September 26, 2022

2020 Mathematics Paper 1 Kenya Certificate of Secondary Education Section I (50 marks) Answer all the questions in this section.

2021 Mathematics Paper 1 Kenya Certificate of Secondary Education Section I (50 marks) Answer all the questions in this section. 1. An empty tank of capacity 18480 litres is to be filled with water using a cylindrical pipe of diameter 0.028 m. The rate of flow of water from the pipe is 2 m/s. Find the time in hours it would take to fill up the tank. (Take π = 22/7). (3 marks) Vol. of water geting to the tank in 1sec = 22/7 x 0.0142 x 2 = 0.001232 m3 Time needed to fill tank = 18.48/0.001232 = 15000 sec = 41/6 hours 2. The first term of a Geometric Progression (G.P) is 2. The common ratio of the G.P is also 2. The product of the last two terms of the G.P is 512. Determine the number of terms in the G.P. (3 marks) nth term 2 x 2n-1 (n-1)th term = 2 x 2n-2 2 x 2n-1 x 2 x 2n-2=512 2n-1 = 9 2n-1 = 29 n = 5 3. The expression ax2 – 30x + 9 is a perfect square, where a is a constant. Find the value of a. (2 marks) 4 x a x 9 = (-30)² a = 900/36 =25 4. Make x the subject of the formula y = bx OVER √cx2 – a5 (3 marks) y² = b ²x ²/cx² – a cx² – y² – ay² = b²x² cx² – y²- b²x² = ay² x² (cy² – b²) = ay² x = ± √ ay ²/cy² – b² 5.The figure below shows a circle and a point outside the circle’. Using a ruler and pair of compasses, construct a tangent to the circle from P. (4 marks) Locating centre O ⊥ bisector of OP Arc showing the correct position of point of contact of circle and tangent tangent drawn b utt 6. Four quantities P Q R and S are such that P varies directly as the square root of Q and inversely as the square of the difference of R and S. Quantity Q is increased by 44% while quantities R and S are each decreased by 10%. Find the corresponding percentage change in P correct to 1 decimal place. (4 marks) P = k √Q/(R – S)2 New value of Pafter changes in Q, R and S = k √1.44Q (0.9R – 0.9S)2 =1.481k √Q/(R – S)2 = (1.481 – 1)100 7. The figure below represents a prism ABCDEFGH of length 6 cm. The cross section BCFG of the prism is a trapezium in which GF = 11 cm, BC = 8 cm, BG = 5 cm and ∠GFC = ∠BCF = 90° Calculate correct to 1 decimal place the angle between the line FA and the plane GFEH. (3 marks) Let point A’ be the projection of point A on the plane GFEH AA’= √(5² – 3²) = 4 FA’ = √(6² + 8²) = 10 Tanθ = 4/10 = 0.4 θ =21.8° 8. The cash price of a gas cooker is Ksh 20 000. A customer bought the cooker on hire purchase terms by paying a deposit of Ksh 10 000 followed by 18 equal monthly instalments of Ksh 900 each, Annual interest, compounded quarterly, was charged on the balance for the period of 18 months. Determine, correct to 1 decimal place, the rate of interest per annum. (4 marks) Balance upon paying deposit: = 20000 – 10000 = 10000 Amount Repaid = 900 x 18 = 16200 Let r =rate of interest per annum 1 + r/400 =6√1.62 = 1.084 r = (1.084 – 1)x 400 = 33.6% or 33.5% 9. The table below shows the values oft and the corresponding values of h for a given relation   t 1 2 3 4 5 6 7 8 h 8 4 2.7 2 1.6 1.3 1.1 1 a. On the grid provided, draw a graph to represent the information on the table given. (2 marks) b. Use the graph to determine, correct to 1 decimal place, the rate of change of h at = 3. (2 marks) Gradient = 0 – 27/6 – 3 = -0.9 ± 0.1 10. The equation of a trigonometric wave is y = 4 sin (ax – 70)o. The wave has a period of 180°. a. Determine the value of a. (1 mark) 360/a – 180 a = 2 b. Deduce the phase angle of the wave. (1 mark) Phase Angle = 70° 11. A point Q is 2000 nm to the West of a point P(40°N, 155°W). Find the longitude of Q to the nearest degree. (3 marks) Let θ = longitude difference between P and Q θ x 60 cos 40 = 2000 θ = 2000/60 cos 40 = 43.51° = 155 + 43.51 = 198.51° Longitude of Q = 360° – 198.51° 161°E 180 – 18.51 = 161°E 12. A box contains 3 brown balls and 9 green balls. The balls are identical except for the colours. Two balls are picked at random without replacement. a. Draw a tree diagram to show all the possible outcomes. (1 mark) b. Determine the probability that the balls picked are of different colours. (2 marks) P(Balls picked are of different colours) =3/12 x 9/11 + 9/12 x 3/11 =27/132 + 27/132< p> =54/132 Accept 9/22 13. The figure below shows triangle XYZ. Using a ruler and a pair of compasses locate point M is 2cm from line YX and is equidistant from lines YX and YZ. Measure length YM (3 marks) YM = (4 ± 0.1) cm Angle bisector of ∠ XYZ construction of a straight line 2 cm from and parallel to line XY OW-1 if point M is not marked 14. The position vectors of points P, Q and Rare OP = 61-23 +3k, OQ = 121 – 5j + 6k and OR =8i-3j+4k. Show that P, Q and R are collinear points. (3 marks) P is a common point Points P, Q and R are collinear 15. In a transformation

2021 Mathematics Paper 1 Kenya Certificate of Secondary Education Section I (50 marks) Answer all the questions in this section. 1. Evaluate 1⅘ ÷ ⅔ of 2¼ -3/10 OVER 5/6 + 22/39 + 1 2/11 Num = 9/5 ÷ 2/3 of 9/4 -3/10 = 9/5 ÷ 3/2 – 3/10 = 9/5 x 3/2 – 3/10 = 6/5 -3/10 or 12 – 3/10 =9/10 Den = 5/6 + 22/39 x 13/11 =5/6 + 2/3 or 5+4/6 =9/6 =3/2 Num ÷ Den = 9/10 ÷ 3/2 =9/10 ÷ 2/3=3/5 2. Two bells ring at intervals of 35 and 42 minutes respectively. The bells ring together at 8.48 a.m. Determine the time when the bells will ring together again. (3 marks) 3. Complete the figure below to show a rotational symmetry of order 3 about O. (3 marks) 4. Solve 5/3 -2x <1 – 2/3x ≤ 2 – x. Hence list the integral values that satisfy the inequalities. (3 marks) 5/3 -2x <1 – 2/3x 5 – 6x < 3 – 2x 2 < 4x 1⁄2 < x 1 – 2/3 x ≤ 2 – x x – 2/3x ≤ 2 – 1 1/3x ≤ 1 x ≤ 3 1⁄2 < x ≤ 3 integral values 1,2,3 5. The size of two interior angles of an irregular polygon each measures 90°. All the other remaining interior angles each measure 150°. (3 marks) Let the polygon ben sided (n – 2)180 = 90 + 90 + 150(n – 2) 180n – 360 – 180 + 1501 – 300 30n = 360 + 180 – 300 – 240 n = 8 Determine the number of sides of the polygon. 6. In a race Kipsang maintained an average speed of 5 m/s. When he was 310 m to the finishing line,Mutunga was 50 m behind him. However, Mutunga finished the race 10 m ahead of Kipsang. Determine Mutunga’s average speed. (3 marks) Time taken by Kipsang to run 300 m = 300/5> = 60 sec Mutungas speed = (310 + 50)/60 = 6 m/s 7. Simplify (4 + 2y)²– (2y – 4)²(2 marks) (4+2y)² – (2y – 4)² =[(4 +2y)-(2y-4][(4 +2y)+(27-4)] =[4 +2y – 2y +4][4 +2y+2y-4] =8 x 4y = 32 8. A table is sold at Ksh 4 500 and a chair at Ksh 2 000. A salesman earns a commission of 8% on every table and 5% on every chair sold. On a certain week, he sold 3 more chairs than tables and his total earnings were Ksh 3 980. Commission camed on selling Table = 8/100 x 4500 = sh 360 Chair = 5/100 x 2000 = sh100 Let the no. of chairs sold = x 360(x – 3) + 100 x 3980 460x = 5060 x = 11 Determine the number of chairs he sold that week. (3 marks) 9. A translation T maps A(-6, 2) onto A'(3,5). a. T = (3 5) – (-6 2) = (9 3) b. (a b) = (-4 2) – (9 3) a = -13, b= 1 P(-13,-1) a. Determine the translation vector T. b. A point P'(-4, 2) is the image of P under T. Determine the coordinates of P. (2 marks) 10. The cost of one litre of Petrol is Ksh 110. John’s vehicle covers 12 km on one litre of petrol. He used Ksh 2 805 on petrol to travel from town A to town B. Jane’s vehicle consumes 12.5 litres of Petrol for every 100 km travelled. Distance from A to B (Using Johns Vehicle) = 12 x 2805 over 110 = 308 km Cost of fuel that Jane would required = (12.5 x 306) x110 over 100 Ksh 4207.50 Calculate the amount of money that Jane would use to travel from town A to B on the same road.(3 marks) 11. Solve for θ 2θ – 15 + 3θ = 90 5θ = 105 θ = 21° sin (2θ -15) = cos 3θ(2 marks) 12. Line AB drawn below is a side of a trapezium ABCD. a. Using a ruler and pair of compasses only, complete trapezium ABCD in which AB is parallel to DC,∠BAD= 67.5°, AD = 5 cm, BC = 5.5 cm and ∠ABC is acute. (3 marks) b. Measure the length of DC. (1 mark) b. DC = 3cm ± 0.1 Construction of 67.5° :at A> Construction of DC//AB Trapezium ABCD 13. Ali left Mombasa for Nairobi on Tuesday at 2.30 a.m. He arrived in Mtito Andei after 3 hours 12 minutes. He stayed in Mtito Andei for 36 hours and then left for Nairobi. He took 5 hours 25 minutes to arrive in Nairobi. Departure from Msa) = 2.30 am – 0230 (Tue) Arrival (Mtito Andei) = 0230 +3h12min 0542h (Tue) NB: 36hrs = 1day 12hours Departure (Mtito Andei) = 0542h (Tue) + Iday: 12 hrs = 0542h (Wed)12hours = 1742hrs (Wed) Determine the day and time in the 12 hour system Ali arrived in Nairobi. (3 marks) Arrival(Nairobi) = 1742 + 5h 25min = 2307h =11.07 pm Wednesday 14. The height of a cone is 12 cm. A frustrum whose volume is one eighth the volume of the cone is cut off. Determine the height of the frustrum. (3 marks) VSF = 7/8 : 1 = 7:8 L.S.F = 3√7: 2 Let the height of frustum = x 12 – x over 12 = 3√7 over 2 = 1.913 over 2 24 – 2x = 22.956 2x = 1.044 x = 0.522 cm 15. Solve the equation 8x+1 – 23x-1 = 120. (4 marks) 8x+1 – 23x+1 = 120 (2³)x+1 – 23x+1 = 120   23x x 2³ – 2over 2x = 120 23x(2³-1/2) = 120 23x= 120x 2/15 = 16 = 24 16. A curve is given by y=2x³- 3x² – 12x + 12. a. Find the gradient function of the curve. (1 mark) = dy/dx = 6×2 – 6x – 12 b. Determine the equation of the normal to the curve at the point (1,-1), in the form y = mx + c, where m and c are constants. (3

4.2 MATHEMATICS ALT. B (I22) Mathematics Alt. B Paper 1 (122/1) SECTION 1 (50 marks) Answer all questions in this section in the spaces provided. 1.Without using a calculator, evaluate: –3(-5 — + 7) + 2(-3 + +6). 2. The first four prime numbers are written in descending order to form a number. (a) Write down the number. (b) Find the total value of the hundreds digit in the numbers, 3. Without using a calculator evaluate:(3 marks) 4. Tito owned Ksh 600 to Nekesa, Ksh 750 to Mwita and Ksh 650 to A uma. He had Ksh 1200 to repay to the three people in proportion to what he owed them. Calculate the amount of money Mwita rcceived more than Nekesa. (3 marks) 5. Given that r — 2 and h = 3r — 1, evaluate 7r2 + 2rh/√ 4h – 2r (3 marks) 6. The surface area of a cube is 1176 cm3. Determine the length of one of” its sides. (3 marks) 7. By construction, divide the line PQ below into six equal parts. (3 marks)   8. Given that tan x = 3/4 and .r is an acute angle, without using mathematical tables or a calculator, find the value of 2 sin x — cosx. (3 marks) 9.A box contains Cve shillings coins and ten shillings coins. The number of ten shillings coins are 6 times as many as the five shillings coins. The total value ot’all the coins in the box is Ksh 2600. Determine the total number of coins in the box. (4 marks) 10. Simplify 3-2 x 813/2/4-3 ÷ 81/3 leaving your answer in index form. Hence evaluate the expression. (4 marks) 11. A retailer bought a mobile phone for Ksh 5750. The marked price at the retailer’s shop was 12% higher than the buying price. After allowing a certain discount, the retailer sold the mobile phone for Ksh 6118. Calculate the percentage discount. (3 marks) 12. Factorise 9a2 — 16/b2c2 (2 marks) 13. Three types of books A, B and C were each piled on a table to attain the same height. The thickness of the books were 12 mm, 28 mm and 54 mm for types A, B and C respectively. Find: (a) the least height attained; (b) the number of type A books piled. (3 marks) 14. The sum of the interior angles of a regular polygon is 1260°. Find the size of each interior angle. (3 marks) 15. The corresponding lengths of two similar triangles are 5 cm and 7.5 cm. If the area of the larger triangle is 22.5 cm2, calculate the area of the smaller triangle. (3 marks) 16. The area of a sector of a circle is 77 cm2‘. The arc of the sector subtends an angle of 45° at the centre of the circle. Find the circumference of the circle. (Take ℿ=22/7 (4 marks) SECTION II (50 marks) Answer only Ave questions in this section in the spaces provided. 17. The figure below represents a solid prism with a semi-circular groove. The dimensions are as shown. (a) Calculate: (i) the volume of the prism; (ii) the total surface area of the prism. (4 marks) (b) All the rectangular faces are painted. Calculate the percentage of the surface of the prism that is painted correct to 1 decimal place. (2 marks) 18. (a) Three vertices of a parallelogram ABCD are A(—7, 3), B( 1. — I) and C(5, 1). On the grid provided, draw the parallelogram ABCD. (b) Determine: (i) the gTadient of the line AB; (2 marks) (ii) the equation or line AB in the form y = m.r + c, where m and c are constants. (2 marks)   (c) Another line L is perpendicular to CD and passes through point (1, 3). Determine: (i) the equation of L in the form ax + by = c where a, b and c are constants; (3 marks) (ii) the coordinates of the y-intercept of line L. (1 mark) 19. (a) The roots of a quadratic equation are 2 and — 1. Write down the quadratic equation in the form ar° + bx + c = 0, where a, b and c are integers. (3 marks) (b) (i) Barasa bought (2y + l ) mangoes at y shillings each. The total cost of the mangoes was Ksh 55. Find the cost of each mango. (4 marks) (ii) Karau spent Ksh 95 more than Barasa to buy the same type of mangoes. For every 6 mangoes he bought, he was given one extra mango. Calculate the total number of mangoes Karau got. (3 marks) 20. The angle of elevation of the top T, of a vertical mast from a point P, 100 m away from the foot F, o(the mast is 14°. (a) Using a scale of l cm to represent 10 m, make a scale drawing to represent the above information. (3 marks) (b) Using the scale drawing, determine the height of the mast. (2 marks) (c) A support cable, 27 m long, is fixed tightly at a point D on the mast 5 m below T and at a point C on the ground. Points P, F and C lie on a straight line with P and C on opposite sides ot’ F. On the scale drawing, show the position of the cable. (2 marks) (d) Use the scale drawing to determine: (i) the angle of depression of C from D; (1 marks) (ii) the distance of C from P. (2 marks) 21. ln the figure below, P, Q, R and S are points on the circumference of the circle centre O. TP and TR are tangents to the circle at P and R respectively. POQ is a diameter of the circle and angle PQR = 64°. Giving reasons in each case, find the size of: (a) ∠ ROP; (2 marks) (b) ∠ PSR; (2 marks) (c) ∠ ORP; (2 marks) (d) ∠ RP; (2 marks) (e) ∠RTP. (2 marks) 22. The figurc below represents a cone whose vertical height is 12

KCSE Past Papers Maths A 2013 MATHEMATICS ALT. A (121) Mathematics Alt. A Paper 1 ( 121/1) SECTION I (50 marks) Answer all the questions in this section in the spaces provided. 1 Evaluate (2 marks) 2 The production of milk, in litres, of 14 cows on a certain day was recorded as follows: 22, 26, 15, 19, 20,16, 27,15, 19, 22, 21, 20, 22 and 28. Determine: (a) the mode; (1 mark) (b) the median. (2 marks) 3 Use logarithms, correct to 4 decimal places, to evaluate (4 marks) 5. A wholesaler sold a radio to a retailer making a profit of 20%. The retailer later sold the radio for Ksh 1560 making a profit of 30%. Calculate the amount of money the wholesaler had paid for the radio. (3 marks) 6 A point P on the line AB shown below is such that AP = %AB. By construction locate P. (3 marks) 7 Chelimo’s clock loses 15 seconds every hour. She sets the correct time on the clock at 0700h on a Monday. Determine the time shown on the clock when the correct time was 1900h on Wednesday the same week. (3 marks) 8 Given that sin (x + 20)° = — 0.7660, find x, to the nearest degree, for 0°< x <360°. (3 marks) 9 A number m is formed by writing all the prime numbers between 0 and 10 in an ascending order. Another number n is formed by writing all the square numbers between 0 and 10 in a descending order. (a) Find m — n; (2 marks) (b) Express (m — n) as a product of its prime factors. (1 mark) 10 The figure below shows a net of a solid. (Measurements are in centimetres). Below is a part of the sketch of the solid whose net is Shown above. Complete the sketch of the solid, showing the hidden edges with broken lines. (3 marks) 11 The interior angles of an octagon are 2x, 1/2x, (x + 40)°, 110°, 135°, 160°, (2x + 10)° and 185°. Find the value of x. (2 marks) 12 A straight line passes through points (-2, 1) and (6, 3). Find: (a) the equation of the line in the form y = mx + c; (2 marks) (b) the gradient of a line perpendicular to the line in (a). (1 mark) 13 A triangle ABC is such that AB = 5 cm, BC = 6cm and AC = 7cm. (a) Calculate the size of angle ACB, correct to 2 decimal places. (2 marks) (b) A perpendicular drawn from A meets BC at N. Calculate the length AN correct to one decimal place. (2 marks) 14 A cylindrical pipe 2 1/2 metres long has an internal diameter of 21 millimetres and an external diameter of 35 millimetres. The density of the material that makes the pipe is 1.25 g/cm‘. Calculate the mass of the pipe in kilograms. (Take n = 22/7). (4 marks) 15 The figure below represents a pentagonal prism of length 12cm. The cross-section is a regular pentagon of side 5 cm. Calculate the surface area of the prism correct to 4 significant figures. (4 marks) Given the inequalities x — 5 < 3x — 8 < 2x — 3. (a) Solve the inequalities; (2 marks) (b) represent the solution on a number line. (1 mark) SECTION ll (50 marks) Answer only five questions in this section in the spaces provided. 17 A farmer had 540 bags of maize each having a mass of 112 kg. After drying the maize, the mass decreased in the ratio 15: l 6. (a) Calculate the total mass lost after the maize was dried. (3 marks) (b) A trader bought and repacked the dried maize in 90 kg bags. He transported the maize in a lorry which could carry a maximum of 120 bags per trip. (i) Determine the number of trips the lorry made. (3 marks) (ii) The buying price of a 90 kg bag of maize was Ksh 1500. The trader paid Ksh 2500 per trip to transport the maize to the market. He sold the maize and made a profit of 26%. Calculate the selling price of each bag of the maize. (4 marks) 18 (a) Solve the equation, x + 3/24 = 1/x-2 (4 marks) (b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136 ml. (i) Calculate the perimeter of the floor. (4 marks) (ii) A rectangular carpet is placed on the floor of the hall leaving an area of 64 mi. If the length of the carpet is twice its width, determine the width of the carpet. (2 marks) 19 A trader bought 2 cows and 9 goats for a total of Ksh 98 200. If she had bought 3 cows and 4 goats she would have spent Ksh 2200 less. (a) F om1 two equations to represent the above information. (2 marks) (b) Use matrix method to determine the cost of a cow and that of a goat. (4 marks) (c) The trader later sold the animals she had bought making a profit of 30% per cow and 40% per goat. (i) Calculate the total amount of money she received. (2 marks) (ii) Determine, correct to 4 significant figures, the percentage profit the trader made from the sale of the animals. (2 marks) 20 Two towns, A and B are 80 km apart. Juma started cycling from town A to town B at 10.00 am at an average speed of 40 km/h. Mutuku started his journey from town B to town A at 10.30 am and travelled by car at an average speed of 60 km/h. (a) Calculate: (i) the distance from town A when Juma and Mutuku met; (5 marks) (ii) the time of the day when the two met. (2 marks) (b) Kamau started cycling from town A to town B at 10.21am. He met Mutuku at the same time as Juma did.

3.3.2 Mathematics Alt. A Paper 2 (121/2) SECTION I (50 marks) Answer all the questions in this section in the spaces provided. 1 The lengths of two similar iron bars were given as 12.5 m and 9.23 m. Calculate the maximum possible difference in length between the two bars. (3 marks) 2 The first term of an arithmetic sequence is —7 and the common difference is 3. (a) List the first six terms of the sequence; (1 mark) (b) Determine the sum of the first 50 terms of the sequence. (2 marks) 3 In the figure below, BOD is the diameter of the circle centre O. Angle ABD = 30° and angle AXD = 70°. (a) reflex angle BOC; (2 marks) Determine the size of: (b) angle ACO. (1 mark) 4 Three quantities L, M and N are such that L varies directly as M and inversely as the square of N. Given that L = 2 when M = 12 and N = 6, determine the equation connecting the three quantities. (3 marks) 5 The table below shows the frequency distribution of marks scored by students in a test. imageeeeee Determine the median mark correct to 2 s.f (4 marks) 6 Determine the amplitude and period of the function, y I 2 cos (3): — 45)°. (2 marks) 7 In a transformation, an object with an area of 5cm2 is mapped onto an image whose area is 30 cm. Given that the matrix of the transformation is find the value of x. (3 marks) 8 Expand (3 — x)’ up to the term containing x‘. Hence find the approximate value of (2.8)7. (3 marks) 9 Solve the equation; 2 log 15 — log x I log 5 + log (x — 4). (4 marks) 10 The figure below represents a cuboid PQRSTUVW. Calculate the angle between line PW and plane PQRS, correct to 2 decimal places. (3 marks) ll Solve the simultaneous equations; 3x I y I 9 x2 — xy I 4 (4 marks) 12 Muga bought a plot of land for Ksh 280000. After 4 years, the value of the plot was Ksh 495 000. Determine the rate of appreciation, per annum, correct to one decimal place. (3 marks) 13 The shortest distance between two points A (40 °N, 20 °W) and B (6 °S, 20 °W) on the surface of the earth is 8008 km. Given that the radius of the earth is 6370km, determine the position of B. (Take TE = 22/7 ). (3 marks) 14 Vectors r and s are such that r=7i+2j—k and s=—i+j—k.Find|r+s|. (3 marks) 15 The gradient of a curve is given by . The curve passes through the point (1,0). Find the equation of the curve. (3 marks) 16 The graph below shows the rate of cooling of a liquid with respect to time. Determine the average rate of cooling of the liquid between the second and the eleventh minutes. (3 marks) SECTION ll (50 marks) Answer only five questions in this section in the spaces provided. 17 A paint dealer mixes three types of paint A, B and C, in the ratios A:B = 3:4 and B:C = 1:2. The mixture is to contain l68 litres of C. (a) Find the ratio A:B:C. (2 marks) (b) Find the required number of litres of B. (2 marks) (c) The cost per litre of type A is Ksh 160, type B is Ksh 205 and type C is Ksh 100. (i) Calculate the cost per litre of the mixture. (2 marks) (ii) Find the percentage profit if the selling price of the mixture is Ksh 182 per litre. (2 marks) (iii) Find the selling price of a litre of the mixture if the dealer makes a 25% profit. (2 marks) 18 In the figure below OS is the radius of the circle centre O. Chords SQ and TU are extended to meet at P and OR is perpendicular to QS at R. OS = 61 cm, PU = 50 cm, UT = 40cm and PQ = 30cm. (a) Calculate the length of: (i) QS; (2 marks) (ii) OR. (3 marks) (b) Calculate, correct to 1 decimal place: (i) the size of angle ROS; (2 marks) 19 The table below shows income tax rates for a certain year. A tax relief of Ksh 1 162 per month was allowed. In a certain month, ofthat year, an employee’s taxable income in the fifth band was Ksh 2108. (a) Calculate: (i) the employee’s total taxable income in that month; (2 marks) (ii) the tax payable by the employee in that month. (5 marks) (b) The employee’s income included a house allowance of Ksh 15 000 per month. The employee contributed 5% of the basic salary to a co-operative society. Calculate the employees net pay for that month. (3 marks) 20 The dimensions of a rectangular floor of a proposed building are such that:   the length is greater than the width but at most twice the width;  the sum of the width and the length is, more than 8 metres but less than 20 metres. if x represents the width and y the length.(a) write inequalities to represent the above information. (4 marks) (b) (i) Represent the inequalities in part (a) above on the grid provided. (4 marks) (ii) Using the integral values of x and y, find the maximum possible area of the floor. (2 marks) 21 Each morning Gataro does one of the following exercises: Cycling, jogging or weightlifting. He chooses the exercise to do by rolling a fair die. The faces of the die are numbered 1,1,2, 3, 4 and 5. If the score is 2, 3 or 5, he goes for cycling. If the score is 1, he goes for jogging. If the score is 4, he goes for weightlifting. (a) Find the probability that: (i) on a given morning, he goes for cycling or weightlifiing; (2 marks) (ii) on two consecutive mornings he goes for jogging. (2 marks) (b) In the afternoon, Gataro plays

KCSE Past Papers Maths A 2014 Section 1 (50 marks) Answer all the questions in this section in the spaces provided. 1 Ntutu had cows, sheep and goats in his farm. The number of cows was 32 and number of sheep was twelve times the number of cows. The number of goats was 1344 more than the number of sheep. If he sold % of the goats, find the number of goats that remained. (4 marks) 2 Use the prime factors of 1764 and 2744 to evaluate (3 marks) 3 The mass of a solid cone of radius 14 cm and height 18 cm is 4.62 kg. Find its density in g/cm}. (3 marks) 4 The figure below represents a triangular prism ABCDEF. X is a point on BC. (a) Draw a net of the prism. (2 marks) (b) Find the distance DX. (1 mark) 5 A businessman makes a profit of 20% when he sells a carpet for Ksh 36 000. In a trade fair he sold one such carpet for Ksh 33 600. Calculate the percentage profit made on the sale of the carpet during the trade fair. (3 marks) 6 Simplify (3 marks) 7 The area of a sector of a circle, radius 2.1 cm, is 2.31 cml. The arc of the sector subtends an angle 6, at the centre of the circle. Find the value of 6 in radians correct to 2 decimal places. (2 marks) 8 Expand and simplify (2 marks) 9 A plane leaves an airstrip L and flies on a bearing of 040° to airstrip M, 500km away. The plane then flies on a bearing of 3 16° to airstrip N. The bearing of N from L is 350°. By scale drawing, determine the distance between airstrips M and N. (4 marks) 10 The sum of interior angles of a regular polygon is 1800 °. Find the size of each exterior angle. (3 marks) 11 A cow is 4 years 8 months older than a heifer. The product of their ages is 8 years. Determine the age of the cow and that of the heifer. (4 marks) 12 Solve 4 S 3x — 2 < 9 + x hence list the integral values that satisfies the inequality. (3 marks) 13 The figure below shows a rectangular container of dimensions 40cm by 25 cm by 90cm. A cylindrical pipe of radius 7.5 cm is fitted in the container as shown. Water is poured into the container in the space outside the pipe such that the water level is 80% the height of the container. Calculate the amount of water, in litres, in the container correct to 3 significant figures. (4 marks) 14 A minor are of a circle subtends an angle of 105° at the centre of the circle. if the radius of the circle is 8.4 cm, find the length of the major arc. imageeeee (3 marks) 15 Twenty five machines working at a rate of 9 hours per day can complete a job in 16 days. A contractor intends to complete the job in 10 days using similar machines working at a rate of 12 hours per day. Find the number of machines the contractor requires to complete the job. (3 marks) 16 Points A (— 2, 2) and B (— 3, 7) are mapped onto A’ (4, — 10) and B’ (0, 10) by an enlargement. Find the scale factor of the enlargement. (3 marks) SECTION ll (50 marks) Answer only five questions in this section in the spaces provided. 17 A line L passes through points (— 2. 3) and (— 1, 6) and is perpendicular to a line P at (— 1, 6). (a) Find the equation of L. (2 marks) (b) Find the equation of P in the form ax + by = c, where a, b and c are constants. (2 marks) (c) Given that another line Q is parallel to L and passes through point (1, 2), find the x and y intercepts of Q. (3 marks) (d) Find the point of intersection of lines P and Q. (3 marks) 18 The lengths, in cm, of pencils used by pupils in a standard one class on a certain day were recorded as follows. (a) Using a class width of 3, and starting with the shortest length of the pencils, make a frequency distribution table for the data. (2 marks) (b) Calculate: (i) the mean length of the pencils; (3 marks) (ii) the percentage of pencils that were longer than 8 cm but shorter than 15 cm. (2 marks) (c) On the grid provided, draw a frequency polygon for the data. (3 marks) 19 The figure below represents a speed time graph for a cheetah which covered 825 m in 40 seconds. (a) State the speed of the cheetah when recording of its motion started.(1 mark) (b) Calculate the maximum speed attained by the cheetah.(3 marks) (c)Calculate the acceleration of the cheetah in:(2 marks) (i) the first 10 seconds;(1 mark) (ii) the last 20 seconds.(2 marks) Calculate the average speed of the cheetah in the first 20 seconds.(3 marks) 20 The figure below shows a right pyramid VABCDE. The base ABCDE is a regular pentagon. AO = 15cm and VO = 36cm.(3 marks) Calculate: (a) the area of the base correct to 2 decimal places; (3 marks) (b) the length AV; (1 mark) (c) the surface area of the pyramid correct to 2 decimal places; (4 marks) (d) the volume of the pyramid correct to 4 significant figures. (2 marks) 21 (a) 22 (a) Using a pair of compasses and ruler only, construct: (i) triangle ABC in Which AB = 5cm, LBAC = 30° and LABC = 105°; (3 marks) (ii) a circle that passes through the vertices of the triangle ABC. Measure the radius. (3 marks) (iii) the height of triangle ABC with AB as the base. Measure the height. (2 marks) (b) Determine the area of the circle that lies outside the triangle correct to 2 decimal places. (2 marks)

SECTION I (50 marks) Answer all the questions in this section in the spaces provided. 1. The length and width of a rectangular piece of paper were measured as 60 cm and 12 cm respectively. Determine the relative error in the calculation of its area. (4 marks) 2. Simplify (2 marks) 3. An arc ll cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle. (4 marks) 4. In the figure below, O is the centre of the circle. A, B, C and D are points on the circumference of the circle. Line AB is parallel to line DC and angle ADC = 55°. Determine the size of angle ACB. (3 marks) 5. Eleven people can complete of a certain job in 24 hours. Determine the time in hours, correct to 2 decimal places, that 7 people working at the same rate can take to complete the remaining job. (3 marks) 6 The length and width of a rectangular signboard are (3x +12) cm and (x — 4) cm respectively. If the diagonal of the signboard is 200 cm, determine its area. (4 marks) 8. Use the expansion of (x — y)5 to evaluate (9.8)5 correct to 4 decimal places. (3 marks) 9. The diameter of a circle, centre O has its end points at M(— 1, 6) and N(5, —2). Find the equation of the circle in the form x2 + yl + ax + by = c where a, b and c are constants. (4 marks) Find the value of x given that log (x — 1) + 2 = log (3x + 2) + log 25. (3 marks) 10. Below is a line AB and a point X. Determine the locus of a point P equidistant from points A and B and 4 cm from X.(3 marks) 11. In a nomination for a committee, two people were to be selected at random fi’0m a group of 3 men and 5 women. Find the probability that a man and a woman were selected. (2 marks) 12. A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. (4 marks) 13. Evaluate (3 marks) 14. The positions of two points P and Q, on the surface of the earth are P(45 °N, 36 °E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place. (3 marks) 15. Solve the equation sin (½x — 30°) = cos x for 0 < x < 90°. (2 marks) 16. The position vectors of points P, Q and R are Show that P, Q and R are collinear. (3 marks) SECTION II (50 marks) Answer any five questions from this section in the spaces provided. 17. In a retail shop, the marked price of a cooker Was Ksh 36 000. Wanandi bought the cooker on hire purchase tenns. She paid Ksh 6400 as deposit followed by 20 equal monthly instalments of Ksh 1750. (a) Calculate: (i) the total amount of money she paid for the cooker. (2 marks) (ii) the extra amount of money she paid above the marked price. (l mark) (b) The total amount of money paid on hire purchase terms was calculated at a compound interest rate on the marked price for 20 months. Determine the rate, per annum, of the compound interest correct to 1 decimal place. (4 marks) (c) Kaloki borrowed Ksh 36 000 from a financial institution to purchase a similar cooker. The financial institution charged a compound interest rate equal to the rate in (b) above for 24 months. Calculate the interest Kaloki paid correct to the nearest shilling. (3 marks) 18. Mute cycled to raise funds for a charitable organisation. On the first day, he cycled 40 km. For the first 10 days, he cycled 3 km less on each subsequent day. Thereafter, he cycled 2 km less on each subsequent day. (a) Calculate: (i) the distance cycled on the 10th day; (2 marks) (ii) the distance cycled on the 16th day. (3 marks) (b) If Mute raised Ksh 200 per km, calculate the amount of money collected. (5 marks) 19. The equation of a curve is given by y = 1 + 3 sin x. (a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place (2 marks) (b) (i) On the grid provided, draw the graph of (3 marks) (ii)State the amplitude of the curve y = 1 + 3 sin x. (1 mark) (d) Use the graphs to solve the equation (l mark) (c) On the same grid draw the graph of y = tan x for 90° 5x 5 270° (3 marks) 20. The figure below represents a cuboid EFGHJKLM in which EF = 40 cm, FG = 9 cm and GM = 30 cm. N is the midpoint of LM. Calculate correct to 4 significant figures: (a) the length of GL; (1 mark) (b) the length of F]; (2 marks) (c) the angle between EM and the plane EFGH; (3 marks) (d) the angle between the planes EFGH and ENH; (2 marks) (e) the angle between the lines EH and GL. (2 marks) 21. A quantity P varies partly as the square of m and partly as n. When P = 3.8, m = 2 and n = -3. When P = -0.2,m = 3 and n = 2. (a) Find: (i) the equation that connects P, m and n; (4 marks) (ii) the

SECTION I (50 marks) Answer all the questions in this section in the spaces provided. 1. (a) Evaluate 540 396 — 726450/ 3 (l mark) (b) Write the total value of the digit in the thousands place of the results obtained in (a) above. (1 mark) 2. Muya had a 62/3ha piece of land. He donated 7/8ha to a school and 11/2ha to a children’s home. The rest of the land was shared equally between his son and daughter. Find the size of land that each child got. (3 marks) 3. The volume of a cube is l728 cm3. Calculate, correct to 2 decimal places, the length of the diagonal of a face of the cube. (3 marks) 4. Use logarithms, correct to 4 significant figures, to evaluate (4 marks)   5. A piece of Wire is bent into the shape of an isosceles triangle. The base angles are each 48° and the perpendicular height to the base is 6 cm. Calculate, correct to one decimal place, the length of the wire. (3 marks) 6. The density of a substance A is given as 13.6 g/cm’ and that of a substance B as 11.3 g/cm3. Determine, correct to one decimal place, the volume of B that would have the same mass as 50 cm3 of A. (3 marks) 7. Below is part of a sketch of a solid cuboid ABCDEFGH. Complete the sketch. (2 marks) 8. A salesman is paid a salary of Ksh 15 375 per month. He also gets a commission of 4½ on the amount of money he makes from his sales. In a certain month, he earned a total of Ksh 28 875. Calculate the value of his sales that month. (3 marks) 9. The sum of interior angles of a regular polygon is 24 times the size of the exterior angle. (a) Find the number of sides of the polygon. (3 marks) (b) Name the polygon. (1 mark) 10. The marks scored by a group of students in a test were recorded as shown in the table below. On the grid provided, and on the same axes, represent the above data using: (a) a histogram; (3 marks) (b) a frequency polygon. (1 mark) ll. Given that P = 5a — 2b where a = and b = Find: (a) column vector P; (2 marks) (b) P’, the image of P under a translation vector (1 mark) 12. Given that a = 3, b = 5 and c =- ½ evaluate (3 marks) 13. The figure below represents the curve of an equation. Use the mid-ordinate rule with 4 ordinates to estimate the area bounded by the curve, lines y=0,x= -3 and x=5. (3 marks) 14. The cost of 2 jackets and 3 shirts was Ksh 1 800. After the cost of a jacket and that of a shirt were increased by 20%, the cost of 6 jackets and 2 shirts was Ksh 4 800. Calculate the new cost of a jacket and that of a shin. (4 marks) 15. A tailor had a piece of cloth in the shape of a trapezium. The perpendicular distance between the two parallel edges was 30 cm. The lengths of the two parallel edges were 36 cm and 60 cm. The tailor cut off a semi circular piece of the cloth of radius 14cm from the 60 cm edge. Calculate the area of the remaining piece of cloth. (3 marks) 16. Musa cycled from his home to a school 6km away in 20 minutes. He stopped at the school for 5 minutes before taking a motorbike to a town 40km away. The motorbike travelled at 75 km/h. On the grid provided, draw a distance-time graph to represent Musa’s journey. (3 marks) SECTION II(50 marks) Answer any five questions in this section in the spaces provided. 17 Three partners Amina, Bosire and Karuri contributed a total of Ksh 4 800 000 in the ratio 4:5:7 to buy an 8 hectares piece of land. The partners set aside i of the land for social amenities and sub-divided the rest into 15 m by 25 m plots. (a) Find: (i) the amount of money contributed by Karuri; (2 marks) (ii) the number of plots that were obtained. (3 marks) (b) The puma: sokl the plots at Ksh 50000 each and spent 30% of the profit realised to pay for administrative costs. They shared the rest of the profit in the ratio of their contributions. (i) Calculate the net profit realised. (3 marks) (ii) Find the difference in the amount of the profit eamed by Amina and Bosire. (2 marks) 18. Two shopkeepers, Juma and Wanjiku bought some items from a wholesaler. Juma bought 18 loaves of bread, 40 packets of milk and 5 bars of soap while Wanjiku bought 15 loaves of bread, 30 packets of milk and 6 bars of soap. The prices of a loaf of bread, a packet of milk and a bar of soap were Ksh 45, Ksh 50 and Ksh 150 respectively. (a) Represent: (i) the number of items bought by Juma and Wanjiku using a 2 X 3 matrix. (1 mark) (ii) the prices of the items bought using a 3 X 1 matrix. (1 mark) (b)Use the matrices in (a) above to determine the total expenditure incurred by each person and hence the difference in their expenditure. (3 marks) (c) Juma and Wanjiku also bought rice and sugar. Jurna bought 36 kg of rice and 23 kg of sugar and paid Ksh 8 160. Wanjiku bought 50 kg of rice and 32 kg of sugar and paid Ksh 11 340. Use the matrix method todetermine the price of one kilogram of rice and one kilogram of sugar. (5 marks) 19. Line AB drawn below is a side Of a triangle ABC. (a) Using a pair of compasses and ruler only construct: (i) triangle ABC in which BC = 10 cm and CAB = 90°; (2 marks) (ii) a rhombus BCDE such that CBE = 120°; (2 marks) (iii) a perpendicular from F, the point of intersection of the diagonals

Kenya Certificate of Secondary Education 2016 Mathematics Paper 2 SECTION I (50 marks) Answer all the questions from this section in the spaces provided 1. Simplify (3 marks) 2. By correcting each number to one significant figure, approximate the value of 788 X 0.006. Hence calculate the percentage error arising from this approximation. (3 marks) 3. The area of triangle FGH is 21 cm. The triangle FGH is transformed using the matrix Calculate the area of the image of triangle FGH (2 marks) 4. Make s the subject of the formula. (3 marks) W = 3√s+t/s 5. Solve the equation 2 log x — log (x-2) = 2 log 3. (3 marks) 6. Kago deposited Ksh 30 000 in a financial institution that paid simple interest at the rate of 12% per annum. Nekesa deposited the same amount of money as Kago in another financial institution that paid compound interest. After 5 years, they had equal amounts of money in the financial institutions. Determine the compound interest rate, to 1 decimal place for Nekesa’s deposit. (4 marks) 7. The masses in kilograms of 20 bags of maize were: 90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102 and 105. Using an assumed mean of 96 kg, calculate the mean mass, per bag of the maize. (3 marks) 8. The first term of an arithmetic sequence is —7 and the common difference is 3. (a) List the first six terms of the sequence; (1 mark) (b) Determine the sum of the first 50 terms of the sequence. (2 marks) 9. A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours. Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the 2 balls are both white. (2 marks) 10. An arc 11 cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle. (4 marks) 11. Given that qi + 1/3j + 2/3k is a unit vector, find q. (2 marks) 12. (a) Expand the expression (1 + 1/2 x)5 in ascending powers of x, leaving the coefficients as fractions in their simplest form. (2 marks) (b) Use the first three terms of the expansion in (a) above to estimate the value of (1½o)5. (2 marks) 13. A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through the point (2,5). Find the value of k. (3 marks) 14. Water and milk are mixed such that the volume of water to that of milk is 4:1. Taking the density of water as 1 gcm3 and that of milk as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture. (3 marks) 15. A school decided to buy at least 32 bags of maize and beans. The number of bags of beans were to be at least 6. A bag of maize costs Ksh 2 500 and a bag of beans costs Ksh 3 500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. (4 marks) 16. (a)Find in radians, the values of x in the interval O’⋜ x 𕲚Πc for which 2 cos2x — sin x = I. (Leave the answer in terms of Π) (4 marks) (b) Calculate the mid-ordinates of 5 strips between x – 1 and x = 6 Use the mid-ordinates rule to approximate, the area under the curve between x-1 ,X = 6 and the x axis.(3 marks) (c) Assuming that the area determined by integration to be the actual area,calculate the percentage error in using the mid-ordinate rule.(4 marks) Section II (50 marks) Answer any five questions from this section in the spaces provided 17. A garden measures 10 m long and 8 m wide. A path of uniform width is made all round the garden. The total area of the garden and the path is 168 m2. (a) Find the width of the path. (4 marks) (b) The path is to be covered with square concrete slabs. Each corner of the path is covered with a slab whose side is equal to the width of the path. The rest of the path is covered with slabs of side 50 cm. The cost of making each corner slab is Sh 600 while the cost of making each smaller slab is Sh 50. Calculate: (i) the number of the smaller slabs used. (3 mark) (ii) the total cost of the slabs used to cover the whole path. (3 marks) 18. In the figure below, P, Q, R and S are points on the circle with centre 0. PRI’ and USTV are straight lines. Line USTV is a tangent to the circle at S. L RST = 50° and L RTV = 150°. (a) Calculate the size of (i) L QRS; (2 marks) (ii) L USP; (1 mark) (iii) L PQR. (2 marks) (b) Given that RT = 7cm and ST = 9 cm, calculate to 3 significant figures: ( ) the length of line PR: (2 marks) (ii) the radius of the circle. (3 marks) 19. The figure ABCDEF below represents a roof of a house. AB = DC = 12m, BC = AD = 6 m. AE = BF = CF = DE = 5 m and EF = 8 m. (a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD. (4 marks) (b) Calculate the angle between: (i) the planes ADE and ABCD; (2 marks) (ii) the line AE and the plane ABCD, correct to 1 decimal place; (2 marks) (iii) the planes ABFE and DCFE, correct to 1 decimal place. (2 marks)

KCSE Past Papers 2016 Mathematics Alt A Paper 1 SECTION I (50 marks) Answer all the questions from this section in the spaces provided 1. Without using a calculator evaluate, (3 marks) (4 marks) 3. The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5 cm respectively. The thickness of the materials making the container is 5mm. If the container has 8 litres of water, calculate the internal height above the water level. (4 marks) 4. The figure below shows a net of a solid (measurements are in centimetres). Below is a part of the sketch of the solid whose net is shown above. Complete the sketch of the solid, showing the hidden edges with broken lines. (3 marks) 5. Given that OA = 2i + 3j and OB = 3i — 2j, find the magnitude of AB to one decimal place. (3 marks) 6. A bus travelling at an average speed of 63 km/h left a station at 8:15 a.m. A car later left the same station at 9:00 a.m. and caught up with the bus at 10:45 a.m. Find the average speed of the car. (3 marks) 7. Given that x is an acute angle and cos x° = 2/5𕔉 find, without using mathematical tables or a calculator, tan (90 — x)°. (2 marks) 8. Without using mathematical tables or a calculator, evaluate 272/3x(81/16)-1/4 (3 marks) 9. A minor arc of a circle subtends an angle of 105° at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc. (Take IC = ). (3 marks) 10. The gradient of the tangent to the curve y = ax3 + bx at the point (1,1) is —5. Calculate the values of a and b. (4 marks) 11. A line with gradient of —3 passes through the points (3, k) and (k, 8). Find the value of k and hence express the equation of the line in the form ax + by = c, where a, b and c are constants. (3 marks) 12. Points L and M are equidistant from another point K. The bearing of L from K is 330°. The bearing of M from K is 220°. Calculate the bearing of M from L. (3 marks) 13. in this question, mathematical tables should not be used. A Kenyan bank buys and sells foreign currencies as shown below: 1 Hong Kong Dollar 1 South African Rand Buying (In Kenya Shillings) 9.74 12.03 Selling (In Kenya Shillings) 9.77 12.11 A tourist arrived in Kenya with 105 000 Hong Kong Dollars and changed the whole amount to Kenya Shillings. While in Kenya, she spent Sh 403 879 and changed the balance to South African Rands before leaving for South Africa. Calculate the amount in South African Rand. that she received. (3 marks) 14. A small cone of height 8cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm’. find the volume of the frustum. (3 marks) 15. The production of milk, in litres, of 14 cows on a certain day was recorded as follows: 22, 26, 15, 19, 20, 16, 27, 15, 19, 22, 21, 20, 22 and 28. Determine: (b) the median. (2 marks) 16. Given that Log 4 = 0.6021 and Log 6 = 0.7782, without using mathematical tables or a calculator, evaluate log 0.096. (3 marks) SECTION 11 (50 marks) Answer any five questions from this section in the spaces provided 17. (a) Solve the equation 3 — 1 24 x — 2 (4 marks) (b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136 m2. (i) Calculate the perimeter of the floor. (4 marks) (ii) A rectangular carpet is placed on the floor of the wall leaving an area of 64 m2. If the length of the carpet is twice its width. determine the width of the carpet. (2 marks) 18. Three business partners: Asha. Nangila and Cherop contributed Ksh 6 000, Ksh 85 000 and Ksh 105 000 respectively. They agreed to put 25% of the profit back into business each year. They also agreed to put aside 40% of the remaining profit to cater for taxes and insurance. The rest of the profit would then be shared among the partners in the ratio of their contributions. At the end of the first year, the business realised a gross profit of Ksh 225 000. (a) Calculate the amount of money Cherop received more than Asha at the end of the first year. (5 marks) (b) Nangila further invested Ksh 25 000 into the business at the beginning of the second year. Given that the gross profit at the end of the second year increased in the ratio 10:9, calculate Nangila’s share of the profit at the end of the second year. (5 marks) 19. The frequency table below shows the daily wages paid to casual workers by a certain company. (a) In the grid provided, draw a histogram to represent the above information. (5 marks) (b) (i) State the class in which the median wage lies. (1 mark) (ii) Draw a vertical line, in the histogram, showing where the median wage lies. ( 1 mark) (c) Using the histogram, determine the number of workers who earn Sh 450 or less per day. (3 marks) 20. In the diagram below, the coordinates of points A and B are (1, 6) and (15, 6) respectively. Point N is on OB and that 30N = 20B. Line OA is produced to L such that OL = 30A (a) Vector LN. (3 marks) (b) Given that a point M is on LN such that LM:MN = 3:4, find the coordinate of M. (2 marks) (c) If line OM is produced to T such that OM:MT = 6:1 (i) Find the position vector of

KCSE Past Papers 2017 Mathematics Alt B Paper 2 Section I (50 marks) Answer all the questions in this section in the spaces provided. 1. Evaluate 190.1 x 30, correct to 3 significant figures. (2 marks) 2. Find the sum of the first 10 terms in the Geometric Progression 3, 6, 12, (3 marks) 3. Given that 5, x, 35 and 84 are in proportion, find the value of x. (3 marks) 4. The base of a triangle is 3 cm longer than its height and its area is 35 cml. Determine the height and base of the triangle. (4 marks) 5. The figure below is a map of a piece of land on a grid of l cm squares. Estimate the area of the map in square centimetres. (3 marks) 6. A chord of a circle, radius 5 cm, subtends an angle of 30° at the centre of the circle. Determine the length of the chord, correct to 2 decimal places. (3 marks) 7. The extension (E), in cm, of a rubber band when pulled by a force (F) was found experimentally and recorded as shown in the table below: a) On the grid provided, draw a graph of extension(E) against force(F). (2 marks) (b) Use the graph to determine the extension when the force is 7 units. (1 mark) 8. The position of towns M and N are M(0 °, 5 l °W) and N(0 °, 37 °E). Find the distance between the two towns in kilometres, correct to one decimal place. (Take the radius of the earth as 6370km and π = 22/7) (3 marks) 9. The table below shows the values of y = 2sin(6 + 30°) for 0° S 95 360°. a) On the grid provided below, draw the graph of y = 2sin(0+ 30°) for 0° S 6 5 360 Use l cm for 30° on the x-axis and 2cm for one unit on the y-axis. (3 marks) (b) Use the graph to determine the value of y when 0 = 162°. (1 mark) 10. The figure below represents the distance covered by a car within a given period of time Find the average speed of the car in kilometres per hour. (3 marks) 11. Kitonga deposited Ksh50000 in a bank which paid compound interest at the rate of 10% per annum. Find the compound interest accrued by the end of the fourth year. (3 marks) 12. The number of different vehicles allowed through a road block was recorded as follows: Represent the above data in a pie chart. (3 marks) 13. Somi bought 2 pencils and 3 rubbers for Ksh 60 from a certain shop. Miheso bought l pencil and 2 rubbers for Ksh 35 from the same shop. Find the price of one pencil and that of one rubber. (3 marks) 14. (a) Find a matrix which, when multiplied by matrix M = gives the identity matrix. (2 marks) (b) Given that N = is a singular matrix, find the value of x. (2 marks) 15. A square QRST with vertices Q(l,1), R(3,1), S(3,3) and T(l,3) is transfomed by the matrix . Find: (a) the area of square QRST; (2 marks) (b) the area of image Q’R’S’T’. (2 marks) 16. Given that p = 6i + Zj, determine the magnitude of p, correct to 2 decimal places. (2 marks) Section II (50 marks) Answer any five questions from this section in the spaces provided. 17. The second term of an arithmetic progressi0n(AP) and fourth tenn of a geometric pr0gression(GP) are each 80. The sixth terms of the AP and GP are each 320. (a) Find: (i) the first term and the common differences of the AP. (2 marks) (ii) the first term and the common ratio of the GP. (2 marks) (b) Determine the 20*“ term of the AP. (2 marks) (c) Determine the difference between the sum of the first 12 terms of the GP and the sum of the first l2 terms of the AP. (4 marks) 18. (a) (i) Complete the table below for the values of y = x2 ex — 6 for -3 5 x S 4. (2 marks) (ii) Find y whenx = (l mark) (b) On the grid provided, draw a graph of y = xi —x ~ 6 for —3 5 x 5 4. (3 marks) (c) On the same grid, draw lme y = 3- x + l and hence solve the equation x2—x~6= ;3x+l. (4marks) 19. The marked price of a wall unit was Ksh 50 000. The price on hire purchase (HP) terms was 175% of the marked price. (a) A customer bought the wall unit in cash and was offered 10% discount. Find the amount of money the customer paid for the wall unit. (2 marks) (b) A second customer decided to purchase a similar wall unit on HP terms. (i) Determine the HP price. (2 marks) (ii) The customer paid 20% of the HP price as deposit and was to pay the balance in 28 equal monthly instalments. Find the amount of each monthly instalment. (3 marks) (c) Athird customer bought a similar wall unit in cash by taking a loan equal to the marked price. The loan was to be repaid in 15 months and the bank charged interest at the rate of 4% compounded monthly. (i) Find, correct to the nearest shilling, the amount of money the third customer paid the bank. (2 marks) (ii) Find the amount of money the third customer spent more than the marked price. (l mark) 20. The figure below shows triangle ABC IN which AB=6cm,BC=8cm,BD=4.2cm and AD=5.3cm.Angle CBD=45° Calculate to one decimal place the length of CD; (3 marks) size of angle ABD; (3 marks) size of angle BCD; (2 marks) area of triangle ABD. (2 marks) 21. Mawira, a poultry farmer carried out the following transactions during the month of February 2017: February l: Had Ksh 10000 carried forward from January 2017 3:Bought 2 bags poultry feed @Ksh 1250