan left Nairobi for Cheptiret a distance of 340 km at 7.00am. The bus traveled at 100km h while the Nissan at 120km h. After 30 minutes, the Nissan had a puncture which took 30 minutes to mend. A How far from Nairobi did the Nissan catch up with the bus?


The bus traveled at 100km h while the Nissan at 120km h. After 30 minutes, the Nissan had a puncture which took 30 minutes to mend. A How far from Nairobi did the Nissan catch up with the bus? 5 marks b At what time of the day did the Nissan catch up with the bus? 2 marks c At what time did the bus reach Cheptiret? 3 marks www.freekcsepastpapers.com207 KIRINYAGA CENTRAL SUB-COUNTY EFFECTIVE 40 JOINT EXAMINATION 2023 Kenya Certificate of Secondary Education 121 2 MATHEMATICS Paper 2 21 2 hours SECTION I: 50 Marks Answer all the questions in this section. 1. Solve for n by completing the square method. 2n2 6n 4 0 3marks 2. The matrix 3x is a singular matrix. Find possible values of x; to 2 d.p. 3 marks 3. Evaluate dx x 3 marks 4. Solve for x in 4 xLog10 2xLog21010 4 marks 5. Make b the subject of the formula 3 marks r1dbbd2 6. The sides of a rectangle are measured as 8cm by 5cm correct to the nearest centimeter. Determine the percentage error in calculating its perimeter correct to 4 significant figures. 3 marks 7. Simply 3 leaving your answer in the form cba where a, b and c are scalars. 3 marks 8. A trader bought two brands of rice. Type A cost sh 100 and type B cost sh 80 per kilogramme. She mixed the two brands and sold the mixture at sh 96 per kilogramme. Determine the ratio in which she mixed the two brands. 3 marks 9. In the figure below, BT is a tangent to the circle at B. AXCT and BXD are straight lines.


3 marks 9. In the figure below, BT is a tangent to the circle at B. AXCT and BXD are straight lines. AX 8cm, CT 8cm, BX 4cm and XD 5cm Calculate the length i XC 2 marks ii BT 1 mark 10. Solve for x in the equation Cos 3x -300 0.5 where 0 x 3600. 3 marks 11. Given that OA 2i 3j and OB 3i -2j. Find the magnitude of AB to one decimal place. 3 marks 12. The equation of a curve is given by y x3 4x2 3x. Find the equation of the normal to the curve at x 1. 3marks 13. The equation of a circle is given by 4x2 4y2 8x 20y 7 0 3marks Determine the centre and the radius of the circle. 14. The 5th and 10th terms of an arithmetic progression are 18 and -2 respectively. Find the common difference and the first term. 3 Marks www.freekcsepastpapers.com208 15. A Expand the expression 1 xin ascending powers of x, leaving co-efficient as fractions in their lowest form upto to x3. 2 marks b Use the first three terms of the expression in part a above to estimate the value of 0.97 5. 2 marks 16. Mogaka and Onduso working together can do a piece of work in 6 days. Mogaka, working alone takes 5 days longer than Onduso. How many days does it take Onduso to do the work alone. 3 marks SECTION II: 50 Marks Answer only FIVE questions in this section. 17. A Using ruler and pair of compasses only. Construct triangle ABC such that angle ABC 450 and angle BAC 600 and AB 6cm. 3 marks b Locate the Locus of P using the triangle in a above such that angle APC 1200.


2 marks f Calculate the angle between planes GFEH and DAFG. 2 marks 20. A matrix 1 represents the transformation T, where the triangle ABC with A 1, 1 , B 5, 1 and C 2, 4 is transformed by T onto A1B1C1 a i Find the coordinates fo the image A1B1C1 of ABC under transformation T. 2 marks ii Draw the triangle A1B1C1 and ABC on the same Cartesian plane. 2 marks D C A E G F B Hwww.freekcsepastpapers.com209 b i Triangle A1B1C1 undergoes another transformation R whose matrix is 1 and is mapped onto A11B11C11. Determine the coordinates of A11B11C11 , hence draw it on the same Cartesian plane. 2 marks iii Describe the transformation in b i above fully. 1 mark c Find, by calculation a single matrix that would map A11B11C11 onto ABC. 3 marks 21. The table below shows marks scored in a Mathematics in a class of 40 students. Marks 10-19 20-29 30-39 40-49 50-59 60-69 70-79 No. Of students 2 6 7 13 6 4 2 a Using an assumed mean of 44.5, determine i the mean of the distribution. 3 marks ii the variance 3 marks iii the standard deviation to 4 decimal places, 1 mark b Estimate the medium of the distribution to 4significant figures 3 marks 22. An Arithmetic Progression A.P has its first term as a and a common difference d. a Find in terms of a and d, the first, third and eleventh terms of the AP.


3 marks ii the variance 3 marks iii the standard deviation to 4 decimal places, 1 mark b Estimate the medium of the distribution to 4significant figures 3 marks 22. An Arithmetic Progression A.P has its first term as a and a common difference d. a Find in terms of a and d, the first, third and eleventh terms of the AP. 2 marks b The AP above is increasing and the first, third and eleventh terms form in the first three terms of a Geometric Progression G.P . The sum of the fifth and ninth terms of the AP is 80. I Find the values of a and d. 4 marks ii Calculate the sum of the first 10 terms of the A.P. 2 marks c Determine the 5th term of the G.P. 2 marks 23. The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM 2 3 OQ and PN 1 4 PQ. Lines PM and ON meets at X. a Given that OP p and OQ q, express in terms p and q the vectors. I PQ 1 mark ii PM 1 mark iii ON 2 marks b You are further given that OX kON and PX hPM. I Express OX in terms of p and q in two different ways. 2 marks ii Find the value of h and k. 3 marks iii Find the ratio PX : XM 1 mark 24. An aircraft leaves town P 300S, 170E and moves directly northwards to Q 600N, 170E . It then moved at an average speed of 300 knots for 8 hours westward to town R. Detemine:- a The distance PQ in nautical miles 2 marks b The position of town R. 4 marks c The local time at R in 24-hour system if the local time at Q is 3.12 pm. 2 marks d The distance moved from P to R in km.


Detemine:- a The distance PQ in nautical miles 2 marks b The position of town R. 4 marks c The local time at R in 24-hour system if the local time at Q is 3.12 pm. 2 marks d The distance moved from P to R in km. Take 1nm 1.853 km 2 marks P N X O M Q p q www.freekcsepastpapers.com183 MBORANU II FORM FOUR JOINT EVALUATION 2023 Kenya Certificate of Secondary Education KCSE 121 1 MATHEMATICS ALT A PAPER 1 SECTION 1 50 marks Answer all the questions in this section. 1. Evaluated: 3mks 2. Use logarithms to evaluate the following to 4 significant figures to: 4mks 3. An electrician made a loss of 30 by selling a multi plug at sh.1400.what percentage profit would he has made if he sold the multi plug at sh. 2300. 3mks 4. In the triangle ABC below, BC 9cm, angle ABC 80 .and angle ACB 30 . A 80 30 B C Calculate, correct to 4 significant figures, the area of the triangle. 3mks 5. Given that the exterior angle of a regular hexagon is 2x. Find the value of x. Hence find the size of each interior angle of the hexagon. 3mks 6. Two numbers t and s are such that t4x s2 5625. Find t and s 3mks 7. Find the obtuse angle the line with equation 2y 5x 2 0 makes with the x-axis. 3mks 8. Simplify the expression 3mks 9. A plot is in the shape of a right-angled triangle. The length of the shorter side is 15m and the area is 456.8m2. Calculate the length of the longest side of the garden. 3mks www.freekcsepastpapers.com184 10.


The Submarine at D on realizing that the ship was heading to the Island P, decides to head straight for the Island to intercept the ship. Using a scale of 1 cm to represent 10 km, make a scale drawing showing the relative positions of A, B, D and P. 4 marks Hence find: b The distance from A to D. 2 marks c The bearing of the Submarine from the ship when the ship was setting off from B. 1 mark d The bearing of the Island P from D. 1 mark e The distance the Submarine had to cover to reach the Island P. 2 marks 23. A Find the inverse of the matrix: 1mk A b Amina bought 20 bags of oranges and 15 bags of mangoes for a total of sh. 9,500. Nafula bought 30 bags of oranges and 20 bags of mangoes for a total of sh. 13,500. If he price of a bag of oranges is X and that of mangoes is y: a Form two equations to represent the information above. 2mks ii Hence use the matrix A-1 above to find the price of one bag of each item. 4mks c The price of each bag of oranges was increased by 10 and that of mangoes reduced by 10 . The businesswomen Amina and Nafula bought as many oranges and as many mangoes as they bought earlier. Find the total cost of oranges and mangoes that each businesswoman bought after the percentage change. 3mks 24. The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s a Find s when t 2 2mks b Determine: i the velocity of the particle when t 5 seconds; 3mks ii the value of t when the particle is momentarily at rest 3mks c find the time , when the velocity of the particle is maximum 2mks www.freekcsepastpapers.com187 MBORANU II FORM FOUR JOINT EVALUATION 2023 Kenya Certificate of Secondary Education KCSE 121 2 MATHEMATICS ALT A PAPER 2 SECTION 1 50 marks Answer all the questions in this section.


Find the total cost of oranges and mangoes that each businesswoman bought after the percentage change. 3mks 24. The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s a Find s when t 2 2mks b Determine: i the velocity of the particle when t 5 seconds; 3mks ii the value of t when the particle is momentarily at rest 3mks c find the time , when the velocity of the particle is maximum 2mks www.freekcsepastpapers.com187 MBORANU II FORM FOUR JOINT EVALUATION 2023 Kenya Certificate of Secondary Education KCSE 121 2 MATHEMATICS ALT A PAPER 2 SECTION 1 50 marks Answer all the questions in this section. SECTION I 50mks Answer all questions in this section 1. Simplify without using mathematical tables or calculator. 4mks 2 log10 2.5 log10 40 3 log100.05 2log102- log100.5 2. Simplify and express your answer in the form a b c where a, b and c are constants. 3mks 3. A wedding committee did a budget for a wedding ceremony as follows: Food: Ksh. 58,205 Chairs:Ksh. 11,950 Entertainment: 8,453 The sum of the budget was done by first rounding each figure to 3 significant figures. A Determine the sum of the budget 2mks b Determine the percentage error in this sum of the budget 2mks 4. Solve the equation 4sin2 4cos 5 for 00 3600 3mks 5. A Expand 1 4 using the binomial expansion 1mk b . Use the first three terms of the expansion in a above to find the value of 0.998 4 Correct to the nearest hundredth 3mks 6. Make w the subject of the formula 3mks P 7. Given that y 3 sin x 60 0 find, amplitude, period and the phase angle of the function. 3mks 8.


Make w the subject of the formula 3mks P 7. Given that y 3 sin x 60 0 find, amplitude, period and the phase angle of the function. 3mks 8. A ship sails due North from latitude 200 S for a distance of 1440nm. Find the latitude of the point it reaches 2mks 9. The equation of a circle is given by 32 3y2 3 42y 30 0. Determine the radius and the coordinates of the centre circle. 3mks 10. A i Draw a straight-line MN such that MN 7cm 1mk ii Construct the locus P such that MPN 900 1mk b On the locus of P in a above, mark point T such that T is equidistant from M and N. 2mks 11. The table below shows tax table for monthly income Monthly taxable income in Ksh. Tax rate in each shilling 0- 9680 9681- 18800 18801-27920 10 15 20 In a certain month, Kamau s tax was sh. 3336. Determine his income during that month. 3mks www.freekcsepastpapers.com188 12. In the figure below OC is the tangent to the circle. If OE 8cm and OC 6cm, find EA. 2mks 13. Evaluate 3mks 14. Liquid P contains 30 of water while liquid Q contains 48 of water. In what ratio should P and Q be mixed so that the mixture contains 42 of water? 3mks 15. The probability that it is rainy in the morning is 0.6. The probability that John carries an umbrella while going to work is 0.4. Find the probability that i It is not rainy and John does not carry an umbrella. 2mks ii It is rainy and John carries an umbrella 1mk 16. Solve the simultaneous equations 2y 1, 2 y2 29 3mks SECTION II 50 MARKS Answer five questions in this section 17.


Calculate the difference between the cash price and the hire purchase price and express it as a percentage of the cash price. 3mks www.freekcsepastpapers.com190 23. In the figure below OPQ is a triangle in which OS OP and PR: RQ 2:1. Lines OR and SQ meet at T. a Given that OP p and OQ q. Express the following vectors in terms of p and q: i. PQ 1mk ii. OR 2mks iii. SQ 2mks b Given that ST mSQ and OT nOR where m and n are consonants, determine the values of m and n 4mks c Find the ratio of ST:TQ 1mk 24. During installation of electricity bulbs in street lighting a dealer is required to supply two types of bulbs A and B. The total number of bulbs should not be more than 400. He must supply more of type A than of type B and type A should not be more than 300 and type B should not be less than 80. A By letting the number of type A bulbs to be x and the number of type B bulbs to be y, write all the inequalities representing the above information. 3mks b On the grid provided draw all the inequalities 4mks c If type A bulbs cost sh.450 per piece and type B cost sh.350 per piece and that the higher the cost the higher the profit: i. Use your graph to determine the number in each type of bulb that he should supply to maximize the profit. 1mk ii. Calculate the maximum cost of lighting the street 2mks www.freekcsepastpapers.com161 KIHARU KAHURO FORM 4 JOINT EXAMINATION KENYA CERTIFICATE OF SECONDARY EDUCATION 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS SECTION 1 50 MARKS Answer all questions in this section. 1. Evaluate without using a calculator; 3 marks 2. In August, Michael donated th of her salary to children s home while Ali donated th of his salary to the same children s home. Their total donation for August was Kshs 11,200.


3 marks Section II 50 marks Answer only five questions in the spaces provided. 17. A truck left Embu at 8.45 a.m and travelled toward Yala at an average speed of 50 km hr. A car left town Embu at 11.1 5 a.m on the same day and travelled along the same road at an average speed of 90 km h. The distance between the two town is 420 km. A Calculate the time of the day when the car overtook the truck. 5 marks b The distance from Yala when the car overtook the truck. 2 marks c After overtaking the bus, both vehicles continued towards Yala at their original speeds. Find how long the car had to wait at town Yala before the truck arrived. 3marks 18. A Complete the table below for the function y x3- 3x2 x 2 marks x -4 -3 -2 -1 0 1 2 y b Using the trapezoidal rule, with 6 strips estimate the area bounded by the curve y x3 3x 2, x -4 and x 2 and the x axis. 3 marks c Calculate the actual area bounded by the curve y x3 3x 2, x -4 and x 2 3 marks d Calculate the percentage error. 2marks 19. Line L1 passes through the points -2, 3 and -1, 6 and is perpendicular to L2 at -1, 6 . A Find the equation of L1 2marks b Find the equation of L2 in the form ax by c 0 where a, b and c are constants. 2 marks c Given that another line L3 is parallel to L1 and passes through point 1, 2 , find the x and y intercepts of L3. 3marks d Find the point of intersection of L2 and L3. 3 marks 20. A pirate boat sails from port A on a bearing of 0500 at a speed of 112 km h, for 2 hours to port B.


The vertices of quadrilateral OABC are O 0, 0 , A 2, 0 B 4, 2 and C 0, 3 . The vertices of its image under a rotation are O 1, -1 , A 1, -3 B 3, -5 and C 4, -1 . A On a grid, draw OABC and its image O A B C. 2 marks b By construction, determine the centre and angle of rotation. 3 marks c On the same grid as a above, draw O A B C , the image of O A B C under a reflection in the line y x and state the co-ordinates of O A B C 3 marks d From the quadrilaterals drawn, state the pairs that are: i. Directly congruent; 1 mark ii. Oppositely congruent: 1 mark 23. Abdalla bought 100 packets of biscuits and 50 packets of sweets for a total of Kshs. 25,000. Jane bought 40 packets of biscuits and 30 packets of sweets for a total Kshs. 12,000. If the price of a packet of biscuit is Kshs. X and a packet of sweet is Kshs. Y, a i Form two equations to represent the information above and simplify them 2 marks ii Use the matrix method to find the prices of one packet of each item. 4 marks b Makoti bought 225 packets of biscuits and 360 packets of sweets. He was given a total discount of Kshs. 4,815. If the discount on the price of a packet of biscuit was 10 , calculate the percentage discount on the price of a packet of sweet. 4 marks 24. The displacement S meters of a body moving along a straight line after t seconds is given by S -2t3 32t2 3t. a Find its initial acceleration. 3marks b Calculate i. The time when the body was momentarily at rest. 3 marks ii. Its displacement by the time it comes to rest momentarily. 2 marks c Calculate the maximum velocity attained.


3 marks ii. Its displacement by the time it comes to rest momentarily. 2 marks c Calculate the maximum velocity attained. 2 marks www.freekcsepastpapers.com165 KIHARU KAHURO FORM 4 JOINT EXAMINATION KENYA CERTIFICATE OF SECONDARY EDUCATION 121 2 MATHEMATICS PAPER 2 TIME: 2 HOURS SECTION I 50 MARKS Answer all questions in the spaces provided. 1. Use logarithm tables to evaluate. 4 marks 693.5 0. 3 0.9823 2 58.32 2. A mixture contains two grades of rice A and B with masses in the ratio 3:5. If the mixture is sold at Ksh 270 per kilogram making a profit of 20 and grade A rice costs Ksh. 200 per Kilogram, find the cost of grade B rice. 3 marks 3. Express the following in surd form and simplify by rationalizing the denominator without using a calculator and leave your answer the form a b 3 marks 1 cos 300 1 sin 600 4. Make n the subject of equation. 3 marks 2 1 23 5. Find the area of a sector that subtends an angle of 0.420c of the centre and has an arc length of 2.31 cm. 3 marks 6. The figure below shows a circle and a point P outside the circle P Using a ruler and a pair of compass, construct a tangent to the circle from P. 4 marks 7. It takes a pipe A 8 hours to fill an empty water tank. Pipe B can fill the same tank in 4 hours. When the tank is full, pipe C can empty it in 5 hours. Pipes A and B are opened at the same time when the tank is empty. Two hours later, pipe C is opened. Find to the nearest minute the total time taken to fill the tank. 3marks 8. The coordinates of the end points of diameter of a circle are A 3,4 and B -3, 6 .


3 marks 15. Solve for x in the equation 3 marks Log3 4 log3x 1 log35 log3 2 16. The table below shows the relationship between two variable x and y. x 0 1 2 3 4 5 6 y 3.0 3.6 4.3 4.7 5.4 6.0 6.6 a Draw a line of best fit for the above values. 2marks b Find the formula connecting x and y. 1mark SECTION II 50 MARKS Answer any five questions. 17. A triangle ABC with vertices at A 1, -1 , B 3, -1 and C 1 ,3 is mapped onto triangle A1 B1 C1 by a transformation whose matrix 1001 Triangle A1 B1 C1 is mapped onto A11 B11 C11 with vertices at A11 2, 2 , B11 6, 2 and C11, 2, -6 by a second transformation. A Find the coordinates of A1 B1 C1 2marks b Find the matrix which map A1 B1 C1 onto A11 B11 C11 3marks c Determine the ratio of the area of triangle A1 B 1 C1 to triangle A11 B11 C11. 3marks d Find the transformation matrix which maps A11 B11 C11 onto ABC. 2marks www.freekcsepastpapers.com167 18. The table below shows the income tax rates for the year 2021 Monthly table income in Kenya shillings Percentage tax rate in each shilling 1 9680 10 9681 18800 15 18801 27930 20 27931 37080 25 Above 37080 30 Mr. Kamau a civil servant paid income tax of Ksh. 27 900 in the month of February 2021. His total monthly taxable allowances amounted to Ksh. 36 700 and was entitled to a monthly personal relief of ksh. 1056, he also had a life insurance policy for which he paid Ksh.