A ship left points P 100 S, 1610 W and sailed to a point Q 100S, 1420 E using the shorter route along parallel of latitude at a speed of 20 knots. A Taking 227 , R 6370 km and 1nm 1.853 km, calculate to 2 decimal places. I The distance travelled by the ship in kilometres. 3 marks ii Time taken from P and Q 2 marks b After docking at port Q the ship took 10 hours to offload goods and then proceeded northwards to a port R a distance of 600 nautical miles. I Find the longitude of port R. 2 marks ii If the ship left P on Tuesday 0700 hours, find the time and day of docking at port R if the speed of the ship between port Q and R was 15 knots. 3 marks www.freekcsepastpapers.com168 22. A Use a ruler and a pair of compasses only to construct triangle ABC such that AB 10cm ABC 300 and BAC 450 3 marks b Draw the locus L1, such that L1 is equidistant from lines AB and AC. 2 marks c Draw the locus L2 such that L2 is equidistant from parts A and B. 2 marks d Draw the locus of point P on the same side of C such that APB 900. Let L1 meet P at X and L2 meet at Y. measure XY. 3 marks 23. The figure below is a right pyramid VEFGH with a square base of 8 cm and a slant edge of 20cm. Points A, B, C and D lie on the slant edges of the pyramid such that VA VB VC VD 10cm and plane ABCD is parallel to the base EFGH. A Find the length of AB. 2 marks b Calculate, correct to 2 decimal places: i. The length of CA 2 marks ii. The perpendicular height of the pyramid VABCD. 2 marks c The pyramid VABCD was cut off. Find the volume of the frustum ABCDEFGH correct to 2 decimal places.


The perpendicular height of the pyramid VABCD. 2 marks c The pyramid VABCD was cut off. Find the volume of the frustum ABCDEFGH correct to 2 decimal places. 4 marks 24. Kamau has at least 50 acres of land on which he plans to plant potatoes and cabbages. Each acre of potatoes requires 6 men and each acre of cabbages requires 2 men. The farmer has 240 men available and he must plant at least 10 acres of potatoes. The profit on potatoes is Ksh. 1,000 per acre and on cabbages is Ksh. 1,200 per acre. If he plants x acres of potatoes and y acres of cabbages. A Write down 3 inequalities in X and Y to describe the information above. 3 mks b Represent these inequalities graphically use a scale of 1:10 for both axes . 4 mks c Use your graph to determine the number of acres for each vegetable which will give maximum profit and find the maximum profit. 3 mks www.freekcsepastpapers.com144 KIRINYAGA WEST FORM 4 SCHOOL BASED EXAMINATIONS 2023 Kenya Certificate of Secondary Education 121 1 MATHEMATICS Paper 1 21 2 hours SECTION 1: 50 Marks Answer all the questions in this section. 1. The product of two factors 12x 5 and 2 5x is -11. Find the two factors. 4 marks 2. Four businessmen shared their profits as follows: Mr. White got a quarter of the profit while Mr. Green got a half of what remained. The rest was shared equally between Mr. Black and Mr. Brown. If the difference between Mr. White and Mr. Black was Sh 7,500, how much did Mr. Green get? 4marks 3. Solve the inequalities x255xand represent your solution on a number line. 3 marks 4. Two athletes were running 10,000m. Mboga was running at a constant speed of 200m per minute while Sukuma was running at a constant speed of 150m in half a minute.


3 marks 4. Two athletes were running 10,000m. Mboga was running at a constant speed of 200m per minute while Sukuma was running at a constant speed of 150m in half a minute. For how long did Sukuma wait for mboga also to finish? 3 marks 5. Simplify completely 82x4xx32 3 marks 6. Find the area of the quadrilateral ABCD below, correct to 1 decimal place. 3 marks 7. A watch gains 10 seconds every hour. It was set right at 0950 hrs on Monday. Determine the time, in a 12 hrs system, the watch will show on the following Monday when the correct time is 1150 hrs, to the nearest minute, 3 marks 8. Jack and Dan both drive a distance of 10 km but Dan s average speed is 10km hr slower than Jack s and consequently he takes 30 minutes longer to complete the journey. Calculate Jack s average speed. 3 marks 9. Three towns A, B and C are such that B is 5km and on a bearing of 0500 from A. C is due south of B and on a bearing of S 650E from A. Using a scale of 1cm represents 1 km, draw a scale diagram to show the relative positions of the three towns, hence state the distance between towns A and C. 4 marks 10. Two interior angles of an irregular polygon are right angles, the rest are 1440 each. Determine the number of sides of the polygon, 3 marks www.freekcsepastpapers.com145 11. A trader converted Ksh 500 000 to sterling pounds. He then spent a total of 1,000. He proceeds to exchange the balance to Euros and bought goods worth 100 Euros. Calculate his balance to the nearest Kenya shillings. 3 marks Currency Buying Selling 1 Sterling pound 130.14 130.50 1 Euro 84.25 84.28 12. Joan has some money in two denominations only: twenty-shilling coins and one hundred shilling notes. She has four times as many twenty shilling coins as one hundred-shilling notes. Altogether she has sh 2160. How many one hundred-shilling notes does she have?


She has four times as many twenty shilling coins as one hundred-shilling notes. Altogether she has sh 2160. How many one hundred-shilling notes does she have? 3marks 13. Given that 2A , find matrix B such that A2 A B 3 marks 14. The heights of two similar containers are 21cm and 28cm respectively. If the larger container holds 3.1 litres, find the capacity of the smaller one. 3 Marks 15. The table below shows the shoe sizes of 20 students in a class. Shoe size 4 5 6 7 8 9 No. Of students 1 4 5 7 2 1 Determine the median shoe size. 2 marks 16. The base ABCD of a right pyramid is a square of side 2cm. Point V is the vertex of the pyramid and the length of the slanting edges is 3 cm. Draw a labelled net of the pyramid. 3 marks SECTION II: 50 Marks Answer only FIVE questions in this section in the spaces provide, 17. Mwajuma and Mwangi entered a partnership. They contributed Ksh 120,000 and Ksh 150,000 respectively. After 18 months of business, Njambi joined the partnership and contributed Ksh 90,000. A Determine the ratio of their contribution after three years of business. 3 marks b After the three years, they realized a profit of Ksh 510,000. They agreed to set aside 30 of the profit to cater for the cost of running the business and share the rest as per their contributions. Determine the difference in Mwangi s and Njambi s share of the profit. 4 marks c Njambi then invested back her share into the business. Determine their new ratio of contributions at the end of the fourth year. 3 marks 18. A solid frustum has a base radius of 21 cm and a top radius of 14cm. The frustum is 22.5 cm high and is made of a metal whose density is 3g cm3.


3 marks 18. A solid frustum has a base radius of 21 cm and a top radius of 14cm. The frustum is 22.5 cm high and is made of a metal whose density is 3g cm3. Take 22 7 a Calculate i The volume of the metal in the Frustum. 5 marks ii The mass of the Frustum in kg. 2 marks b The Frustum is melted down and recast into a solid cube. In the process 20 of the metal is lost. Calculate to 2 decimal places the length of each side of cube. 3 marks 19. A rhombus has vertices at A -1, 1 , B 0,8 , C 5, 3 and D x, y . T is the intersection of the diagonals of the rhombus. A Find the coordinates of D and T. 2 marks b Given the CBT a, express BAD in term of a. 2 marks c Calculate the lengths of diagonals AC and BD, to one decimal place. 4 marks d Calculate the area of the rhombus. 2 marks www.freekcsepastpapers.com146 20. A Using a ruler and a pair of compasses only, construct a parallelogram ABCD such that AB 8cm, diagonal AC 12cm and BAC 22.50. 4 marks b Measure: i The diagonal BD 1 mark ii The angle ABC. 1 mark c Draw the circumcircle of triangle ABC. 2 marks d Calculate the area of the circle drawn. 2 marks 21. The table below shows marks scored by a group of students in a Mathematics test. Marks No. Of Students X fX Cf 10-24 6 25-39 8 40-54 11 55-69 12 70-84 9 85-99 4 a State the modal class. 1 mark b Calculate the mean mark. 3 marks c Draw a histogram to represent the information above. 3 marks d Use the histogram to determine the median amount of money spent. 3 marks 22.


3 marks c Draw a histogram to represent the information above. 3 marks d Use the histogram to determine the median amount of money spent. 3 marks 22. A Sketch the curve y x 5 x and the line y x. 5 marks b Use integration method to determine the area bound by the curve y x 5 x and the line y x. 5 marks 23. A room measuring 2.5m long, 2m wide and 3m high is to be renovated by covering all the four walls and floor with tiles. The room has one door measuring 2m high and 90cm wide and a 1.2m high window on the opposite wall measuring 1.5m long and 40cm wide. The walls are to be covered with tiles to a height of 1.2m. The remaining part of the walls except door and window and ceiling are to be painted. Each tile measures 12 cm by 5cm. A Calculate; i Number of tiles to be bought. 4 marks ii The area to be painted. 3marks b 1 tile cost sh. 25 and one litre of paint covers 3m2 and costs sh, 2450. Determine the cost of the materials needed to renovate the room. 3 marks 24. A quadrilateral ABCD has vertices A 4, -4 , B 2,-4 , C 6,-6 and D 4, -2 . A On a grid draw quadrilateral ABCD 1 mark b A1B1C1D1 is the image of ABCD under positive quarter turn about the origin on the same grid draw the image A1B1C1D1 and state its coordinates. 3 marks c A11B11C11D11 is the image of A1B1C1D1 under transformation given by the matrix 1 i Determine the coordinates of A11B11C11D11 .


Calculate the time it would take certain borrowed amount to double. Give your answer to one decimal place. 3 marks 5. A Expand 1 2x 5 to the fourth term. 1 mark b Hence evaluate 1.02 5 correct to 3 d.p. 2 marks 6. A uniform distributor is required to supply two sizes of skirts to a school; medium and large sizes, she was given the following conditions by the school. I The total number of skirts must not exceed 600. Ii The number of medium size skirts must be more than the number of large size skirts. Iii The number of medium size skirts must not be more than 350 and the number of large size skirts must not be less than 150. If the distributor supplied x medium size and y large size skirts. Write down in terms of x and y all the linear inequalities representing the conditions above. 4 marks 7. Given that 3 - 2 15Tan 0 . Find without using Mathematical tables or calculator Tan 750. 3 marks 8. The position vectors of A and B are a 3i 7j 8k and b 6i 5j 3k. Given that x divides lines AB in the ratio 2 : -3. Determine the co-ordinates of point x. 3 marks 9. Determine the quartile deviation for the following set of numbers. 6, 10, 7, 6, 9, 8, 3, 2, 9, 8, 5, 4, 5 3 marks 12. The points 5, 5 and -3, -1 are ends of diameter of a circle centre A. Determine:- a The co-ordinates of A. 1 mark b The equation of the circle expressing it in the form x2 y2 ax by C 0. 2 marks 13. In the figure below BT is a tangent to the circle at B. AXCT and BXD are straight lines XC 4cm, CT 8cm, BX 9.6cm and XD 2.5cm.


2 marks 13. In the figure below BT is a tangent to the circle at B. AXCT and BXD are straight lines XC 4cm, CT 8cm, BX 9.6cm and XD 2.5cm. Find the length of: a AX 1 mark A B D X T Cwww.freekcsepastpapers.com148 b BT 2 marks 14. Tap A can fill a bath in 4 min. Tap B can fill the same bath in 6 min and Tap C can empty the bath in 8 min. A Calculate how long it would take to fill the bath if all the taps were left running. 1 mark b Calculate how long it would take to fill the bath if all taps were left running for 2 min after which tap C was closed. 2 marks 14. A transformation whose matrix is 2 maps quadrilateral ABCD of area 18cm2 onto another quadrilateral PQRS, what is the area of PQRS? 3 marks 14. Given that 1 x1 x xy2 is the equation of a curve, find the gradient of the tangent to the curve at the point 2, 4 . 2 marks 16. A two-digit number is made by combining cards labeled with the digits 1, 4, 6 and 9 at random. The cards are picked at random with replacement. A Make a table of possible numbers that can be made. 1 mark b Find the probability that the number formed is a prime number or even number. 2 marks 17. The table below shows the rate of cooling of a liquid with respect to time. Time Min 0 2 4 6 8 10 12 14 16 Temp 0C 80 60 46 35 26 20 16 14 12 a Draw the temperature time graph. 2 marks b Use the graph to determine the average rate of cooling of the liquid between the 5th and 13th minutes. 2 marks SECTION II: 50 Marks Answer only FIVE questions in this section.


Time Min 0 2 4 6 8 10 12 14 16 Temp 0C 80 60 46 35 26 20 16 14 12 a Draw the temperature time graph. 2 marks b Use the graph to determine the average rate of cooling of the liquid between the 5th and 13th minutes. 2 marks SECTION II: 50 Marks Answer only FIVE questions in this section. 19. The table below shows income tax rates for the year 2018. Monthly taxable income KSh. Percentage rate of tax Per shilling Upto 9680 10 From 9681 to 18800 15 From 18801 to 27920 20 From 27921 to 37040 25 From 37041 and above 30 In May 2018 Christine s basic salary was Sh 18000. She was also paid a house allowance of Sh 5000, a commuter allowance of Sh 3800 and a medical allowance of Sh 2600. In June that year her basic salary was increased by 3 . A Calculate her June s i basic salary 2 marks ii total taxable income 2 marks b If the monthly personal relief was Ksh 1056. Calculate the net tax that Christine paid in June. 4 marks c In addition to income tax the following deductions were also made from her salary every month. NHIF Sh 2000 Loan recovery Sh 3500 Calculate her monthly net income. 2 marks www.freekcsepastpapers.com149 20. The figure below is a square based pyramid ABCDV with AD DC 6cm and height VO 10cm. A State the projection of VA on the base ABCD. 1 mark b Find; i The length of VA. 3 marks ii The angle between VA and ABCD. 2 marks iii The angle between the planes VDC and ABCD. 2 marks iv Volume of the pyramid. 2 marks 19. A Complete the table below given y x3 4x2 x 6.


2 marks iv Volume of the pyramid. 2 marks 19. A Complete the table below given y x3 4x2 x 6. For -2 x 4 2 marks x -2 -1 0 1 2 3 4 y 6 0 b On the gird provided draw the graph of y x3 4x2 x 6 for -2 x 4. Use the scale of 1 cm represent 5 units on the y- axis and 2 cm represent 1 unit on the x axis. 3 marks c Use your graph to solve the equation x3 4x2 x - 6 2 marks d By drawing a suitable straight line on the same axis solve the equation x3 4x2 - 5x 7 0. 3 marks 20. The following table shows the distribution of marks obtained by 50 students in a maths test. Marks 45-49 50-54 55-59 60-64 65-69 70-74 75-79 Frequency 3 15 13 9 4 1 5 Calculate: i Mean 4 marks ii Variance 4 marks iii Standard deviation 2 marks 21. 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 westwards to town R. Determine a The distance PQ in nautical miles. 3 marks b The position of town R. 3 marks c The local time at R if local time at Q is 3.12 pm. 2 marks d The total distance moved from P to R in KM. Take 1 nautical mile 1.853 Km 2 marks V C D 10cm 6cm O A Bwww.freekcsepastpapers.com150 22. A Complete the table below, giving the values correct to 2 decimal places.


2 marks d The total distance moved from P to R in KM. Take 1 nautical mile 1.853 Km 2 marks V C D 10cm 6cm O A Bwww.freekcsepastpapers.com150 22. A Complete the table below, giving the values correct to 2 decimal places. 2 marks x 0 30 60 90 120 150 180 210 240 270 300 330 360 Sin 2x 0 -0.87 0 3 Cos x 2 1 -3.5 -4.60 c On the grid provided draw the graph of y Sin 2x and y 3 Cos x 2 for 00 x 3600, on the same axes. Use the scale of 1cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis. 5 marks c Use to graph in b above to solve the equation 3 Cos x Sin 2x 2. 2 marks d State the amplitude of y 3 Cos x -2. 1 mark 23. A An arithmetric progression is such that first term is -5, the last term is 135 and the sum of the progression is 975. Calculate: i The number of terms in the progression. 3 marks ii The common difference of the progression. 3 marks b The sum of the first two terms of an increasing Geometric Progression G.P is 20. The sum of the second term and third term of the same GP is 30. Determine the common ratio of the GP. 4 marks 24. A Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve y -x2 6x 1, the lines x 0, y 0 and x 6. 5 marks b Calculate i the area of the region in a above by integration. 3 marks ii the percentage error of the estimated area to the actual area of the region correct to 2 d.p.


Calculate the perimeter of the rhombus. 3marks SECTION II 50 marks Answer 5 questions only in this section 17. Three business partners Abila, Bwire and Chirchir contributed Ksh120,000, 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 Ksh225,000 was realised. A. Calculate the amount. I Put back into the business. 2marks ii Used for official operations. 1mark b. Calculate the amount of profit each partner got. 4marks www.freekcsepastpapers.com126 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. 3marks 18. One day Mr. Makori bought some oranges worth Ksh 45, on another day of the same week his wife Mrs.Makori spent the same amount of Money but bought the oranges at a discount of 75 cents per orange a If Mr.Makori bought an orange at Kshs x, write down and simplify an expression for the total number of oranges bought by the two in the week. 3marks b If Mrs.Makori bought 2 oranges more than her husband, find how much each spent on an orange. 5 marks c Find the number of oranges bought by the two. 2 marks 19. Two lines L1:2y 3x -6 0 and L2 3y x 20 0 intersect at a point A. a Find the coordinates of A 3 marks b A third line L4 is perpendicular to L2 at point A. Find the equation of L3 in the form y mx c, where m and c are constants. 3 marks c Another line L4 is parallel to L1 and passes through -2, 3 . Find the x and y intercepts of L4 4 marks 20.


Find the equation of L3 in the form y mx c, where m and c are constants. 3 marks c Another line L4 is parallel to L1 and passes through -2, 3 . Find the x and y intercepts of L4 4 marks 20. The mases to the nearest kilogram of some student were recorded in table below Mass kg 41-50 51-55 56-65 66-70 71-85 Frequency 8 12 16 10 6 Height of rectangle 0.2 a . Complete the table above to 1 decimal 2 marks b On a grid, draw a histogram to represent the above information 3 marks c Use the histogram to i State the class in which the median mark lies. 1 mark ii Estimate the median mark 2 marks iii The percentage number of students with masses of at least 74kg. 2marks 21. Use a ruler and compass only for all the constructions in this question. A Construct a triangle XYZ in which XY 6cm, YZ 5cm and angle XYZ 1200. 2marks b Measure XZ and angle YXZ. 2 marks c Construct the perpendicular bisector of XZ and let it meet XZ at M. 1 mark d Locate a point W on the opposite of XZ as Y and that XW ZW and YW 9cm and hence complete triangle XZW. 2 marks e Measure WM and hence calculate the area of triangle XZW. 3 marks 22. 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. Www.freekcsepastpapers.com127 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 b A van left Nairobi at 8.00 a.m and travelled towards Mombasa at an average speed of 80 km h .


Www.freekcsepastpapers.com127 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 b A van left Nairobi at 8.00 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 120km 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 23. While designing the water circulation system, planners of an estate used assumption that each housing unit in the estate will require at least 0.32m3 of water per day. To satisfy this need, they are to use a water pipe of radius 8cm to distribute the water. The water will be flowing in the pipe for only 14 hours a day at the rate of 24cm s. a Determine the amount of water to the nearest litres, supplied in one hour. 3marks b What is the maximum number of housing units that can be supported by the water circulation system? Assume that a housing unit requires at most 0.32m3 of water per day . 2marks c Each housing unit will pay a flat rate of sh. 280 per month for the supply of water. If the number of housing units in the estate is to be maximum and all end up being occupied, calculate the amount of money that will be collected in a month. 2 marks d The maximum number of housing units were constructed and all got occupied. The estate ended up using on average 0.35m3 of water per housing unit per day. How much longer was the water pumped per day to satisfy the estate s water demand? 3marks 24.


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. Calculate the Angle CAE makes with the plane ADEF 3marks SECTION II: 50 MARKS ANSWER ANY 5 QUESTIONS IN THIS SECTION 17. In the figure below, . 23 3: 1 a Express the following vectors in terms of a and c only: i AB 1 mark ii OD 2 marks b Given that OE hOD and AE kAB where h and k are scalars express OE in two different ways hence find the scalars h and k. 5 marks c If OC produced meets AB produced at F, find OF. 3 marks 18. A The 5th term of an AP is 82 and the 12th term is 103. Find: i the first term and common difference. 3marks ii the sum of the 21 terms. 2 marks b A stair case was built such that each subsequent stair has a uniform difference in height. The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145. Calculate the height of the 1st stair and the uniform difference in height of the stairs. 3 marks c During the construction of the staircase, each step was supported by a vertical piece of timber. If the staircase has 11 stairs, calculate the total length of timber used. 2 marks 19. A Complete the table below given that 2 12 for 4 5.


Using a ruler and compasses only. I Construct a parallelogram ABCD such that AB 10cm, BC 7cm and angle ABC 105 . 3 marks ii Construct the loci of P and Q within the parallelogram such that 6cm. 4 and 6 3 marks iii Calculate the area within the parallelogram but outside regions bounded by the loci of P and Q. 4 marks 22. Below is the histogram representing marks obtained in Mathematics test a Develop a frequency distribution table for the data 3 Marks b Using an assumed mean of 60.5 find the mean. 3 marks c Calculate Standard deviation. 4 marks 23. A Use the mid ordinate rule with 5 strips to estimate the area bounded by the curve 2 3 4, 2, 3 and 3 marks b Calculate the exact area above 5 marks c Find the percentage error involve in using the mid-ordinate role. 2 marks 24. Eldoret Airport is planning to build a fire fighting plant on a space of 250m2. Two types of machines are to be installed, machine x which occupies a space of 5m2 and machine Y which occupies 10m2. The airport can have a maximum of 40 machines at a time. At most 15 machines of type Y are used at any given time. A Write down three inequalities other than x 0, and y 0. 3marks b On the grid below, show the region satisfying the given conditions. 4marks c The profit from a type x machine is Ksh 1000 and that of type y is Ksh 4000. Use the graph to obtain the number of machines of each type that should be installed to obtain maximum profit. Calculate the maximum profit. 3marks www.freekcsepastpapers.com106 CEKENAS PREMOCK EXAMINATION, 2023 121 1 MATHEMATICS ALT.


Use the graph to obtain the number of machines of each type that should be installed to obtain maximum profit. Calculate the maximum profit. 3marks www.freekcsepastpapers.com106 CEKENAS PREMOCK EXAMINATION, 2023 121 1 MATHEMATICS ALT. A Paper 1 Time: 2 Hours SECTION I 50MKS ANSWER ALL THE QUESTIONS IN THE SECTION 1. Two similar solids have surface areas 48cm2 and 108cm2 respectively. Find the smaller solid if the bigger one has a volume of 162cm3 3mks 2. An electrician made a loss of 30 by selling a multi plug at sh. 1400 what profit would have made if he sold the multi plug at sh. 2300. 3mks 3. Find the exact value of 19.143.2 4mks 4. The graph below not drawn to scale is a plot for the function y ax2 bx k where a,b and k are constant Determine the values of a,b and k. 3mks 5. Solve the following inequalities and represent the solutions on a number line x 1 4x-5 3x 2 3mks 6. Dr.June needs to import a car from Japan that costs US dollars USD 5000 outside Kenya. He intends to buy the car through an agent who deals in Japanese Yen JPY . The agent charges a 20 commission on the price of the car and a further 80 325 JPY for shipping the car to Kenya. Find the amount in Kenya shillings that Dr. June need to sent to the agent to get the car given that: 3mks 1 USD Ksh 120 1USD 135 JPY 7. For x in the equation. 3mks 9x 1 32x 810 8. A lampshade is the shape of a cone such that its slanting height is 30cm white the top and bottom radii of the lampshade are 10cm and 17.5cm respectively. Calculate the surface area of the material used to make the lampshade. 4mks 9. Simplify xxx 2mk 10.


Calculate the surface area of the material used to make the lampshade. 4mks 9. Simplify xxx 2mk 10. A translation vector yyx2maps a point A 4,6 onto A1 9,12 . Find the value of x and y. 3mks 11. In the figure below A 62 42 , bc 8.4 cm and CN is a bisector of angle ACB. Calculate to 1dp the length of CN. 3mks www.freekcsepastpapers.com107 12. The figure below show a triangular prism whose cross-section is an equilateral triangle. A On the prism, show the positions of the lines of symmetry. 1mk b Draw the net of the prism. 1mk 13. In Boresha Bank customers may withdraw cash through one of the three tellers at the counter. On average, one teller takes 3minutes, the others take 5 minutes and 6minutes respectively to serve a customer. If the three tellers start to serve the customers at the same time, find the shortest time it takes to serve 210 customers. 4mks 14. An arc length of 11cm subtends an angle of 140 at the center of the circle. Find the area of the enclosed sector. 4mks 15. It would take 15men 8days to dig a trench of 240m long. Find how many days it would take 18men to dig trench 360 meters long working at the same rate. 3mks 16. Determine the quartile deviation for the following distribution. 3mks 3,4,9,5,4,7,6,2,1,6,7,8,9 SECTION II 50MARKS Answer any five questions in this section. 17. A straight line L1 has a gradient- 21 and passes through the p -1,3 .


3mks 3,4,9,5,4,7,6,2,1,6,7,8,9 SECTION II 50MARKS Answer any five questions in this section. 17. A straight line L1 has a gradient- 21 and passes through the p -1,3 . Another line l 2 Passes through the points Q 1,-3 and R 4,5 Find: a i The equation of l1 in the form y mx c, where m and c are constants. 2mks ii Hence find k given that S 0.k 1mk b i The gradient of l 2 1mk ii The equation of l2 in the form ax by c, where a, b and c are integral values. 2mks c The equation of a line l3 makes with the x-axis. 1mk d Calculate the acute angle l3 makes with the x-axis. 1mk 18. The triangle ABC with coordinates A 2,3 ,B 4,2 and C 1,1 is mapped onto triangle A1B1C1 by a reflection in the line y x 0 a i Draw triangle ABC and its image A1B1C1 on the same plane. 3mks ii Triangle A1B1C1 is mapped onto A11B11C11and describe felly a single transformation that maps triangle ABC onto triangle A11B11C11. 4mks b Triangle ABC is mapped onto xyz with A being mapped onto x, B onto Y and C onto Z. given that the coordinates of x is -4,3 Y is 0,2 and z is -1,1 find the matrix representing the transformation. 3mks 19. A bus left Nairobi at 7.00am and traveled towards Eldoret at an average speed of 80km hr. A t 7.45am a car left Eldoret towards Nairobi at an average speed of 120km hr. The distance between Nairobi is 300km. Calculate a The time the bus arrived at Eldoret. 2mks b The time of the day two met.


The distance between Nairobi is 300km. Calculate a The time the bus arrived at Eldoret. 2mks b The time of the day two met. 4mks c The distance of the bus from Eldoret when the car arrived in Nairobi 2mks d The distance from Nairobi when two met. 2mks www.freekcsepastpapers.com108 20. Two equal circles with centres P and Q and radius 8cm intersects at point A and B as shown below. Given that the distance between their centres is 12 cm, find, correct to 4 significant figures; a The length of chord AB. 2mks b The length of shaded region. Use 3.142. 8mks 21. The figure below shows a triangle OAB with as the origin. OA a OB b, OM 2 5a and ON 2 3b. A Express in terms of a and b the vectors. I BM. 1mk ii AN. 1mk b Vector OX can be expressed in two ways: OB Kbm or Han, where k and h are constants. Express OX in term of: i a b and k. 2mks ii a b and h. 2mks c Find the values of k and h. 4mks 22. In the figure below P,Q,R,S and T lie the circumference of a circle centre O. Line UPV Is a tangent to the circle at P. Chord ST of the circle is produced to intersect with the tangent at U. Angle UPT,RST and ORQ ARE 28 ,100 AND 50 respectively. A Determine the sizes of the following angles; 3mks i RTP ii QTP. 3mks b Given that PQ 6cm, calculate correct to 1 decimal place, the circle. 4mks www.freekcsepastpapers.com109 23. A Complete the table below y 2x2 5x-7 for the range -4 x 2.


Given that the sum of the first three terms of the progression is 76,find the whole number value of x and hence the first term. 5mks 18. A Complete the table below. 2mks b On the graph provided below on the same axis draw the graph of y 2cox and y sin 2x 300 for 1800 x take the scale 1cm for300 on the x axis and 2cm for 1unit on the y axis. 5mks c Use your graph to estimate the value of x for which Cos x Sin 2x 300 0 2mks d Use your graph to state the amplitude and period of the function y sin 2x 300 . 2mks 19. A pentahedron with faces marked 6,5,1,2 and 7 is biased so that when rolled, the probability of a number t showing up, is given by P t K t where K is a constant. If the pentahedron is rolled twice, find the probability that the total score is 8. 4marks b The probability of the three horses X, Y and Z jumping over a fence are 0.5.,. 0.2 and 0.3 respectively i Draw a tree diagram to represent the information 1mark ii Find the probability that all the horses jump successfully 1mark iii Find the probability that only one horse jumps successfully 2marks iv Find the probability that at most one horse misses to jump over the fence 2marks 20. The position of three cities P, Q, and Rare 150N 200W , 500N , 200W and 500N 600E respectively. A Find the distance in nautical miles between i Cities P and Q 2marks ii Cities P and R, via city Q 3marks b A plane left city P at 0250h and flew to city Q where it stopped for 3 hours then flew to city R, maintaining a speed of 900 knots throughout .Find.


4marks b The probability of the three horses X, Y and Z jumping over a fence are 0.5.,. 0.2 and 0.3 respectively i Draw a tree diagram to represent the information 1mark ii Find the probability that all the horses jump successfully 1mark iii Find the probability that only one horse jumps successfully 2marks iv Find the probability that at most one horse misses to jump over the fence 2marks 20. The position of three cities P, Q, and Rare 150N 200W , 500N , 200W and 500N 600E respectively. A Find the distance in nautical miles between i Cities P and Q 2marks ii Cities P and R, via city Q 3marks b A plane left city P at 0250h and flew to city Q where it stopped for 3 hours then flew to city R, maintaining a speed of 900 knots throughout .Find. X -1800 -1500 -1200 -900 -600 -300 00 600 900 1200 1500 1800 2cos x -2.0 -1.73 -1.00 2.00 sin 2x-300 1.00 -0.5 1.00www.freekcsepastpapers.com112 i The local time in city R when the plane left city P 3marks ii The local time to the nearest minute at city R when the plane landed at R 2marks 21. The marks scored by 40 Mathematics students were shown in the table below. Marks 42-46 47-57 52-56 57-61 62-66 67-71 Number of students 3 4 10 12 8 3 a State the upper class limit of the modal class 1mark b Estimate the standard deviation. 3marks c If the pass mark is 55 how many students passed? 3marks d Find the range of marks scored by the middle 50 of the students 3marks 22. Karuku, Jaoko and Ezra contributed a total of Ksh.3, 579,000 to purchase a van.


3marks c If the pass mark is 55 how many students passed? 3marks d Find the range of marks scored by the middle 50 of the students 3marks 22. Karuku, Jaoko and Ezra contributed a total of Ksh.3, 579,000 to purchase a van. The ratio of Karuku s contribution to Jaoko s contribution was 4:3 while Ezra s contribution to Karuku s contribution was 5:7 a Determine the amount each contributed towards the project 4marks b The van purchased had a capacity of 14 seats including the driver s seat and charges Ksh. 650 from Migori to Kisumu. The van operates from Migori to Kisumu and back to Migori on a daily basis for six days per week .On a daily basis, Ksh 10,000 collected is used in fencing the van, 31 of the remainder is set aside for maintenance and drivers salary and the rest is saved for the owners which will be divided in the ratio of their contribution. Determine: i The amount saved for the maintenance of the van after 56 weeks if the driver was paid a total of Ksh 268,800 3marks ii The amount each received after 56 weeks 3marks 23. Use the line below to construct triangle ABC such that BC 5.3cm and angle ABC 750. 2marks Locate point M that is equidistance from points A, B and C 2marks Construct the locus of P such that angle APC Angle ABC 1800 2marks Construct the locus of Q to meet the locus of P at R such that angle ABQ CBQ 1mark Measure MR 1mark Shade the region S inside the triangle such that angle ABS angle CBS and AS CS 2marks 24. A school has to take 560 people for a tour .There are two types of buses available. Type X and type Y. Type X can carry 70 passengers and type Y can carry 40 passengers. They have to use at least 10 buses of each type must not be less than 3.


Type X and type Y. Type X can carry 70 passengers and type Y can carry 40 passengers. They have to use at least 10 buses of each type must not be less than 3. A Form all linear inequalities to represent the above equation 3marks b On the grid provided draw the inequalities and shade the unwanted region 3marks c If the charges for hiring the buses are; Type X; Shs 40,000 Type Y: Shs 30,000 i Use your graph to determine the number of buses of each type that should be hired to minimize the cost 3marks ii Find the minimum costwww.freekcsepastpapers.com 86 IMENTI SOUTH EXAMINATIONS, 2023 121 1 MATHEMATICS Paper 1 TIME: 2 HRS SECTION I 50 marks Answer all the questions in this section 1. Evaluate 12 245 of 8 6 2 425 12 of 6 8 313 3 marks 2. Arrange all prime numbers between 10 and 20 in ascending order to form a number. State the total value of fourth digit from the left of the number that is formed. 2 marks 3. The volume of water in a measuring cylinder is 25.2cm3. After a solid metal sphere is immersed into it, the measuring cylinder reads 29.4cm3. Calculate the radius of the sphere. Use 227 3 marks 4. Mary and Jane working together can cultivate a piece of land in 6 days. Mary alone can complete the work in 15 days. After the two had worked together for 4 days Mary withdrew the services. Find the time taken by Jane to complete the work alone. 4 marks 5. Solve the simultaneous equation 2p 7q 19 12 p 3q 7 3 marks 6. The angles of a quadrilateral are in the ratio 6 : 4 : 3 : 2. Calculate the sizes of the angles. 3 marks 7. EFGH is rhombus and triangle DEF is equilateral. Calculate HDG given that HED 18o. 2 marks HGFED18o 8.


Find the equation of l in the form y mx c where m and c are constants. 3 marks 16. Mercy bought the following goods from supermarket 3kgs of sugar Ksh 160.00, 2 loaves of bread Ksh 120.00, 6 packets of milk Ksh 65.00www.freekcsepastpapers.com 87 a How much did she pay for the goods 2 marks b How much money did she receive in change if she gave a note of a thousand and a note of five hundred 2 marks SECTION II 50 marks Answer any FIVE questions in this section 17. A Fill the table below for function y x2 4x 2 for -1 5 2 marks x 1 0 1 2 3 4 5 y b i Draw the graph of the function y x2 4x 2 for -1 5 4 marks ii On the same axes draw a line y x 1 2 marks c Determine the values of x at the points of intersection between the curves y x2 4x 2 and y x 1 2 marks 18. In the figure below DA is a diameter of the circle ABCD centre O, radius 10cm. TCS is a tangent to the circle at C, AB BC and angle DAC 38o. ABCDO38oTS a Find the size of angle i ACS 2 marks ii BCA 2 marks b Calculate the length of i AC 3 marks ii AB 3 marks 19. Two circles of radii 3.5cm and 4.2 cm with centres O1 and O2 respectively intersect at points A and B as shown in the figure below. The distance between the two centres is 6cm. 4.2cm3.5cmABO1O2 Calculate: a The size of AO1B 3 marks b The size of AO2B 3 marks c The area of quadrilateral O1AO2B to 2 dp 2 marks d The area of the shaded region to 2 s.f 2 marks 20.


Two circles of radii 3.5cm and 4.2 cm with centres O1 and O2 respectively intersect at points A and B as shown in the figure below. The distance between the two centres is 6cm. 4.2cm3.5cmABO1O2 Calculate: a The size of AO1B 3 marks b The size of AO2B 3 marks c The area of quadrilateral O1AO2B to 2 dp 2 marks d The area of the shaded region to 2 s.f 2 marks 20. In the figure below OY : YA 1 : 3, AX : XB 1 : 2, OA a and OB b. N is a point of intersection of BY and OX AOBXYNab 2www.freekcsepastpapers.com 88 Determine: a i OX 2 marks ii BY 1 mark b Given that BN mBY and ON nOX, express ON in two ways in terms of a, b, m and n 3 marks c Find the values of m and n 4 marks 21. A Use a ruler and a compass only. Construct triangle ABC where AB 7cm, angle CBA 75o and BC 5cm. 4 marks b i Locate a point T inside the triangle which is equidistant from points A and B and also equidistant from line AB and AC 3 marks ii Measure TB 1 mark c By shading the wanted region P inside the triangle if its nearer to point B than to point A and also nearer to the line AB than AC. 2 marks 22. The diagram below shows the speed time graph for a lorry travelling between two stations. The lorry starts from rest and accelerated uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds. 650Speed m s Time in seconds Given that the distant between the two stations is 10450m, calculate the a Maximum speed in m s attained by the lorry 2 marks b Acceleration 2 marks c Distance the lorry travelled during the last 100 seconds.


The lorry starts from rest and accelerated uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds. 650Speed m s Time in seconds Given that the distant between the two stations is 10450m, calculate the a Maximum speed in m s attained by the lorry 2 marks b Acceleration 2 marks c Distance the lorry travelled during the last 100 seconds. 3 marks d Time the lorry takes to travel first half of the journey. 3 marks 23. Three quantities A, B and C are such that A varies directly as square of B and inversely as the square root of C. a Given that A 20 when B 5 and C 9, i Find the equation connecting A, B and C 3 marks ii Find A when B 7 and C 25 2 marks b If B increases by 20 and C reduces by 36 ; find the percentage increase in A 5 marks 24. A The ratio of Juma s and Akinyi s earnings was 5 : 3. Juma s earnings rose to Ksh. 8400 after an increase of 12 . Calculate the percentage increase in Akinyi s earnings given that the sum of their new earnings was Ksh. 14,100 6 marks b Juma and Akinyi contributed all the new earnings to buy beans at Ksh 1175 per bag. The beans were then sold at Ksh 1762.50 per bag. The two shared all the money from the sale of beans in the ratio of their contributions. Calculate the amount that Akinyi got. 4 marks www.freekcsepastpapers.com 89 IMENTI SOUTH EXAMINATIONS, 2023 121 2 MATHEMATICS PAPER 2 TIME: 2 HRS SECTION I 50 marks Answer all the questions in this section 1. Make u the subject of the formula z w u2 v2 3 marks 2. Betty withdrew sh 84,528 from a financial institution which included both the principal and compound interest that had accrued within two and half years. If the compound interest rate was 18 per annum calculate the principal 3 marks 3.


Make u the subject of the formula z w u2 v2 3 marks 2. Betty withdrew sh 84,528 from a financial institution which included both the principal and compound interest that had accrued within two and half years. If the compound interest rate was 18 per annum calculate the principal 3 marks 3. Expand 1 3x 9 in ascending powers of x up to the term x4 and use your expansion to estimate 0.949 correct to three decimal places. 3 marks 4. Given that 1525 , 512 1 and Z and XY YZ, determine the values m, n, p, q and z. 4 marks 5. A quantity E is partly constant and partly varies as the square root of F. a Using constants k and c, write down an equation connecting E and F 1 mark b If F 25 when E 22 and F 49 when E 28, Find the values of k and C 2 marks 6. The base and height of a right angles triangle are 5.4cm and 3.5cm respectively. Calculate the relative error in the area of the triangle. 3 marks 7. Determine the quartile deviation for the following set of numbers 6, 10, 7, 6, 9, 8, 3, 2, 9, 8, 5, 4, 5 3 marks 8. In the figure below O is the centre of the circle. ABC and CD is a tangent to the circle at C. If angle CDB 24o, determine the size of BCD 3 marks ABDCO24o 9. Show that number 1. 5 23 consist of a whole number and a fraction. 2 marks 10. Solve the equation 4 2 5 4 sin for 0o 360o. 3 marks 11.


A In a geometrical progression the sum of the second and third and fourth term is -36. Find the first term and the common ratio. 4 marks b In an arithmetic progression the 12th term is 25 and the 7th term is three times the second term. Find i The first term and the common difference 4 marks ii The sum of the first 10 terms of the arithmetic progression 2 marks www.freekcsepastpapers.com 91 20. Triangle MNP on the grid below has vertices M 1, 4 , N 3, 1 and P 4, 3 a Draw triangle MINIPI the image of MNP under a negative quarter turn about the origin 2 marks b Triangle MINIPI is reflected on the line x y onto MIINIIPII . Draw triangle MIINIIPII . 2 marks c Triangle MIIINIIIPIII is the image of MIINIIPII under a rotation of 90o about the origin. Draw MIIINIIIPIII. 3 marks d A single transformation T maps MNP onto MIIINIIIPIII . Find matrix of transformation. 3 marks 21. In an agricultural research centre, 100 carrots were harvested a few months after application of a new type of fertilizer to a carrot garden. Their masses to the nearest gram were measured and recorded as shown below. Mass 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 95 - 99 100 - 104 105 - 109 110 - 114 115 - 119 Frequency 3 7 8 15 19 16 14 9 6 3 a State the modal class 1 mark b Calculate the mean mark 4 marks c Find the i Mean squared deviation 4 marks ii Standard deviation 1 mark www.freekcsepastpapers.com 92 22. The diagram below represents a pyramid standing on a rectangular base ABCO. V is the vertex of the pyramid and VA VB VC VD 26cm. M and N are the midpoints of BC and AC respectively. AB 24cm and BC 18cm.


V is the vertex of the pyramid and VA VB VC VD 26cm. M and N are the midpoints of BC and AC respectively. AB 24cm and BC 18cm. ABCODV24cm18cm Calculate a The length of line AC 2 marks b The length of projection of VA on the plane ABCD 1 mark c The angle between line VA and the plane ABCD 2 marks d The vertical height of the pyramid 2 marks e The size of the angle between the plane VBC and ABCD 3 marks 23. A Complete the table below for the functions y 3 sin 2x 30o and y cos 2x for x values in the range 0 x 180o. X 0 15 30 45 60 75 90 105 120 135 150 165 180 y 3 sin 2x 30o 1.5 3 1.5 -1.5 -2.60 -1.50 1.5 y cos 2x 1 0 -0.866 -0.866 -0.5 0.866 1 b Using the scale horizontal axis 1cm represent 15o vertical axis 1cm represent 1 unit, draw the graphs of y 3 sin 2x 30 and y cos 2x 6 marks c Use your graph to solve the equation 3 sin 2x 30 cos 2x 1 mark d Determine the following from your graph i Amplitude of y 3 sin 2x 30o 1 mark ii Period of y 3 sin 2x 30o 1 mark iii Period of y cos 2x 1 mark 24. Two inlet taps P and Q opened at the same time can fill a tank in 2 hours. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find; a The fractions of the tank filled by both taps for 1 hour.


Two inlet taps P and Q opened at the same time can fill a tank in 2 hours. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find; a The fractions of the tank filled by both taps for 1 hour. 1 mark b The fraction of the tank filled by tap P after Q was closed. 2 marks c The time which each tap working alone would have taken to fill the tank. 7 marks www.freekcsepastpapers.com70 MURANG A SOUTH PREMOCK EXAMINATION Kenya Certificate of Secondary Education, 2023 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS SECTION I 50 Marks Answer all the questions in this section 1. A man withdrew some money from a bank. He spent 310 of the money on his daughter s school fees and 35 of the remainder on his son s school fees. If he remained with Ksh 10 500, calculate the amount of money he spent on son s school fees. 3 marks 2. Solve for 3 marks 9 1 3 2 1 108 3. The volume of two similar solid spheres are 4752 cm3 and 1408 cm3. If the surface area of the smaller sphere is 352 cm2, find the surface area of the larger sphere. 3 marks 4. The figure below represents a sketch of the cross section of a solid ABCDEFGH and its edge CF. Complete the sketch of the solid showing the hidden edges using dotted lines. 3 marks 5. When a given length of a piece of wire is divided into pieces measuring 20 cm or 24 cm or 26 cm or 28 cm, a piece of wire 7cm always remained. Find the length of wire. 4 marks 6. Solve the equation 6 2 13 6 0 using the completing the square method. 3 marks 7.


4 marks 6. Solve the equation 6 2 13 6 0 using the completing the square method. 3 marks 7. Using a ruler and a pair of compasses only, construct a trapezium ABCD in which 5 , 6 , 10 , 105 and AB is parallel to DC. Draw a perpendicular from B to DC hence measure the height of the trapezium. 4 marks 8. Given that 2 where 34 and 164 Find column vector . 2 marks 9. Two friends Ojwang and David live 40 km apart. One day Ojwang left his house at 9.00 a.m. and cycled towards David s house at an average speed of 15 km h. David left his house at 10.30 a.m. on the same day and cycled towards Ojwang s house at an average speed of 25 km h. Determine; i. The time taken before the two friends met. 3 marks ii. The time they met. 1 mark 10. In the figure below, ABCD is a parallelogram in which AB 12 cm, BC 8 cm and angle ABC 108 . Calculate the area of the parallelogram correct to 3 significant figures. 3 marks 11. Without using mathematical tables or a calculator evaluate. 3 marks tan 30 tan 60 sin 60 cos 30 12. Given that 4523 and 231 1 , find 1 3 marks www.freekcsepastpapers.com71 13. Simplify completely; 5 2 5 23 2 75 2 3 marks 14. Use logarithms to evaluate.


Given that 4523 and 231 1 , find 1 3 marks www.freekcsepastpapers.com71 13. Simplify completely; 5 2 5 23 2 75 2 3 marks 14. Use logarithms to evaluate. 3 marks 39.51 6140.758 15. Dr. June needs to import a car from Japan that costs US dollars USD 5 000 outside Kenya. He intends to buy the car through an agent who deals in Japanese Yen JPY . The agent charges a 20 commission on the price of the car and a further 80 325 JPY for shipping the car to Kenya. Find the amount in Kenya shillings that Dr. June will need to send to the agent to get the car given that 1 USD Ksh. 120 and 1USD 135 JPY 3 marks 16. In a right angled triangle, the two sides enclosing the right angle measure 3 2 cm and 2 cm. If the area of the triangle is 17.5 2, find the length of these two sides. 3 marks SECTION II 50 Marks Answer any five questions only in this section 17. The diagram below shows a frustum which represents a bucket with an open end diameter of 30 cm and bottom diameter 24 cm. The bucket is 30cm deep. Use 3.142 a Calculate the capacity of the tank in litres. 5 marks b The bucket is used to fill an empty cylindrical tank of diameter 1.4m and height 1.2m. i. Calculate the capacity of the tank in litres. 3 marks ii. Determine the number of buckets that must be drawn in order to fill the tank. 2 marks 18. Three islands P, Q, R and S are on an ocean such that island Q is 400Km on a bearing of 030 from island P. Island R is 520 km and a bearing of 120 from island Q. A port S is sighted 750 km due South of island Q.


Three islands P, Q, R and S are on an ocean such that island Q is 400Km on a bearing of 030 from island P. Island R is 520 km and a bearing of 120 from island Q. A port S is sighted 750 km due South of island Q. a Taking a scale of 1cm to represent 100Km, give a scale drawing showing the relative positions of , , . 4 marks b Use the scale drawing to find the bearing of: i Island R from island P 1 mark ii Port S from island R 1 mark c Find the distance between island P and R 2 marks d A warship T is such that it is equidistant from the islands P, S and R. by construction locate the position of T. 2 marks 19. The vertices of a triangle ABC are A 1,1 , B 4,1 and C 6,4 a On the grid below, draw the triangles. I. ABC. 1 mark ii. ,. The image of triangle ABC under a negative quarter turn about the origin. 2 marks iii. ,. The image of triangle , under reflection in the line . 2 marks b Triangle , with vertices 1, 5 4, 5 6, 2 , is the image of , triangle , under a transformation T. i. Draw the triangle , 1 mark ii. Describe fully the transformation T. 2 marks www.freekcsepastpapers.com72 c State any pair of triangles which are: i. Directly congruent. 1 mark ii.


The diagram below represents a cuboid PQRSTUVW in which UV 4.5cm, VW 8cm and WR 6cm Calculate the size of the angle between the lines UR and UW 3 marks 13. Given that , , and O is the origin, determine the coordinates of P if . 3 marks 14. Bag contains 14 beads of which are red and the remainder blue .When 4 Red beads are removed ,the probability of selecting a red bead is 25 .Find the value of 3 marks 15. Calculate the area of the unshaded region given that AC is an arc of a circle centre B. Given that AB BC 14cm, CD 8cm and angle 75 3 marks 16. If 2.3, 8.7 2.2, find the percentage error in 4 marks SECTION B 50 Marks 17. The mass, m, grams of a cylinder varies jointly as the square of its radius, r, and its height, h. a Find the percentage change in the mass if the radius is tripled and the height is halved. 3 marks b Given that 990 when 3 and 7 ; i. Find the equation connecting m, r and h. 3 marks ii. Calculate the value of m when r 3.5cm and h 5cm. 2 marks c Taking 227 calculate the density of the cylinder 2 marks 18. The table below shows the distribution of marks scored by 60 students in a test.


Calculate the value of m when r 3.5cm and h 5cm. 2 marks c Taking 227 calculate the density of the cylinder 2 marks 18. The table below shows the distribution of marks scored by 60 students in a test. Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 Frequency 2 5 6 10 14 11 9 3 a On the grid provided draw a cumulative frequency curve of the data. 3 marks Take 1cm to represent 5 students on the vertical scale and 1 cm to represent 10 marks on the horizontal scale . B From the curve in a above i. Estimate the median mark 1 mark ii. Determine the quartile deviation. 2 marks iii. Determine the 10th and 90th percentile range. 2 marks c It is given that students who score over 45 marks pass the test. Use your graph in a above to estimate the percentage of students that pass. 2 marks PQRSTWVU4.5cm8cm6cmwww.freekcsepastpapers.com75 19. Seats in the theatre area arranged in rows. The number of seats in this theatre form the terms of an arithmetic series. The sixth row has 23 seats and the fifteenth row has 50 seats. The theatre has 20 rows in total. Find: i. The number of seats in the first row. 4 marks ii. The number of seats in the eleventh row. 2 marks iii. The number of seats in this theatre. 4 marks 20. The figure below represents a model of a solid structure in the shape of a frustum of a cone with a hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 30 cm and slant height of 60 cm use 3.142 Calculate a The area of the hemispherical surface. 2 marks b The slant height of cone from which the frustum was cut. 2 marks c The surface area of the frustum.


The frustum has a base diameter of 30 cm and slant height of 60 cm use 3.142 Calculate a The area of the hemispherical surface. 2 marks b The slant height of cone from which the frustum was cut. 2 marks c The surface area of the frustum. 2 marks d The area of the base 2 marks e The total surface area of the model. 2 marks 21. The table below shows income tax rates in a certain year. Taxable Income Ksh per month Tax Rate 0 13 450 10 13 451 26 350 15 26 351 39 250 20 39 251 52 150 25 52 151 30 In that year, the monthly earnings for Amilo were as follows: basic salary Ksh 35 500, House allowance Ksh 12 600 and other allowances that amount to Ksh. 5 872 were exempted from taxation. Amilo contributes 12.5 of her basic salary to a pension scheme. She is entitled to a personal tax relief of Ksh 1 845 per month. Calculate:www.freekcsepastpapers.com76 a Amilo s taxable income in Ksh per month. 2 marks b Amilo s P.A.Y.E that month. 5 marks c Amilo s net pay that month, given that the following are deducted monthly from her salary; 3 marks NHIF Ksh 1000, Union dues Kshs 455 BBF Ksh 200. 22. Machine K makes 45 of the biscuits. Machine J makes 30 of the biscuits. The rest of the biscuits are made by machine L. It is known that 2 of the biscuits made by machine J are broken, 3 of the biscuits made by machine K are broken and 5 of the biscuits made by machine L are broken. A biscuit is selected at random. A. Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. 2 marks b. Using the tree diagram, calculate the probability that the biscuit is: i.


Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. 2 marks b. Using the tree diagram, calculate the probability that the biscuit is: i. Made by machine J and is not broken. 3 marks ii. Broken. 3 marks iii. Broken but not made by machine K. 2 marks 23. The diagram below shows a circle center O. BF is a tangent to the circle at B. Angle 200 and angle FBD 500 Giving reasons in each case, find; a Angle AEC 2 marks b Angle CAB 2 marks c Angle ADB 2 marks d Angle BCD 2 marks e Angle AOB reflex 2 marks 24. The figure below shows two circles centres A and B and radii 6 cm and 8 cm respectively. The circles intersect at P and Q. Angle PAB 420 and angle ABQ 300. A Find the size of angle PAQ and angle PBQ. 2 marks b Calculate, to one decimal place the area of: i. Sector APQ and PBQ. 2 marks ii. Triangle APQ and PBQ. 2 marks iii. The shaded area Take 227 4 marks 42 30 B 8cm 6cm Q A Pwww.freekcsepastpapers.com70 MURANG A SOUTH PREMOCK EXAMINATION Kenya Certificate of Secondary Education, 2023 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS SECTION I 50 Marks Answer all the questions in this section 1. A man withdrew some money from a bank. He spent 310 of the money on his daughter s school fees and 35 of the remainder on his son s school fees. If he remained with Ksh 10 500, calculate the amount of money he spent on son s school fees. 3 marks 2. Solve for 3 marks 9 1 3 2 1 108 3. The volume of two similar solid spheres are 4752 cm3 and 1408 cm3.


3 marks 2. Solve for 3 marks 9 1 3 2 1 108 3. The volume of two similar solid spheres are 4752 cm3 and 1408 cm3. If the surface area of the smaller sphere is 352 cm2, find the surface area of the larger sphere. 3 marks 4. The figure below represents a sketch of the cross section of a solid ABCDEFGH and its edge CF. Complete the sketch of the solid showing the hidden edges using dotted lines. 3 marks 5. When a given length of a piece of wire is divided into pieces measuring 20 cm or 24 cm or 26 cm or 28 cm, a piece of wire 7cm always remained. Find the length of wire. 4 marks 6. Solve the equation 6 2 13 6 0 using the completing the square method. 3 marks 7. Using a ruler and a pair of compasses only, construct a trapezium ABCD in which 5 , 6 , 10 , 105 and AB is parallel to DC. Draw a perpendicular from B to DC hence measure the height of the trapezium. 4 marks 8. Given that 2 where 34 and 164 Find column vector . 2 marks 9. Two friends Ojwang and David live 40 km apart. One day Ojwang left his house at 9.00 a.m. and cycled towards David s house at an average speed of 15 km h. David left his house at 10.30 a.m. on the same day and cycled towards Ojwang s house at an average speed of 25 km h. Determine; i. The time taken before the two friends met. 3 marks ii. The time they met. 1 mark 10.


3 marks ii. The time they met. 1 mark 10. In the figure below, ABCD is a parallelogram in which AB 12 cm, BC 8 cm and angle ABC 108 . Calculate the area of the parallelogram correct to 3 significant figures. 3 marks 11. Without using mathematical tables or a calculator evaluate. 3 marks tan 30 tan 60 sin 60 cos 30 12. Given that 4523 and 231 1 , find 1 3 marks www.freekcsepastpapers.com71 13. Simplify completely; 5 2 5 23 2 75 2 3 marks 14. Use logarithms to evaluate. 3 marks 39.51 6140.758 15. Dr. June needs to import a car from Japan that costs US dollars USD 5 000 outside Kenya. He intends to buy the car through an agent who deals in Japanese Yen JPY . The agent charges a 20 commission on the price of the car and a further 80 325 JPY for shipping the car to Kenya. Find the amount in Kenya shillings that Dr. June will need to send to the agent to get the car given that 1 USD Ksh. 120 and 1USD 135 JPY 3 marks 16. In a right angled triangle, the two sides enclosing the right angle measure 3 2 cm and 2 cm. If the area of the triangle is 17.5 2, find the length of these two sides. 3 marks SECTION II 50 Marks Answer any five questions only in this section 17. The diagram below shows a frustum which represents a bucket with an open end diameter of 30 cm and bottom diameter 24 cm. The bucket is 30cm deep. Use 3.142 a Calculate the capacity of the tank in litres.


The diagram below shows a frustum which represents a bucket with an open end diameter of 30 cm and bottom diameter 24 cm. The bucket is 30cm deep. Use 3.142 a Calculate the capacity of the tank in litres. 5 marks b The bucket is used to fill an empty cylindrical tank of diameter 1.4m and height 1.2m. i. Calculate the capacity of the tank in litres. 3 marks ii. Determine the number of buckets that must be drawn in order to fill the tank. 2 marks 18. Three islands P, Q, R and S are on an ocean such that island Q is 400Km on a bearing of 030 from island P. Island R is 520 km and a bearing of 120 from island Q. A port S is sighted 750 km due South of island Q. a Taking a scale of 1cm to represent 100Km, give a scale drawing showing the relative positions of , , . 4 marks b Use the scale drawing to find the bearing of: i Island R from island P 1 mark ii Port S from island R 1 mark c Find the distance between island P and R 2 marks d A warship T is such that it is equidistant from the islands P, S and R. by construction locate the position of T. 2 marks 19. The vertices of a triangle ABC are A 1,1 , B 4,1 and C 6,4 a On the grid below, draw the triangles. I. ABC. 1 mark ii. ,. The image of triangle ABC under a negative quarter turn about the origin. 2 marks iii. ,. The image of triangle , under reflection in the line .


, the image of triangle ABC under a negative quarter turn about the origin. 2 marks iii. ,. The image of triangle , under reflection in the line . 2 marks b Triangle , with vertices 1, 5 4, 5 6, 2 , is the image of , triangle , under a transformation T. i. Draw the triangle , 1 mark ii. Describe fully the transformation T. 2 marks www.freekcsepastpapers.com72 c State any pair of triangles which are: i. Directly congruent. 1 mark ii. Oppositely congruent. 1 mark 20. The figure below shows a triangle inside a circle. 8 , 10 and 13 Calculate a The area of triangle ABC. 3 marks b Angle BAC 2 marks c The radius of the circle. 2 marks d Area of the shaded region. 3 marks 21.


Given the function 2 cos 30 for 0 540 , state: i. The period 1 mark ii. The phase angle 1 mark 11. Determine the interquartile range for the following set of numbers 2 marks 10,15,14,17,12,13www.freekcsepastpapers.com74 12. The diagram below represents a cuboid PQRSTUVW in which UV 4.5cm, VW 8cm and WR 6cm Calculate the size of the angle between the lines UR and UW 3 marks 13. Given that , , and O is the origin, determine the coordinates of P if . 3 marks 14. Bag contains 14 beads of which are red and the remainder blue .When 4 Red beads are removed ,the probability of selecting a red bead is 25 .Find the value of 3 marks 15. Calculate the area of the unshaded region given that AC is an arc of a circle centre B. Given that AB BC 14cm, CD 8cm and angle 75 3 marks 16. If 2.3, 8.7 2.2, find the percentage error in 4 marks SECTION B 50 Marks 17. The mass, m, grams of a cylinder varies jointly as the square of its radius, r, and its height, h. a Find the percentage change in the mass if the radius is tripled and the height is halved.


If 2.3, 8.7 2.2, find the percentage error in 4 marks SECTION B 50 Marks 17. The mass, m, grams of a cylinder varies jointly as the square of its radius, r, and its height, h. a Find the percentage change in the mass if the radius is tripled and the height is halved. 3 marks b Given that 990 when 3 and 7 ; i. Find the equation connecting m, r and h. 3 marks ii. Calculate the value of m when r 3.5cm and h 5cm. 2 marks c Taking 227 calculate the density of the cylinder 2 marks 18. The table below shows the distribution of marks scored by 60 students in a test. Marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 Frequency 2 5 6 10 14 11 9 3 a On the grid provided draw a cumulative frequency curve of the data. 3 marks Take 1cm to represent 5 students on the vertical scale and 1 cm to represent 10 marks on the horizontal scale . B From the curve in a above i. Estimate the median mark 1 mark ii. Determine the quartile deviation. 2 marks iii. Determine the 10th and 90th percentile range. 2 marks c It is given that students who score over 45 marks pass the test. Use your graph in a above to estimate the percentage of students that pass. 2 marks PQRSTWVU4.5cm8cm6cmwww.freekcsepastpapers.com75 19. Seats in the theatre area arranged in rows. The number of seats in this theatre form the terms of an arithmetic series. The sixth row has 23 seats and the fifteenth row has 50 seats. The theatre has 20 rows in total. Find: i. The number of seats in the first row.


The theatre has 20 rows in total. Find: i. The number of seats in the first row. 4 marks ii. The number of seats in the eleventh row. 2 marks iii. The number of seats in this theatre. 4 marks 20. The figure below represents a model of a solid structure in the shape of a frustum of a cone with a hemispherical top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 30 cm and slant height of 60 cm use 3.142 Calculate a The area of the hemispherical surface. 2 marks b The slant height of cone from which the frustum was cut. 2 marks c The surface area of the frustum. 2 marks d The area of the base 2 marks e The total surface area of the model. 2 marks 21. The table below shows income tax rates in a certain year. Taxable Income Ksh per month Tax Rate 0 13 450 10 13 451 26 350 15 26 351 39 250 20 39 251 52 150 25 52 151 30 In that year, the monthly earnings for Amilo were as follows: basic salary Ksh 35 500, House allowance Ksh 12 600 and other allowances that amount to Ksh. 5 872 were exempted from taxation. Amilo contributes 12.5 of her basic salary to a pension scheme. She is entitled to a personal tax relief of Ksh 1 845 per month. Calculate:www.freekcsepastpapers.com76 a Amilo s taxable income in Ksh per month. 2 marks b Amilo s P.A.Y.E that month. 5 marks c Amilo s net pay that month, given that the following are deducted monthly from her salary; 3 marks NHIF Ksh 1000, Union dues Kshs 455 BBF Ksh 200. 22. Machine K makes 45 of the biscuits.


5 marks c Amilo s net pay that month, given that the following are deducted monthly from her salary; 3 marks NHIF Ksh 1000, Union dues Kshs 455 BBF Ksh 200. 22. Machine K makes 45 of the biscuits. Machine J makes 30 of the biscuits. The rest of the biscuits are made by machine L. It is known that 2 of the biscuits made by machine J are broken, 3 of the biscuits made by machine K are broken and 5 of the biscuits made by machine L are broken. A biscuit is selected at random. A. Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. 2 marks b. Using the tree diagram, calculate the probability that the biscuit is: i. Made by machine J and is not broken. 3 marks ii. Broken. 3 marks iii. Broken but not made by machine K. 2 marks 23. The diagram below shows a circle center O. BF is a tangent to the circle at B. Angle 200 and angle FBD 500 Giving reasons in each case, find; a Angle AEC 2 marks b Angle CAB 2 marks c Angle ADB 2 marks d Angle BCD 2 marks e Angle AOB reflex 2 marks 24. The figure below shows two circles centres A and B and radii 6 cm and 8 cm respectively. The circles intersect at P and Q. Angle PAB 420 and angle ABQ 300. A Find the size of angle PAQ and angle PBQ. 2 marks b Calculate, to one decimal place the area of: i. Sector APQ and PBQ. 2 marks ii. Triangle APQ and PBQ. 2 marks iii. The shaded area Take 227 4 marks 42 30 B 8cm 6cm Q A Pwww.freekcsepastpapers.com54 12. Use reciprocal, square and square root tables to evaluate, to 4 significant figures, the expression.2346.456.241 3 mks 13. Two similar cans have different heights 8cm and the other one 10cm.


After 20 minutes the matatu had a puncture which took 30 minutes to mend. It then continued with the journey. A How far from Nairobi did the matatu catch up with the bus? 6mks b At what time did the matatu catch up with the bus 2mks c At what time did the bus reach Moi s Bridge? 2mks A -2, -1 B 4, 7 Y X 2x 3y 6 0 A O B Cwww.freekcsepastpapers.com56 23. Wanjiku is standing at a point P, 160m south of a hill H on a level ground. From point P she observes the angle of elevation of the top of the hill to be 670 a Calculate the height of the hill 3 mks b After walking 420m due east to the point Q, Wanjiku proceeds to point R due east of Q, where the angle of elevation of the top of the hill is 350. Calculate the angle of elevation of the top of the hill from Q 3 mks c Calculate the distance from P to R 4 mks 24. A Find the inverse of the matrix. 2 mks 2543 b A transport company has two types of vehicles for hire: Lorries and buses. The vehicles are hired per day. The cost of hiring two lorries and five buses is Sh. 156,000 and that of hiring 4 lorries and three buses is Sh. 137,000. I Form two equations to represent the above information. 2 mks ii Use matrix method to determine the cost of hiring a lorry and that of hiring a bus. 3 mks c Find the value of x given that 2 11 21 is a singular matrix 3 mks www.freekcsepastpapers.com57 GATUNDU SOUTH EXAMINATIONS, 2023 KENYA CERTIFICATE OF SECONDARY EDUCATION 121 2 MATHEMATICS PAPER 2 TIME: 2 HOURS SECTION A 50 MARKS 1. Evaluate using reciprocals, square and square root tables only. 07245.01101. 3mks 2.


3mks 10. Make b the subject of the formula. 3mks a bd b2 d 11. A Using binomial expansion, determine the first five terms of the expansion: x 2mks b Use the expansion above to evaluate 875.1 2mks 12. A globe representing the earth has a radius of 0.2m. Points P 600N, 1400E and Q 600N, 1200W are marked on the globe. If O is the centre of the latitude 600N, find the area of the minor sector OPQ 3 mks 13. Show that 4y2 4x2 12x 12y 7 is the equation of a circle, hence find the co-ordinates of the centre and the radius. 3mks 14. A quantity V is partly constant and partly varies as U. If U 1 when V 12 and U 3 when r 22. Find the V when U 5. 3 marks 15. The surface area of two similar bottles are 12cm and 108cm respectively. If the larger one has a volume of 810cm . Find the volume of the smaller one 2mks 16. A two-digit number is formed from the first four prime numbers. A Draw the table to show the possible outcomes, if each number can be used only once. 1mk b Calculate the probability that a number chosen from the digit numbers is an even number 2mks www.freekcsepastpapers.com58 SECTION II 50 marks Answer only five questions from this section. 17. John bought 3 brands of tea A, B and C. The cost price of the three brands were Sh. 25, Sh. 30 and Sh. 45 per kilogram respectively. He mixed the three brands in the ratio 5:2:1 respectively. After selling the mixture he made a profit of 20 . A How much profit did he make per kilogram of the mixture? 4 marks b After one year the cost price of each brand was increased by 12 . I For how much did he sell one kilogram of the mixture to make 20 profit?


A How much profit did he make per kilogram of the mixture? 4 marks b After one year the cost price of each brand was increased by 12 . I For how much did he sell one kilogram of the mixture to make 20 profit? Give your answer to the nearest 5cts 3 marks ii What would have been his percentage profit if he sold one kilogram of the mixture at Sh. 40.25? 3mks 18. A Fill in the table below for the function y -6 x 4x2 x3 for -4 x 2 2mks x -4 -3 -2 -1 0 1 2 -6 -6 -6 -6 -6 -6 -6 -6 x -4 -3 -2 -1 0 1 2 4x2 16 4 x3 y b Using the grid provided draw the graph for y -6 x 4x2 x3 for -4 x 2 3mks c i Use the graph to solve the equations: - i x3 4x2 x 4 0 2mks ii -6 x 4x2 x3 0 1mk iii -2 4x2 x3 0 2mk 19. On the grid provided, draw triangle PQR with P 2,3 , Q 1,2 and R 4,1 . On the same axes draw triangle P11Q11R11 with vertices P11 -2,3 , Q11 -1,2 and R11 -4,1 . 2mks a Describe fully a single transformation which will map triangle PQR onto triangle P11Q11R11. 1mk b On the same plane, draw triangle P1Q1R1 the image of triangle PQR under reflection in the line y -x. 2mks c Describe fully a single transformation which maps triangle P1Q1R1 onto triangle P11Q11R11.


2mks a Describe fully a single transformation which will map triangle PQR onto triangle P11Q11R11. 1mk b On the same plane, draw triangle P1Q1R1 the image of triangle PQR under reflection in the line y -x. 2mks c Describe fully a single transformation which maps triangle P1Q1R1 onto triangle P11Q11R11. 2mks d Draw triangle P111Q111R111 such that it can be mapped onto triangle PQR by a position quarter about 0,0 2mks e State all pairs of triangles that are oppositely congruent. 1mk 20. 40 form four students sat for a mathematics test and their marks were distributed as follows: Marks 1 10 11- 20 21- 30 31 40 41 50 51 60 61 70 71 80 81 90 91 - 100 No. Of students 1 3 4 7 12 9 2 1 0 1 a Using 45.6 as the working mean, calculate; i The actual mean. 4mks ii The standard deviation. 3mks b When ranked from first to last, what mark was scored by the 30th student? Give your answer correct to 3 s.f. 3mks 21. Use ruler and a pair of compasses only in this question. A Construct triangle ABC in which AB 7 cm, BC 8 cm and ABC 600. 3mks b Measure i side AC ii ACB 2mks c Construct a circle passing through the three points A, B and C. Measure the radius of the circle. 2mks d Construct PBC such that P is on the same side of BC as point A and PCB ACB, BPC BAC measure PBC.


3mks b Measure i side AC ii ACB 2mks c Construct a circle passing through the three points A, B and C. Measure the radius of the circle. 2mks d Construct PBC such that P is on the same side of BC as point A and PCB ACB, BPC BAC measure PBC. 3mkswww.freekcsepastpapers.com59 22.The figure below is a pyramid of a rectangular base PQRS of length 12cm and width 9cm. The slanting edge has a length of 19.5cm a Determine the height of the pyramid2mks b The angle PO makes with base PQRS3mks c The angle POS makes with QOR3mks d The volume of the pyramid2mks 23.A company produces shirts and jerseys using two types of machines. Every shirt made requires 2 hours onmachine A and 2 hours on machine B. Every Jersey made requires 3 hours on machine A and I hour on machine B. In one day, the time limit on machine A is 24hours but that on machine B is 12hrs. The numberof Jerseys produced must not be more than the shirts produced in one day. The company makes a profit ofshs.200 on each shirt and shs.200 on each Jersey.


In one day, the time limit on machine A is 24hours but that on machine B is 12hrs. The numberof Jerseys produced must not be more than the shirts produced in one day. The company makes a profit ofshs.200 on each shirt and shs.200 on each Jersey. The company produces x shirts and y jerseys per day a Write down four inequalities which must be satisfied by x and y 4mks b Represent these inequalities on a grid 4mks c Find the values of x and y which will give the company maximum daily profit and also state themaximum profit2mks24.A particle P moves in a straight line so that its velocity, Vm s at time t seconds where t 0 is given byv 28 t 2t2Find; a the time when P is instantaneously at rest2mks b the speed of P at the instant when the acceleration of P is zero2mks c Find the acceleration of P when the article is instantaneously at rest3mks d Find the distance covered by the particle during the 3rd second, when at t 0 D 5M3mks O R Q S P 19.5cm 9cm 12cmwww.freekcsepastpapers.com53 GATUNDU SOUTH EXAMINATIONS, 2023 KENYA CERTIFICATE OF SECONDARY EDUCATION 121 1 MATHEMATICS PAPER 1 TIME: 2 HOURS SECTION 1 Answer all the questions 50 marks 1. Evaluate -12 -3 x 4 -15 3 marks -5 x 6 2 -5 2. Simplify 2yxxxyy 3mks 3. A watch which loses a half-minute every hour was set to read the correct time at 0445h on Monday. Determine the time in 12-hour system, the watch will show on the following Friday at 1845h 3mks 4. Three angles of a polygon are 125,140 and 160. The remaining angles are 1450 each. Calculate the sum of the interior angles of the polygon. 3 mks 5.


The remaining angles are 1450 each. Calculate the sum of the interior angles of the polygon. 3 mks 5. Find the integral values of the inequalities x 2x 7 - 1 3x 14 hence represent the solution on a number line. 3mks 6. Evaluate without using a calculator. 3mks 31of 7. Find the value of y in the equation. 4mks 12 2 yyy 8. The position vectors of A and B are given as a 2i 3j 4k and b -2i j 2k respectively. Find to 2 decimal places, the length of vector AB. 3 Marks 9. Foreign exchange on 27 5 2010 was given as follows: Currency Buying Kshs Selling Kshs 1 Euro 84.15 84.26 1 Sterling pound 118.35 121.47 A tourist came to Kenya from London with 6000 Euros which he converted to Kenya shillings at a bank. While in Kenya he spent a total of Kshs.300,000 then converted the balance into sterling pounds at the Same bank. Calculate the amount in sterling pounds he received. 3 mks 10. Use ruler and a pair of compasses only in this question. A Construct triangle ABC in which AB 7 cm, BC 8 cm and ABC 600. 2 mks b Measure side AC 1 mk 11. In the figure below ABCD is a trapezium with DC parallel to AB.


4marks b The angles of elevation of the top of a tree from P and Q which are 30m apart are 220 and 320 respectively. Given that the two points are on the same side of the tree and on a straight line, determine the height of the tree. 6marks 19. Two security personnel were together at a road junction. Each had a walkie talkie. The maximum distance at which one could communicate with the other was 2.5km. One of the personnel walked due East at 3.2km h while the other walked due North at 2.4km h. The personnel who headed east travelled for x km while the one who headed North travelled for y km before they were unable to communicate. A Draw a sketch to represent the relative positions of the policemen. 1 mark b i From the information above form two simultaneous equations in form of x and y. 2 marks www.freekcsepastpapers.com37 ii Find the value of x and y. 5 marks iii Calculate the time in minutes taken before the security personnel were unable to communicate. 2 marks 20. ABCD is a rectangle with A as the point -3,1 . A If AB is parallel to the line3 4, find the equation of line AB. 2 marks b Find the equation of line AD. 2marks d If C has coordinates 2,6 , find the equations of the line BC and CD in the form 1 4marks e Find the coordinates of B 2marks 21. The figure below shows a rectangular sheet of metal whose length is twice its width. An open rectangular tank is made by cutting equal squares of length 60 cm from each of its four corners and folding along the dotted lines shown in the figure above. Given that the capacity of the tank so formed is 1920 litres and the width of the metal sheet used was x cm; a i Express the volume of the tank formed in terms of x cm. 3 marks ii Hence or otherwise obtain the length and width of the sheet of metal that was used.


An open rectangular tank is made by cutting equal squares of length 60 cm from each of its four corners and folding along the dotted lines shown in the figure above. Given that the capacity of the tank so formed is 1920 litres and the width of the metal sheet used was x cm; a i Express the volume of the tank formed in terms of x cm. 3 marks ii Hence or otherwise obtain the length and width of the sheet of metal that was used. 3 marks b If the cost of the metal sheet per m2 is Kshs 1000 and labour cost for making the tank is 300 per hour. Find the selling price of the tank in order to make a 30 profit if it took 6 hours to make the tank. 4 marks 22. A The ratio of Juma s and Akinyi s earnings was 5: 3. Juma s earnings rose to Ksh 8 400 after an increase of 12 . Calculate the percentage increase in Akinyi s earnings given that the sum of their earnings was Ksh. 14 100 6 marks b Juma and Akinyi contributed all the new earnings to buy maize at Ksh 1 175 per bag. The maize was then sold at ksh 1 762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got. 4 marks 23. A Given that A 3423 find inverse of A 1mark b Two colleges, Utalii and Huduma purchased beans and rice . Utalii bought 90 bags of beans and 120 bags of rice for a total of sh 360 000 . Huduma bought 200 bags of beans and 300 bags of rice for a total of sh 850 000. Use the inverse of A obtained in a above to find the price of one bag of each item. 6marks c The price of beans later decreased in the ratio 4: 5 while that of rice increased by 20 . A businessman bought 20 bags of beans and 30 bags 0f rice. How much did he pay? 3marks 24. The figure below shows a model of a solid in the shape of a frustum of a cone with a hemispherical top.


How much did he pay? 3marks 24. The figure below shows a model of a solid in the shape of a frustum of a cone with a hemispherical top. The diameter of the hemispherical top is 70cm and is equal to the diameter of the top of the frustum. The frustum has a base diameter of 28cm and a slant height of 60cm. A Calculate the area of the hemispherical surface. 1mark b Calculate the slant height of the cone from which the frustum was cut. 4marks c Calculate the total surface area of the model. 5 marks 60cm 28cm 70cmwww.freekcsepastpapers.com38 MECS I JOINT EXAMINATION TERM 1 2023 121 2 MATHEMATICS PAPER 2 TIME: 2 HOURS 30 MINUTES Section I 50 Marks Answer ALL questions in this section. 1. Solve for x log3 2 12 log3 32 4 2. In the figure below PT is a tangent to the circle from an external point P. 24 and 25 . Calculate the area of the shaded region correct to 2 decimal places 4 3. Find the value of in the expression 2 32 116 is a perfect square , given that is a constant 2 4. Simplify 3 marks 5. The cost C of hiring a conference facility for one day consists of two parts, one which is fixed and the other varies as the number of participants attending the conference. If Kshs 45000 is charged for hiring the facility for 100 participants and Kshs 40000 for 60 participants, Find the number of participants if 63000 is used to hire the facility. 3 6.


Wambui bought it on hire purchase by making a deposit of kshs. 10000 followed by 24 monthly instalments of kshs 2000 each. Calculate the monthly rate at which compund interest was charged 3 11. A merchant blends 350kg of KAKUZI tea costing shs. 84 per kg with 140 kg of KETEPA tea costing sh.105 per kg. Calculate the price at which he must sell 1kg of the mixture to attain 20 profit. 3 12. The graph below is part of the straight line graph obtained from the initial equation Write down the equation of a straight line in the form of hence use the graph to find the of and 3 www.freekcsepastpapers.com39 13. State the amplitude, period and phase angle of 2 sin 12 300 i Amplitude 1 mark ii Period 1 mark iii Phase angle 1 mark 14. 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 15. The table below shows income tax rates in a certain year.


In a bookstore, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, 46 cartons in next and so on. A How many cartons will be there in 8th row? 2 marks b If there are 20 rows in total, find the total number of cartons in the books store. 2 marks 11. Find the value of x if. 3 marks x3 12. The mean ages of a group of ten boys in a Math s club is 15. The ages of nine of the boys are 14, 15, 14, 16, 17, 14, 16, 15 and 13. What is the age of the remaining boy? 3 marks 13. The figure below is a velocity time graph for a car. A Find the total distance travelled by the car 2 marks b Calculate the deceleration of the car. 1 marks 80m s Time inwww.freekcsepastpapers.com22 14. Security light poles have been erected along both sides of a street in Bahati town. The poles are 50m apart along the left-hand side of the road while they are 80m apart along the right-hand side. At one end of the road the poles are directly opposite each other. How many poles will be erected by time the poles are directly opposite each other at end of the road? 3 marks 15. The exterior angle of a regular polygon is equal to one third of the interior angle. Calculate the number of sides of the polygon. 3 marks 16. Write down the inequalities that define the unshaded region marked R in the figure, below. 3 marks Section II. Choose any five questions from this section 17. Nakuru county government is to construct a floor of an open wholesale market whose area is 800m2. The floor is to be covered with a slab of uniform thickness of 200mm. In order to make the slab, sand, cement and ballast are to be mixed such that their masses are in the ratio 3:2:3 respectively.


Nakuru county government is to construct a floor of an open wholesale market whose area is 800m2. The floor is to be covered with a slab of uniform thickness of 200mm. In order to make the slab, sand, cement and ballast are to be mixed such that their masses are in the ratio 3:2:3 respectively. The mass of dry slab of volume 1m3 is 2000kg. A Calculate i The volume of the slab. 2 marks ii The mass of the dry slab. 2 marks iii The mass of cement to be used. 2 marks b If one bag of cement is 50kg, find the number of bags to be purchased. 1 mark c If a lorry carries 10 tonnes of ballast, calculate the number of Lories of ballast to be purchased. 3 marks 18. Paul is a sale executive earning sh 20,000 and a commission of 8 for the sales in excess of 100,000. In January 2014 he earned a total of 48000 in salaries and commissions. A Determine the amount of sales he made in that month. 4 marks b If the total sales in the month of February and March increased by 18 and then dropped by 25 respectively. Calculate. I Paul s commission in the month of February. 3 marks ii His total earnings in the month of March. 3 marks 19. Two tanks are similar in shape. The capacity of the tanks are 1,000,000 litres and 512,000 litres respectively. A Find the height of the smaller tank if the larger one is 300cm tall. 5 marks b Calculate the surface area of the tank if the smaller one has a surface area of 768cm2 3 marks c Calculate the mass of the larger tank if the mass of the smaller one is 800kg. 2 marks 20. The equation of a curve is given by y x3 - x2 - 8x 3 a Find the value of y when x 1. 1 mark b Determine the stationary points of the curve.


2 marks 20. The equation of a curve is given by y x3 - x2 - 8x 3 a Find the value of y when x 1. 1 mark b Determine the stationary points of the curve. 5 marks c Find the equation of the normal to the curve at x 1 in the form ax by c 4 marks L1 L3 L2www.freekcsepastpapers.com23 21. Peter owns a farm that is triangular in shape as shown below a Calculate the size of angle BAC. 2 marks b Find the area of the farm in hectares. 3 marks c Peter wishes to irrigate his farm using a sprinkler machine in the farm such that it is equidistant from points A. B and C. The sprinkler rotates in a circular motion so that the maximum point reached by the water jets is the vertices A, B and C. Calculate the area outside the farm that will be irrigated. 5 marks 22. Transline bus left Nairobi at 8.00 am and travelled to Nakuru at an average speed of 80km h. A car left Nakuru at 3.30 am and travelled to Nairobi at an average speed of 120km h. Given that the distance between Nairobi and Nakuru is 400km, calculate: a The time the car arrived in Nairobi. 3 marks b The time the two vehicles met. 4 marks c The distance from Nairobi to the meeting point. 2 marks d The distance of the bus from Nakuru when the car arrived in Nairobi. 2 marks 23. Town B is 102km on the bearing of 1220 from town A. Town C is 94 km on bearing of N620 E from B. Town D is on a bearing of 0730 from A and N240W from C. a Using a scale of 1cm to represent 20km, draw a scale diagram to show the relative positions of town A, B, C and D. 4 marks b Using your diagram, determine. I The bearing B from D. 1 mark ii The bearing of A from C. 1 mark iii The distance from town A to D.


I The bearing B from D. 1 mark ii The bearing of A from C. 1 mark iii The distance from town A to D. 2 marks iv The distance from town B and D. 2 marks 24. The table below gives some of the values of x and y for the functions y x2 22x 1 in the interval 0 x 6. A Complete the values in the table above. 1 mark b Use the values in the table to draw the graph of function on the grid provided below. 2 marks c Using the graph and the mid-ordinate rule with 6 strips, estimate the area bounded by the curve, the x-axis, the y-axis and the line x 6. 3 marks d Using integration, calculate the exact area and hence find the percentage error made when mid-ordinate rule is used. Give your answer correct to 2.dp. 4 marks x 0 1 2 3 4 5 6 y 1 23.5 250 M 320 M 440 M A B Cwww.freekcsepastpapers.com24 EASTERN CLUSTER, 2023 Kenya Certificate of Secondary Education 121 2 MATHEMATICS PAPER 2 TIME: 2 HOURS SECTION I 50 MARKS Answer ALL questions in this section 1. Use logarithms to evaluate .04666.02347 x 4mks 2. In 100m race there are three main competitors namely Simiyu, Ondiek and Kamau. Simiyu is three times likely to win as Ondiek, while Ondiek is twice as likely to win as Kamau. Find the probability that i Ondiek wins the race. 2 marks ii Either Simiyu or Kamau. 1mark 3. A Find the expansion in ascending powers of x of xup to the term in x2 . 1mark b Hence evaluate 0.99 7 to four significant figures. 2marks 4. Given that Tan, hence determine Tan 150 leaving your answer in the form cba 3marks 5.


1mark b Hence evaluate 0.99 7 to four significant figures. 2marks 4. Given that Tan, hence determine Tan 150 leaving your answer in the form cba 3marks 5. PQR is an equilateral triangle of sides 3cm. S is a variable point on the same side of PQ as R and on the same plane such that PSQ 300. Locate by construction the possible location of S use a ruler and a pair of compasses only . 3marks 6. The overall grade A attained by a student is directly proportional to the teacher s effort t , square of student s effort s and the general discipline level d of the school. A student doubled his effort; teacher went further by 5 but the school discipline dropped by 40 . Find the percentage change in the overall grade. 3marks 7. A circle of radius 7 units has it s Centre at the point of intersection between the lines x 2y 1 0 and 2x 3y 3 0. Find the equation of the circle expressing it in the form x2 y2 gx fy c 0. 4marks 8. Kitheka deposited ksh.50,000 in a financial institution in which interest is compounded quarterly. If at the end of second year he received a total amount of ksh79,692.40. Calculate the rate of interest p.a. 3marks 9. Evaluate 1 2 12 1 3marks 10. Chords AB and CD in the figure below intersect externally at Q. If AB 5cm BQ 6cm and DQ 4cm, calculate the length of chord CD. 3 marks 11. Find the value of x leaving your answer as a mixed fraction. 3marks log4 3 23 52 log x 12. Make the subject of the formula. Www.freekcsepastpapers.com25 A 2 3marks 13. Two grades of tea, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by weight.


Simplify 32yxxxyy 3marks 7. Find greatest integral value of x which satisfies xxx 3marks 8. One of the roots of the equation 2 xkxis 4. Find the values of k and hence the second root 4marks 9. Solve for x in the following without using a calculator or mathematical table. Oxx91 3marks 10. A shear parallel to the x-axis maps point 1, 2 onto a point 5, 2 . Determine the shear factors and hence state the shear matrix invariant line is y 0 3marks 11. A solid is in the shape of a right pyramid on a square base on side 8cm and height 15cm. A frustum whose volume is a third of the pyramid is cut off. Determine the height of the frustum. 3 marks 12. The interior angle of a regular polygon is 20o more than three times the exterior angle. Determine the number of sides of the polygon 2marks 13. Three fifths of work is done on the first day. On the second day 43 of the remainder is completed. If the third day 87 of what remained id done, what fraction of work still remain to be done. 3marks 14. A two-digit number is such that the sum of the digits is ten. If the digits are reversed, the new number formed is less than the original number by 18. Find the number 3marks 15. In the figure bellow, CBD 2 CAD. Find the value of x 3marks 16. Two boys, Ababu and Chungwa, on the same side of a tall building are 100m apart. The building and the two boys are in a straight line and the angles of elevation from the boys to the top of the building are 30o and 20o respectively calculate the height of the building. 3marks www.freekcsepastpapers.com2 SECTION II 50 MARKS Attempt only five Questions from this section 17. A business lady bought 100 quails and 80 rabbits for sh25600. If she had bought twice as many rabbits as half as many quails she would have paid sh7400 less.


3marks www.freekcsepastpapers.com2 SECTION II 50 MARKS Attempt only five Questions from this section 17. A business lady bought 100 quails and 80 rabbits for sh25600. If she had bought twice as many rabbits as half as many quails she would have paid sh7400 less. She sold each quail at a profit of 10 and each rabbit at a profit of 20 . A Form two equations to show how much she bought the quails and the rabbits. 2marks b Using matrix method, find the cost of each animal. 5mrks c Calculate the total percentage profit she made from sale of the 100 quails and 80 rabbits. 3marks 18. A 3,7 B 5,5 , C 3,1 , D 1,5 are vertices of a quadrilateral a On the grid provided below, plot ABCD on a Cartesian plan 2marks b A1B1C1D1 is the image of ABCD under a translation T 96 plot A1B1C1D1and state its coordinates 2marks c Plot A11B11C11D11 the image of A1B1C1D1 after a rotation about -1,0 through a positive quarter turn. State its coordinates. 3marks d A111B111C111D111 is the image of A11B11C11D11 after a reflection in the line y x 2. Plot A111B111C111D111 and state its coordinates 3marks 19. The figure below shows a velocity time graph of a journey of a car. The car start from rest and accelerates at2 sm for t seconds until it is 22m s Brakes are applied bringing it uniformly to rest. The total journey is 847m long. Find. A The value of t, the acceleration time 2marks b The distance travelled during the first t seconds. 2marks c The value of x, the deceleration time 4marks d The rate of deceleration 2marks 20. The diagram below shows a histogram representing the mass of some pupil in a school.


A The value of t, the acceleration time 2marks b The distance travelled during the first t seconds. 2marks c The value of x, the deceleration time 4marks d The rate of deceleration 2marks 20. The diagram below shows a histogram representing the mass of some pupil in a school. A Prepare a frequency distribution table of the data 3marks b From the table above, estimate i The mean mass of the pupils to 3 s.f 3marks ii The median mass 3marks www.freekcsepastpapers.com3 iii How many pupils were 40kg and above 1marks 21. In the figure below OY:YA 1:3 AX:XB 1:2 OA a and OB b . N is the point of intersection of BY and OX a Determine i OX 2marks ii BY 1mark b Give that BYkBN and ON hOX, express ON in two ways in terms of kandhba , 3marks c Find the value of h and k and hence show that O,N and X are collinear 4marks 22. Using a ruler and a pair of compass only, construct triangle XYZ where XY is 6cm and XYZ is 135o and YZ 7cm 2marks a Measure XZ 1mark b Drop a perpendicular from Z to meet line XY at K , measure ZK. 2marks c Bisect line XY and let the bisector meet line XZ at Q 1mark d Join Q to Y and measure angle XQY 2marks e Find the area of triangle XYZ 2marks 23. Four towns are situated in such that a way that town Q is 500km on a bearing of 120o from P.


Using a ruler and a pair of compass only, construct triangle XYZ where XY is 6cm and XYZ is 135o and YZ 7cm 2marks a Measure XZ 1mark b Drop a perpendicular from Z to meet line XY at K , measure ZK. 2marks c Bisect line XY and let the bisector meet line XZ at Q 1mark d Join Q to Y and measure angle XQY 2marks e Find the area of triangle XYZ 2marks 23. Four towns are situated in such that a way that town Q is 500km on a bearing of 120o from P. Town R is 240 km on a bearing of 210o from town P, while town S is due north of town Q and due east of town P a Draw a sketch diagram showing the relative position of P,Q,R and S scale:1cm :100km 3marks b Find by calculation i The distance QR 1mark ii The distance QS 2marks iii The angle PRSQ 2marks iv The area of triangle PQS 2marks 24. The figure below shows a sketch of the graph of 62 xy. A Estimate the area bounded by the curve, the x-axis and the line x -4 and x 4 using i The trapezium rule with 8 sides 3marks ii The mid- ordinates rule with and strips 3marks b What percentage error is caused by estimating the area of the curve using the mid ordinates rule as in a ii above 4marks www.freekcsepastpapers.com4 CEKENAS FORM FOUR MOCK EXAMINATION, 2023 Kenya Certificate of Secondary Education. 121 2 MATHEMATICS ALT. A Paper 2 Time: 2 Hours SECTION A 50 MARKS Answer All Questions in this section 1. The area of a rectangle is 48.4cm2 and its length is 9.37cm. Calculate the percentage error in width 3marks 2. The base of a triangle is 23 xcm. The height of the triangle is 5cm shorter than its base. Given that the area of the triangle is 25cm2. Find length of the base. 4marks 3.


Given that the area of the triangle is 25cm2. Find length of the base. 4marks 3. Find the area of the triangle shown below 3marks 4. Express the following expression in surd form and simplify by rationalising the denominator 2 3marks 5. Solve for x in the expression 10loglog2 xx 3marks 6. The table below is part of the tax for monthly income for the year 2007 Monthly income ksh Rate Under ksh 10165 10 From 10165 but under ksh19741 15 From 19741 but under ksh29317 20 In that year, John s monthly gross tax was Ksh 2885. Calculate his monthly income 3marks 7. A quantity E is partly constant and partly varies as square root of F. i Write down an equation connecting E and F where K and C are constants respectively. Ii If F 25 where E 22 and F 49 when E 28. Find the value of K and C 3marks 8. A Expand 1 xin ascending power of x 1mark b Using the first four times of the expansion in a above estimate the value of 1 2marks 9. Find the number of terms of the series 5 8 11 14 17 .. that will give a sum of 2183 3marks 10. Find the inverse of the matrix 4M hence find the co-ordinates of the point at which line 34 yxandyxintersect 3marks 11. A trader mixed grade I, II and III of coffee in the ratio 2:3:5 respectively. Grade I cost Sh650 per kg, grade II costs sh 500 per kg and grade III costs sh 420 per kg. A Find the cost of one kg of the mixture 2marks b If the trader sold the mixture at a profit of 20 calculate the selling price of 3kg of the mixture 2marks 12.


A trader mixed grade I, II and III of coffee in the ratio 2:3:5 respectively. Grade I cost Sh650 per kg, grade II costs sh 500 per kg and grade III costs sh 420 per kg.a Find the cost of one kg of the mixture 2marks b If the trader sold the mixture at a profit of 20 calculate the selling price of 3kg of the mixture 2marks 12.Solve for the equation xxsin42 for 3600 xo 3marks 13.The figure below has a cross-section of the prism which is an isosceles triangle of side AE 8cm, DE 8cm and AD 6cm, where AB 20cm.