**KNEC KCPE Past Papers Mathematics 2015**

## KCPE 2015

## MATHEMATICS

Time: 2 hours

**INSTRUCTIONS TO CANDIDATES (Please read these instructions carefully)**

1. You have been ‘given this question booklet and a separate answer sheet. The question booklet contains 50 questions.

2. D0 any necessary rough work in this booklet.

3. When you have chosen your answer, mark it on the AN SWER SHEET, not in this question booklet.

HOW TO USE THE ANSWER SHEET

4. Use only an ordinary pencil.

5. Make sure you have written on the answer sheet:

YOUR INDEX NUMBER

YOUR NAME

NAME OF YOUR SCHOOL

6. By drawing a dark line inside the correct numbered boxes mark your full Index Number (i.e. School Code Number and the three-ﬁgure Candidate’s Number) in the grid near the top of the answer sheet.

7. Do not make any marks outside the boxes.

8. Keep the sheet as clean as possible and do not fold it.

9. For each of the questions l—50 four answers are given. The answers are lettered A, B, C and D. In each case only

ONE of the four answers is correct. Choose the correct answer.

10. On the answer sheet the correct answer is to be shown by drawing a dark line inside the box in which the letter you have chosen is Written.

Example: » In the Question Booklet:

11. What is the value of 7

A. -30 6 .

B. 25

C.10

D. 28 The correct answer is C (10).

On the answer sheet:

11 [A1 [B1 [C] [D] 21 [A] [B] [C] [D] 31.[A] {B1 [01 [D]

_ In the set of boxes numbered 11, the box with the letter C printed in it is marked. ‘

11. Your dark line MUST be within the box.

I2. For each question ONLY ONE box is to be marked in each set of four boxes.

1. What is 6090428 written in words?

A. Sixty million ninety thousand four hundred and twenty eight.

B. Six million ninety thousand four hundred and twenty eight.

C. Sixty million nine thousand four hundred and twenty eight.

D. Six million nine thousand four hundred and twenty eight.

2. What is the value of (549 — 243 / 27 ) /27

A. 540

B. 118/2/3

c. 102%

D. 20

3. What is the value of 5/6 +7/4+7/12-1/3

A. 3/1/2

B. 1 /24/48

c. 4/2/21

D. 10/1/3

4. What is the value of 0.204 + (0.02 >< 0.17)?

A. 0.06

B. 0.6

C. 6

D. 60

5. What is 2806198 rounded off to the nearest tens?

A. 2806190

B. 2806210

C. 2806208

D. 2806200

6. What is the measure of the reﬂex angle Working Space PQR drawn below? ‘ A.315

B . 225°

C. 135°

D. 45°

7. What is the diﬁerence in the value of the square root of 2/14/25 and the square of 2/5?

A 2/2/5

B. 1/19/25

C. 1/11/25

D.. 11/5

8: In a kiosk the prices of food were shown as follows:

Items …………. ‘PRICE of Items in Shillings

Tea …………….20

Andazi …………..10

seefszew …………80

Fish …………….. 75

Ugali ………….25

Chapati …………20

Githeri………………..4

Three boys ordered beef stew, ugali and a cup of tea each while eight girls ordered ﬁsh and chapati each. What was their total bill?

A. sh 220

B. sh 1075

sh l 135

sh l 295

9. What is the simpliﬁed fonn of the expression it 3(3x—y+l)+2(3y—x+4)?.

A. 8x+5y+5

B. lh+9y+ll

7x+3y+ll

2x+2y+l0

10. A strip of metal was painted in three different colours. Two ﬁﬁhs of the strip was painted white, é of the strip was painted green and the remaining part was painted black. Which is the correct order of writing the fractions of the strip, painted from the smallest to the largest?

A 1/8 ,2/5 ,19/40

B- 19/40, 2/5, 1/8

C- 19/40,1/8,2/5

D- 2/5,1/8,19/40

11. Mwakio fenced a rectangular piece of land measuring 15 m and 31 m. He used six strands of wire, leaving a space of 5 m for the gate. What was the total length of the wire used?

A. 552 m

B. 522 m

547 m

87 M

12. The price of an item was reduced by sh 360. This represented a 20% discount. What was the price of the item after the discount?

A. sh 450

B. sh 1440

C. sh 1800

D. sh 2 160

13 What is the next number in the pattern 5, 13, 25,41,61, …..?

A 102

B 85

C 81

D 65

14. What is the value of U S(T-R)*2/(T+R)*2 ifS=3,R=4,T=9?

A. 1 2/13;

B. 1/2/17

C. 3

D. 9

15. The ﬁgure below is an incomplete Wﬂlikillg Spaee parallelogram KLMN. Complete the parallelogram.

16 What is the length of the diagonal KM in centimetres‘?

A. 2.5

B. 4.0

C. 5.7

D. 3.5

17 The marked price ofa T.V set is sh 20000. A 20% discolmt is allowed when buying the T.V. on cash. On hire purchase terms, only 12 monthly installments of sh 2000 each is paid. How much more does it cost to buy the T.V. set on hire purchase terms than cash?

A. sh 24 000

B. sh l6 000

C. sh 8 000

D. sh 4 000

18. Ngenya refuels his car aﬁer every two days, Kerubo refuels hers after every four days while Masai refuels his aﬁer every eight days. If they all reﬁrelled their cars on 3rd March 2013, on which date did they refuel their cars together again?

A. 17th March

B. llth March

C. 7th March

D.5th March

19 Pupils contributed some money to help needy people. They bought twenty four 2-kg packets of ﬂour, thirty six l-kg packets of ﬂour and a ﬁfty kilogram bag of sugar. The ﬂour was packed in 500g packets and the sugar in 250 g packets. How many people got both a packet of ﬂour and a packet of sugar?

A. 368

B. 200

C. 168

D. 120

20 A sales girl earns a salary of sh 3 000 per month plus a commission of 5% on the value of goods she sells above sh 10000. In a certain month, she earned a total of sh 7000. What was the value of goods she sold that month?

A. sh 70 000

B. sh 80 000

C. sh 90 000

D. sh 140 000

21. The table below shows arrival and departure times for buses from a certain company serving route P to T.

Town ………….Arrival Time …………… Departure Time

P ………. ………………… 7.30 a.m.

Q……………… 8.30 a.m. ……………………9.00 a.m.

R…………………… 11.30 a.m……………. 11.45 a.m.

S ………………….1.45 p.m. …………………1.55 p.m.

T …………………..4.15 p.m.

How long does a bus take to travel from town Q to town S‘?

A. 4 h 45 min

B. 4 h 55 min

C. 5 h 15 min

D 5 h 25 min

21 The volume of Water in a pond is 1084 m3. What is the amount of Water in litres?

A. 10840000

B. 1084000

C. 108400

D. 10840

22. In the triangle JKL below, construct the Working SPICE perpendicular bisectors of lines JL and KL to meet at point M. Join ML.

WHAT is the length of line ML?

.0575?’

A 1.2 cm

B 2.5 cm

C 8.0 cm

D. 4.8cm

23. The of ﬁve numbers is 9. Four of the numbers are 5, 10, 5 and 14. What is the median of the ﬁve numbers?

A. 5

B. 9

C. 10

D 11

24. The price of an item increased from sh 400 to sh 500. What was the percentage increase?

A. 125%

B. 80%

C. 25%

D. 20%

25. The pie-chart below shows the angles of Working Space the sectors representing the different types of Fruits sold by Mwanaisha.

A.30

B.70

C.120

D.150

26. The area of the curved surface of a cylinder is 1320 cm’. The height of the cylinder is 10 cm. What is the radius of I the cylinder in centimetres? (Take III = g) A 21 Mangoes

A 30

B 70

C 120

D 150

27. What is the value of n in the inequality 14n + 9< 41-6n

A n<6/1/4

B n<4

C n<2/1/2/

D n<1/2/5

28. The table below shows the number of patients who attended a clinic on certain days of the week. The number of male patients on Friday and that of children on Wednesday are not recorded.

Days ….. Monday …. Wednesday …. Friday59

Patients Male …….1…….. 74 ………. 5659

Female …….. 11…………0………..5959

29. A total of 623 patients attended the clinic that week. The number of patients who attended the clinic on Wednesday Was 226. How many more children than male patients attended the clinic that week?

A. l9

B. 23

C. 37

D. 56

29. What is the difference in value between the largest and the smallest 6-digit number formed using the digits 3, 0, 4, 5, 2, 9?

A. 954320

B. 203459

C. 930861

D. 750861

30. Akello and Muhu shared some oranges in the ratio 4:5 respectively. Muhu received 3 more oranges ﬂ1anAkello. How many oranges did Akello get?

A. 9

B. 12

C. l5

D. 27

31. A mother shared part of her money to three children Senda, Mila and Kilo. Mila received % while Kilo received % of the money. Senda received % of the remainder. What fraction of the money was shared out?

A. 30

B. 1

c. 15

D. 9

32 Which one of the following sets of measurements will form a right angled triangle when constructed?

A. 3 cm, 5 cm, 6 cm

B. 4 cm, 6 cm, 15 cm

C. 8 cm, 12-cm, 15 cm

D. 6 cm, 8 cm,10 cm

33 How many blocks are used to make the stack drawn below?

A. 60

B. 55

C. 53

D. 45

34 An aeroplane reached its destination on a Wednesday at 01 15h. The ﬂight had taken 4% hours. On what day and at what time in a.m./p.m. system did the plane start its ﬂight?

A. Tuesday 8.45 a.m.

B. Tuesday 8.45 p.m.

C. Wednesday 8.45 a.m.

D. Wednesday 8.45 p.m.

35 A piece of land in the shape of a trapezium is drawn on a map using the scale 1:500. The parallel sides are 5 cm and 2 cm, while the perpendicular distance between parallel sides is 4 cm. What is the actual area of the plot in ml?

A. 35000

B. 3500

C. 350

D. 35

36. In the ﬁgure below PQ is pamllel to RS. UT and VW are straight lines. What is the size of the angle marked x°?

A. 44°

B. 73° ,

C. 107°

D. 117°

37. In a certain country, the populatipn of goats is 51907. The number of female goats is 453 more than that of male goats. The number of male goats is 18549 and therestarekids. What is The number of kids?

A. 14356

B. 15262

C. 19002

D. 32905

38. The table below shows the postal charges, in Working Space shillings, on small packets in a certain year.

Aﬁbas from Mombasa sent the following packets:

A 900g packet to Uganda

A 5 kg packet to Ghana

A 251 g packet to China

How much money did he pay altogether?

A. sh3091

B. sh2884 C . sh2881

D. shl83l

_ 39. Six men can complete digging a shamba in 8 days. How many days will it take four men, working at the same rate, to complete digging the shamba?

A. 12

B. 5 /1/3

C .4

_D. 3

40. The ﬁgure below is made up of squares. How many squares are there altogether?

A. 14

B. 13

C.10

D.9

41 The prices of items sold in a shop were as follows:

Ikg sugar @ sh 120 _

1 kg rice @ sh 160

1 kg cookingfat @ sh 144

1 loaf of bread @ sh 45

42 Subira bought 2 kg of sugar, 1 kg of rice, %kg of cooking fat and 3 loaves of bread. She gave the shopkeeper a sh 1 000 note. What balance did she get?

A. sh 321

B. sh 393

. C. sh 531

D. sh 607

42 The diagram below represents a solid cube of side 6 cm from which a cylinder of diameter 2.8 cm has been removed.

What is the volumezgf the remaining solid in cm’? (Take 1: = —)

A. 36.96 7

B. 68.16

C. 179.04

D. 2 1 6.0

43. A plot of land is in the shape of a rhombus of side 200 m. The length of one of the diagonals is 240 m. What is the area of the plot in hectares?

A. 3.84

B. 4

C. 4.8

D. 7.68

44. Ndemo bought 2r oranges while Maua Working Space bought 4s oranges. Haifa bought 2“ oranges more than a half the total number ‘ of oranges bought by both Nderno and Maua. How many oranges did they buy altogether?

A. 3r + 6s + 2 ,

B. 4r + 8s + 2 ,

C. 6r + 12s + 2

D. 3r + 6s —- 2

45. The graph below shows joumeys of Musa and Serah. Musa travelled from P to Q while Serah travelled from Q to P.

What was the difference intheir average speeds?

A. 0

B. 10

C. 70

D. 80

46 On a certain day a miller prepared 63 kilograms of uji ﬂour and 286 kilograms of ugali ﬂour. The miller charged sh 7 per kilogram of uji ﬂour and sh 4 per kilogram of ugali ﬂour. The millconsumed 7 litres of fuel costing sh 108 per litre. The miller also paid sh 250 as wages and sh 300 as loan repayment.

What was the miller’s proﬁt that day?

A. i sh 279

B. sh 579

C. sh 927

D. sh 948 .

47 Mundia bought 90 bananas for sh 450. After selling all the bananas he made a proﬁt of 60%. What was the selling price per banana?

A. sh 5

B. sh 8

C. sh 270

D. sh 720

48 Ngoko deposited sh 120000 in a bank that gave compound interest at the rate of 6% per annum. What was the amount in the bank aﬂer 2 years?

A. sh 134 832

B. sh 134400

C. sh 127 200

D. sh 14832 5

49 Senteu left home at 6.00 a.m. for school which is 8 km away. He cycled at a speed of 6km/h. After cycling for 4km the bicycle had a puncture which took him 15 minutes to repair. He continued cycling at the same speed. At what time did he arrive at school?

A. 6.40 a.m.

B. 6.55 a.m.

C. 7.20 a.m.

D. 7.35 am.

50. In the triangle EFG shown below, ‘Working Space construct a circle that touches the sides of ~ the triangle.

What is the radius of the circle, in \ centimetres?

A. 2.5

B. 5.0

c. 5.6

D. 11.2

## 2015 KCPE Mathematics Past Paper-Marking Scheme/Answers

1.B 2.D 3.A 4.D 5.D 6.B 7.C 8.C 9.C 10.A 11.B 12.B 13.B 14.C 15.D 16.C 17.A 18.B 19.C 20.D 21.C 22.C 23.A 24.D 25.C 26.B 27.A 28.A 29.D 30.C 31.D 32.D 33.C 34.C 35.C 36.B 37.A 38.A 39.A 40.A 41.B 42.C 43.A 44.B 45.B 46.A 47.B 48.B 49.D 50.A