KCPE Past Papers Mathematics 2014
1. ln a certain country the population was Working Space 38898756. What was the population to thc nearest ten thousand?
2. What is the largest 6-digit number written in words that can be formed using the symbols 4,2,0,8,3 and 6?
A. Four hundred and twenty thousand eight hundred and thirty six
B. Eight hundred and sixty four thousand three hundred and twenty
C. Eight million and sixty four thousand three hundred and twenty
D. Two hundred and three thousand four hundred and sixty eight
3. What is the value of
26+s2+62 —5e+7><2 3+2 ‘
D. 24 5
4. In the number 3078642, the total value of digit 7 is added to the total value of digit 4. Which one of the following is the correct answer?
5. What is the value of
(l/5+ l/4of l/2-2/5 +l/3)/3
6. Triangle XYZ shown below, has been Working Space drawn accurately.
What is the measure of angle ZXY?
7. The following are prime factors of three numbers:
my 21 >< 5
(m) 24 >< 32
What is the L.C.M. ofthe three numbers?
8. Which one of the following statements is correct?
9. Which one of the following statements is true about the number of faces and edges of a square based pyramid?
A 5 faces and 5 edges
B 4 faces and 6 edges
C 5 faces and 8 edges
D 4 faces and 4 edges
10. In a certain month a businessman made a proﬁt of sh 8 000. The following month his proﬁt was sh 12 000. What was the percentage increase of the proﬁt?
A. 66 § %
11. A rectangular tank is 7.5 m long, 5 in wide and 3.2 m high. How many litres ofwater can it hold when full?
C. 12 000
D. 120 000
12. What is the value of x in the equation x+3(x+3)=23?
13. Tuku spent é of his money on school uniforms, % on books, % of the remainder on food and saved the rest. What total fraction of his money did he save and spend on books?
14. Kerubo bought a T.V. set by paying a deposit of sh 2 400 plus 15 equal monthly instalments of sh 500 each. The hire purchase price was 10% more than the marked price. What was the marked price?
A. sh 8 910
B. sh 9 000
C. sh 9 900
D. sh 11 000
15. The ﬁgure below represents a right-angled triangle PQR. The area of the triangle is 24 cm? and the height is 6 cm.
What is the length of the longest side?
A. 7.2 cm
B. 8 cm
C. 10 cm
D. 14 cm
16. The perimeter of a rectangular plot of land is 57.98 m. Ifthe Width of the plot is 8.6 m. What is its length?
A. 20.39 m
B. 24.69 m
C. 40.78 m
D. 49.38 m
17. The following are properties of a certain quadrilateral 1
(1) opposite sides are parallel
(ii) all sides are equal
(m) apposite angles are equal
(iv) diagonals are unequal and bisect
each other at right angles
What is the name of the quadrilateral?
18. Construct a circle centre O using line ROS, given below, as diameter. Working Space
Construct angle QRS I 30°. Mark point Q on the circumference and draw line QO. What is the size of angle QOS?
19. The table below shows the number of fruits sold by Fatuma and Bidii on a certain day. The number ofBananas sold by Fatuma and Bidii has not been shown.
How many more bananas did Bidii sell than Fatuma?
20. Below are four different types of triangles. I Working Space
Which one of the following pairs of triangles correctly describes the types of triangles above?
A. (i) and (m) are isosceles triangles
B. (ii) and (iv) are scalene triangles
C. (ii) and (m) are right angled triangles
D. (i) and (ii) are equilateral triangles
21. A road measuring 5 cm on a map has an actual distance of 15 kilometres. What is the scale used in drawing the map?
A. 1 :3
C. 1:3 000
D :3 00 000
_ 22. A car dealer was left with sh 855 000 after paying out a 5% commission to an agent for the sale of a car. What was the selling price of the car?
A. sh 17 100 000
B. sh 900 000
C. sh 897 750
D. sh 812 250
made by Bakari and Ouma. Both started at 7.00 am; Bakari started from town J to town K While Ouma started from
30 minutes. How far from town J was A. 300 km
B .240 km
C. 180 km
D. 140 km
25. An open cylindrical tank has an internal Working Space diameter of 5.6 cm and an internal height of4 cm. The inside ofthe tank was painted. What area of the tank, in square centimetres, was painted? (Take Tc I 27-2)
26. Kibet left school by bicycle at 8.00 am and took 1 % hours to reach the market 20 km away. Akinyi left the school for the market by car at 8.30 am. The average speed of the car was 80 km/h. What was the difference between their arrival times?
A. 1 hour 15 minutes
B. 45 minutes
C. 30 minutes
D. 15 minutes
Z7. Muli invested sh 10 000 in a bank which paid compound interest at the rate of 8% per annum. How much money did Muli have in the bank after two years, altogether?
A. sh l 664
B. sh 11 600
C. sh 11 664
D. sh 10 864
28. What is the next number in the pattern 7,12,19,30,43,*:>
29. The table below shows a bus timetable for Isiolo to Mombasa route.
How long is a bus expected to take to travel from Nyeri to Mtito Andei?
A. 10 h 15 min
B. 10 h 30 min
C. 10 h 45 min
30. Below is part ofa rhombus PQRS. Line Working Space 1. Sixty people were hired to complete construction of a road in 6 days. Forty of the people did not turn up. How many more days did it take the remaining people to complete the construction?
31. QS is one ofthe diagonals and line QR is one of the sides of the rhombus. Complete the rhombus
What is the difference in the lengths of the diagonals?
A. 6 cm
B. 6.5 cm
C. 12.5 cm
D. 18.5 cm
32. Kadogo was born on 4th January 2009. How old was he on 4th March 2011?
A. 2 years 62 days
B. 2 years 61 days
C. 2 years 59 days
D. 2 years 60 days
33. In the ﬁgure below, lines PQ and TS are parallel. Lines RQ and RS are equal. Angle QPR = 36° and angle STR = 50°. P. What isthe size
of angle PQS?
° C. 94°
34. The area ofa square garden is 3136 mz. What is the length of one side of the garden in metres?
35. The table below shows the International Postage charges For surface mail.
Chebet sent a 150 g letter to her friend in Nigeria, a 1.5 kg letter to her friend in Europe and a 1 kg letter to a friend in America. I-low much did she pay for the postage of the letters?
A. sh l 890
B. sh 1 920
C. sh 2 285
D. sh 2 485
36 A train left station P on Tuesday at 20 15h and took 4% hours to reach town Q. On what day and at what time in am/pm system did the train arrive at station Q? A. Wednesday 12.45 a.m
B. Wednesday 12.45 p.m
C. Tuesday 12.45 a.m
D. Tuesday 12.45 p.m
37 Maria bought 3 trays of eggs each containing 30 eggs. She paid sh 270 for each tray of eggs. Nine eggs were eaten at home and the rest were sold. If Maria made a proﬁt of 20%, how much did she sell each egg?
A. sh 15.50
B. sh 12.00
C. sh 10.80
D. sh 8.00
38 The perimeter of a rectangular ﬁeld is 56 m. The length of one of its sides is 7 m. What is the area of the ﬁeld?<
A. 392 m2
39 The total amount of milk produced by a certain cow in ten days was 115 litres. The daily produce in nine of the days was recorded in litres as l3,l2,l5,9,8.7,l3,l3 and 15. What was the median produce in the ten days?
40 The number of people Who visited a game park on Monday was 65, on Tuesday was 49 and on Wednesday was 58. On Thursday the number of people was 12 less than those Who visited the park on Wednesday. The number of people Who visited the game park on Friday was half the number that visited the game park on Saturday. A total of 374 people visited the game park during the six days. How many people visited the game park on Friday?
41 Which one of the expressions below is the simplest form of ?
4(2r + p) — r
C. D_ 7l;_18’
42 Simuyu paid sh 1 560 to buy a blanket after getting 2%% discount. How much less would he have paid had he been offered a 4% discount?
A. sh 24
B. sh 40
C. sh 64
D. sh 1536
43. The table below shows how Mutua Working Space
If a pie chart was drawn to represent the use of the farm, by how many degrees more would the angle sector representing sugarcane growing be than the angle sector representing grazing?
44. A lorry was packed with cartons each utilized his fann.containing packets of cooking fat. There were packets of 500 g and 250 g. The total mass of the packets was 900 kg. If the number of 500 g packets was 1000, what was the number of 250 g packets?
A. 1 600
45. A design was made up of straight edges of Working Space length 2.6 cm and arcs of circles of radii 1.4 cm as shown in the ﬁgure below 2.6 cm
What is the area ofthe design?
(Take 1: 1 %)
A. 16.00 cm
B. 22.16 cm
C. 25.24 cm
D. 28.32 cm
46. The area of a square plot of land is 1156 1n2. The plot is to be fenced with three strands of wire. What is the length of the wire that is needed?
A. 867 m
B. 408 m
C. 136 m
47. A tank contained 22.5 m3 of water. More water was poured into the tank at the rate of 1.45 m3 per minute. The tank was full at the end 0f30 minutes. What is the capacity ofthe tank in litres?
A. 23 950
B. 43 500
C. 66 000
D. 718 500
48. Wanja bought 2 kg ofpeas @sh 80, 3 kg of maize @ sh 60 and 10 kg of potatoes for sh 100. If Wanja spend sh x to buy the peas, sh y to buy the maize and sh z to buy the potatoes, which one of the equations below represents the total amount of money spent by Wanja?
A. x + y + 2 I 440
B. x + y + z I 240
C. x + y + z I 340
49. Mwachia and Mbuu shared some money in the ratio 5:2. Mbuu received sh 30 less than Mwachia. How much money did Mbuu get?
A. sh 20
B. sh 50
C sh 70
D sh 80
50. The ﬁgure below shows a pattern of shapes. Which one of the shapes below should be drawn in the blank box above to continue with the pattern?
2014 KCPE Mathematics Past Paper-Marking Scheme/Answers
1.A 2.B 3.C 4.B 5.D 6.B 7.D 8.C 9.C 10.B 11.D 12.C 13.A 14.B 15.C 16.A 17.C 18.D 19.A 20.A 21.D 22.B 23.C 24.D 25.C 26.B 27.C 28.B 29.A 30.B 31.C 32.B 33.B 34.D 35.D 36.A 37.B 38.D 39.D 40.C 41.D 42.A 43.D 44.A 45.C 46.B 47.C 48.A 49.A 50.B