KCPE 2010 Mathematics
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Question 1 of 50
1. Question
2 pointsWhich one of the following is 60,400,502 in words?
Correct
Incorrect

Question 2 of 50
2. Question
2 pointsWhat is the number 5826.3407 rounded off to 3 decimal places?
Correct
Incorrect

Question 3 of 50
3. Question
2 pointsHow many days are there between 15th July and 15th September?
Correct
Incorrect

Question 4 of 50
4. Question
2 pointsWhat is the place value of digit 6 in the number 706053?
Correct
First step is to introduce commas from the rightmost side after every three numbers. Thus this becomes 706,053. From this we can then easily read 3 as being in the ones column, 5 in the tens column, 0 in the hundreds, 6 in the thousands, 0 in the ten thousands and 7 in the hundred thousands.
Incorrect
First step is to introduce commas from the rightmost side after every three numbers. Thus this becomes 706,053. From this we can then easily read 3 as being in the ones column, 5 in the tens column, 0 in the hundreds, 6 in the thousands, 0 in the ten thousands and 7 in the hundred thousands.

Question 5 of 50
5. Question
2 pointsWhat is the value of
Correct
Incorrect

Question 6 of 50
6. Question
2 pointsTeckla bought the following items from a shop
3kg of sugar @sh 68
250g of tea leaves @sh 85
2bars of soap @sh38
1kg of cooking fat for sh 109
2kg packet of rice for sh149
Teckla paid for the items using sh1000 note. How much balance did she receive?Correct
3kg of sugar @sh 68 becomes 3 x 68 = 204
250g of tea leaves @sh 85 = 85
2bars of soap @sh38 becomes 2 x 38 = 76
1kg of cooking fat for sh 109 =109
2kg packet of rice for sh149 = 149
Thus the total becomes 204+85+76+109+149 = 623
Subtracting this from the 1000 paid with we get = 1000623 = 377
Incorrect
3kg of sugar @sh 68 becomes 3 x 68 = 204
250g of tea leaves @sh 85 = 85
2bars of soap @sh38 becomes 2 x 38 = 76
1kg of cooking fat for sh 109 =109
2kg packet of rice for sh149 = 149
Thus the total becomes 204+85+76+109+149 = 623
Subtracting this from the 1000 paid with we get = 1000623 = 377

Question 7 of 50
7. Question
2 pointsIn the figure below, lines EF and GH are parallel. Lines JK and MN transversal which intersect at V.angle MQF=50???? and angles HSK=30?
What is the size of angle QVS?
Correct
Incorrect

Question 8 of 50
8. Question
2 pointsWhich one of the numbers below is the square of 2 4/5?
Correct
Firstt convert the number into an improper fraction i.e this becomes 14/5.
Squaring this number we get = 14/5 x 14/5 = 196/25.
We then? convert this number back into its mixed fraction number = 7 21/25
Incorrect
Firstt convert the number into an improper fraction i.e this becomes 14/5.
Squaring this number we get = 14/5 x 14/5 = 196/25.
We then? convert this number back into its mixed fraction number = 7 21/25

Question 9 of 50
9. Question
2 pointsWhat is the next number in the pattern 10, 11, 15, 24, 40, 65?
Correct
We first try and find the pattern here. Subtracting the successive number we get the differences as follows: 1, 4, 9, 16, 25
Here we see that the numbers are squares of 1, 2, 3, 4, 5 and thus the next number should be the square of 6 i.e. 6 x 6 = 36
Adding 36 to the last number in our series we get = 65 + 36 = 101
Incorrect
We first try and find the pattern here. Subtracting the successive number we get the differences as follows: 1, 4, 9, 16, 25
Here we see that the numbers are squares of 1, 2, 3, 4, 5 and thus the next number should be the square of 6 i.e. 6 x 6 = 36
Adding 36 to the last number in our series we get = 65 + 36 = 101

Question 10 of 50
10. Question
2 pointsWhat is the simplified form of? 5x + 1/4 (8x2y) ?
Correct
We first solve what is in the brackets i.e. 1/4 (8x2y) which becomes (1/4 x 8x) – (1/4 x 2y) = 2x – 1/2y
Adding this to the whole equation we get = 5x + 2x – 1/2y which becomes 7x – 1/2y
Incorrect
We first solve what is in the brackets i.e. 1/4 (8x2y) which becomes (1/4 x 8x) – (1/4 x 2y) = 2x – 1/2y
Adding this to the whole equation we get = 5x + 2x – 1/2y which becomes 7x – 1/2y

Question 11 of 50
11. Question
2 pointsBelow is a bus timetable from town J to town P
TOWN ARRIVAL TIME DEPARTURE TIME J 7.00 a.m. K 9.30 a.m. 10.00 a.m. L 11.15 a.m. 11.30 a.m. M 1.50 p.m. 12.25 p.m. N 1.10 p.m. 1.20 p.m. P 1.50 p.m. 2.00 p.m. How long did the bus take to travel from town K to town N?
Correct
Here we just find the time difference from when it left town K (departure time – 10.00a.m) and the time it arrived at town N (1.10 p.m. or 13.10hrs written in 24hr clock system)
Thus the difference becomes 13.10 – 10.00 = 3.10 or 3hrs 10min
Incorrect
Here we just find the time difference from when it left town K (departure time – 10.00a.m) and the time it arrived at town N (1.10 p.m. or 13.10hrs written in 24hr clock system)
Thus the difference becomes 13.10 – 10.00 = 3.10 or 3hrs 10min

Question 12 of 50
12. Question
2 pointsThe perimeter of a rectangular plot of land is 280 meters. The width of the plot is 60 meters. What is the length of the plot?
Correct
Perimeter is the sum of all the lengths and widths of a shape. For a rectangle, this is given as L+ W + L + W or 2(L + W)
where L is the Length of the rectangle and W is the Width
Thus if we have the width W given as 60m, we get
2(L+60) = 280
Opening the brackets we get
2L + 120 = 280
Taking 120 to the other side of the equals sign, the plus changes to a minus and we get
2L = 280 – 120
2L = 160
Dividing both sides of the equation by 2 we get
L = 80Incorrect
Perimeter is the sum of all the lengths and widths of a shape. For a rectangle, this is given as L+ W + L + W or 2(L + W)
where L is the Length of the rectangle and W is the Width
Thus if we have the width W given as 60m, we get
2(L+60) = 280
Opening the brackets we get
2L + 120 = 280
Taking 120 to the other side of the equals sign, the plus changes to a minus and we get
2L = 280 – 120
2L = 160
Dividing both sides of the equation by 2 we get
L = 80 
Question 13 of 50
13. Question
2 pointsPoint S and line QR are shown in the space below. Using a pair of compasses, drop a perpendicular from point S to meet line QR at T
What is the length of line ST?Correct
Incorrect

Question 14 of 50
14. Question
2 pointsWhat is the value of??
Correct
Incorrect

Question 15 of 50
15. Question
2 pointsTumbo paid sh 10,200 for a cupboard after getting a discount of 15 %. What was the market price of cupboard?
Correct
With a discount of 15% the new price is sh.10,200
100% – 15% = 85%
Thus this 85% = sh 10,200
So 100% price becomes =100/85 x 10,200
= sh 12,000
Incorrect
With a discount of 15% the new price is sh.10,200
100% – 15% = 85%
Thus this 85% = sh 10,200
So 100% price becomes =100/85 x 10,200
= sh 12,000

Question 16 of 50
16. Question
2 pointsThree bells are set to ring out at intervals of 4 minutes, 6 minutes and 9 minutes respectively. If they all ring together now, after how many minutes will they ring together next?
Correct
Here we are supposed to find the LCM of the three number which will give us the next time the three bells will ring together
LCM
4
6
9
2
2
3
9
2
1
3
9
3
1
1
3
3
1
1
1
Thus we have LCM = 2 x 2 x 3 x 3 = 36
Thus the bells will ring together again after 36 minutes
Incorrect
Here we are supposed to find the LCM of the three number which will give us the next time the three bells will ring together
LCM
4
6
9
2
2
3
9
2
1
3
9
3
1
1
3
3
1
1
1
Thus we have LCM = 2 x 2 x 3 x 3 = 36
Thus the bells will ring together again after 36 minutes

Question 17 of 50
17. Question
2 pointsA rectangular container is 2m long, 0.9m wide and 2.5m high. The container has water to a height of 1.5m. How much more water in litres is needed to fill the container?
Correct
The volume of the container which is not filled is found as = L x W x H = 2 x 0.9 x (2.5 – 1.5) = 1.8 cubic metres
1 cubic metre (1m3) = 1000 litres
So 1.8 cubic meters = 1.8 x 1000 = 1800 Litres
Incorrect
The volume of the container which is not filled is found as = L x W x H = 2 x 0.9 x (2.5 – 1.5) = 1.8 cubic metres
1 cubic metre (1m3) = 1000 litres
So 1.8 cubic meters = 1.8 x 1000 = 1800 Litres

Question 18 of 50
18. Question
2 pointsThe fractions 3/7, 2/5, 5/8, 1/2 are to be arranged from the smallest to the largest. Which one of the following is the correct order?
Correct
Incorrect

Question 19 of 50
19. Question
2 pointsWhich one of the following properties is TRUE for both a square and a rhombus?
Correct
Incorrect
Diagonals and angles are equal only in regular shapes like squares and rectangles. Rhombuses have the two diagonals measuring different sizes with one longer than the other.
Two right angles add upto 180 degrees. Opposite angles add up to 180 degrees only in squares and rectangles as well

Question 20 of 50
20. Question
2 pointsThe number of birds observed in a certain area during certain months of the year is shown in the table below.
MONTHS APRIL
MAY
JUNE
JULY
AUGUST
NUMBER OF BIRDS 96
104
80
118
94
Which one of the following numbers is the highest mean of the birds recorded into two consecutive months?
Correct
The 2 consecutive months with high number would be July and August.
The sum for the 2 months would be found as = 118 + 94 = 212
The mean is found as =212 divide by 2 = 106
Incorrect
The 2 consecutive months with high number would be July and August.
The sum for the 2 months would be found as = 118 + 94 = 212
The mean is found as =212 divide by 2 = 106

Question 21 of 50
21. Question
2 pointsConstruct a triangle XYZ in which XY = 7.2cm, YZ = 5.8cm, ZX = 6.2cm
What is the size of angle XYZ?
Correct
Incorrect

Question 22 of 50
22. Question
2 pointsWhat is the value of x in the equation
?
Correct
We begin by opening the brackets
1/2x + 1/2 + 2/3x – 1/3 = 5
Grouping together like terms we get
(1/2x + 2/3x) + (1/2 – 1/3) = 5
=(3/6x + 4/6x) + (3/6 – 2/6) = 5
=7/6x + 1/6 = 5
Thus 7/6x = 5 – 1/6 when the +1/6 crosses the equals sign the plus changes to minus (1/6)
7/6x = 4 5/6
7/6x = 29/6
x = 29/6 x 6/7
x = 29/7? = 4 1/7
Incorrect
We begin by opening the brackets
1/2x + 1/2 + 2/3x – 1/3 = 5
Grouping together like terms we get
(1/2x + 2/3x) + (1/2 – 1/3) = 5
=(3/6x + 4/6x) + (3/6 – 2/6) = 5
=7/6x + 1/6 = 5
Thus 7/6x = 5 – 1/6 when the +1/6 crosses the equals sign the plus changes to minus (1/6)
7/6x = 4 5/6
7/6x = 29/6
x = 29/6 x 6/7
x = 29/7? = 4 1/7

Question 23 of 50
23. Question
2 pointsA packet is in the form of a pyramid with a square base. Which one of the following statements is true of the number of faces, edges and vertices the packet has?
Correct
Incorrect

Question 24 of 50
24. Question
2 pointsA factory hired 9 people to complete a piece of work in 15 hours. How many more hours did it take them to complete the work if 3 people did not turn up?
Correct
If 9 people = 15 hours, then (9 – 3) people = ?
9 x 15 = 6 x y where y is the number of hours taken by 6 people
y = (9 x 15)/6 = 45/2? = 22 1/2 hours
Now the question asks, how many more hours did it take to complete the work?
So we have 22 1/2 – 15 = 7 1/2 hours
Incorrect
If 9 people = 15 hours, then (9 – 3) people = ?
9 x 15 = 6 x y where y is the number of hours taken by 6 people
y = (9 x 15)/6 = 45/2? = 22 1/2 hours
Now the question asks, how many more hours did it take to complete the work?
So we have 22 1/2 – 15 = 7 1/2 hours

Question 25 of 50
25. Question
2 pointsWhich one of the following sets of measurements will form a right angled triangle when drawn?
Correct
For a right angled triangle, we look for the measurements which will have the sum of the squares of two sides equal to the square of the remaining one i.e. the hypotenuse
(Length x Length)? + (Width x Width) = Hypotenuse x Hypotenuse
Incorrect
For a right angled triangle, we look for the measurements which will have the sum of the squares of two sides equal to the square of the remaining one i.e. the hypotenuse
(Length x Length)? + (Width x Width) = Hypotenuse x Hypotenuse

Question 26 of 50
26. Question
2 pointsA pick up track was loaded with 4 cartons of fat and 60 bales of flour. Each carton contained twenty four 250g packets of fat. The mass of each empty carton was 500g. Each bale contained twelve 2kg packets of flour. What is the total load in tones?
Correct
Incorrect

Question 27 of 50
27. Question
2 pointsKamau bought a piece of land for 2million shillings. He subdivided it into 25 plots of equal area. He then sold all the plots and made a 20 ?profit.what was the selling price of each plot?
Correct
Incorrect

Question 28 of 50
28. Question
2 pointsThe table below shows how Kigen utilizes his piece of land.
Purpose Homestead
Maize Cultivation
Tea Cultivation
Grazing
Number of Hectares 3/4
1 1/4
1
1 1/2
Which one of the bar graphs below correctly represents the information above?
Correct
Incorrect

Question 29 of 50
29. Question
2 pointsIrimu deposited sh 10,000 in? a financial institution that offered simple interest at the rate of 5% per annum. Ndege deposited sh 10,000 in? a financial institution that offered compound interest at the rate of 5% per annum. How many much more interest had Ndege?s money earned than Irimu?s after 2 years?
Correct
Incorrect

Question 30 of 50
30. Question
2 pointsAt a sports meeting the number of men was 200. The number of girls was three times that of men and 120 more than that of women. The number of boys was 30 more than that of girls. What was the total number of people at the meeting?
Correct
Incorrect

Question 31 of 50
31. Question
2 pointsThe cash price of a radio was sh 4500. The hire purchase price of the radio was 60 ?more than the cash price. Muya bought the radio on hire purchase terms. He paid a deposit and 12 equal monthly installments of sh 540 each. How much did he pay as deposit?
Correct
Incorrect

Question 32 of 50
32. Question
2 pointsA rectangle 25cm long and 12cm wide has the same area as a triangle whose height is 10cm. What is the length of the base of the triangle?
Correct
Incorrect

Question 33 of 50
33. Question
2 pointsWhat is the value of
0.77 + 5.00 of (0.570.33) + 0.88 x 0.4?
Correct
Incorrect

Question 34 of 50
34. Question
2 pointsA salesman is paid a salary of sh 5,000 per month. He is also paid a 2.5% commission on the sales above sh 100,000. If the salesman sold goods worth sh 500,000 in a certain month. What was his total earnings?
Correct
Incorrect

Question 35 of 50
35. Question
2 pointsOn a map whose scale is 1:50 000 a piece of land is represented by a rectangle measuring 3cm by 2cm. What is the actual size of this land in hectares?
Correct
Incorrect

Question 36 of 50
36. Question
2 pointsThree schools Mwangaza, Kivuli, and Nuru received a total donation of 165 text books. Kivuli got 8 books more than Mwangaza while Nuru got half the total of what Mwangaza and Kivuli got. If the number of books donated to Mwangaza is represented by the letter m which one of the following equations can be used to get the value of m?
Correct
Incorrect

Question 37 of 50
37. Question
2 pointsAt the beginning of year 2005, there were 800 pupils in a school of whom 55% were boys. At the end of the year the number of girls had increased by 20% and that of boys had decreased by 10%. What was the total number of pupils in the school at the end of the year?
Correct
Incorrect

Question 38 of 50
38. Question
2 pointsThe height of an isosceles triangle is 4cm. Each of the two equal sides measures 5cm. What is the area of the triangle?
Correct
Incorrect

Question 39 of 50
39. Question
2 pointsThe table below shows the number of crates of soda Mutuma sold in one week. The number of crates sold on Friday was not recorded.
DAY OF WEEK MON
TUE
WED
THUR
FRI
SAT
SUN
NUMBER OF CRATES 8
10
11
18
–
16
8
If the total number of crates of soda sold in seven days was 84, what was the median sale?
Correct
Incorrect

Question 40 of 50
40. Question
2 pointsA teacher had a certain number of books. She gave 1/3 of the books to John and 1/4 to Lucy. She also gave 1/10 of the remaining books to Patel. If the teacher was left with 18 books, how many books had she given to Lucy?
Correct
Incorrect

Question 41 of 50
41. Question
2 pointsThe perimeter of a rectangle is 24 cm .The length of the rectangle is 2cm more than the width. What is the area of the rectangle?
Correct
Incorrect

Question 42 of 50
42. Question
2 pointsA cyclist took 15 minutes to travel from his home to town at a speed of 18km/h. He took 24 minutes to travel back from town to his home. What was his speed in km/h from town to his home?
Correct
Incorrect

Question 43 of 50
43. Question
2 pointsSera shared part of her land among her four children. Their shares were 0.29, 0.26, 0.21 and 0.14 of the land. If the part that was shared was 36 hectares, how many hectares of the land remained?
Correct
Incorrect

Question 44 of 50
44. Question
2 pointsA farmer harvested 144 bags of maize in one season. In the second season, the yield increased in the ratio 4:3. The farmer supplied all the bags of maize harvested in the second season equally to three millers. How many bags of maize did each miller get?
Correct
Incorrect

Question 45 of 50
45. Question
2 pointsA rectangular water tank whose base is 1.5m by 0.5m is to be filled with water using 50litre containers. How many such containers will be required to fill the tank to a height of 1 meter?
Correct
Incorrect

Question 46 of 50
46. Question
2 pointsA watch loses 30 seconds every hour. If the watch was set right on Sunday at 11:30pm.what day and time did it show after 10 hours?
Correct
Incorrect

Question 47 of 50
47. Question
2 pointsThe graph below shows the journey of two motorists Karimi and Nzomo
Correct
Incorrect

Question 48 of 50
48. Question
2 pointsThe figure below represents a half of a cylindrical piece of wood of diameter 28cm and a length of 30 cm.
What is the surface area of the solid in cm2? (Take pi = 22/7 )
Correct
Incorrect

Question 49 of 50
49. Question
2 pointsOn the line QR given below construct a triangle PQR such that PQ=PR=7cm.
Construct a bisector of angle PQR to meet line PR at X.
What is the size of angle QXR?
Correct
Incorrect

Question 50 of 50
50. Question
2 pointsThe figure below shows a pattern of shapes.
Which one of the shapes below should be drawn in the blank box to continue with the pattern?
Correct
Incorrect