KCPE 2005 Mathematics
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Question 1 of 50
1. Question
2 pointsWHich one of the following is 50205082 in words?
Correct
Try putting first commas to separate the number in thousands as follows 50,205,082 and then read it.
Incorrect
Try putting first commas to separate the number in thousands as follows 50,205,082 and then read it.
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Question 2 of 50
2. Question
2 pointsWhat is the place value of the digit 6 in the number 2649053?
Correct
Again ifrst, put commas from the left-most side, grouping the nmbers in thousands (3 digits) to get the place value of the number ie. 2,649,053
Incorrect
Again ifrst, put commas from the left-most side, grouping the nmbers in thousands (3 digits) to get the place value of the number ie. 2,649,053
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Question 3 of 50
3. Question
2 pointsWhat is the number 29.34046 rounded off to the nearest thousandth?
Correct
Incorrect
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Question 4 of 50
4. Question
2 pointsWhat is the smallest number that can be divided by 12, 18 and 27 without a remainder?
Correct
This is the LCM of the three numbers
Incorrect
This is the LCM of the three numbers
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Question 5 of 50
5. Question
2 pointsA shopkeeper bought 30 eggs. He then sold each egg at sh.6, making a profit of 20%. How much had he paid for the eggs?
Correct
By selling each egg at sh.6, the shopkeeper obtained = 30 x 6 = Sh.180
If he made a profit of 20% on this amount ie sh.180 = 120%;
then the buying price was = 100%/120% x 180
= Sh.150Incorrect
By selling each egg at sh.6, the shopkeeper obtained = 30 x 6 = Sh.180
If he made a profit of 20% on this amount ie sh.180 = 120%;
then the buying price was = 100%/120% x 180
= Sh.150 -
Question 6 of 50
6. Question
2 pointsWhat is the value of 8 ? 0.02 + 1.35 x 0.4?
Correct
Using BODMAS, we would start with the division first, then multiplication and finally addition last.
(8 ? 0.02) + 1.35 x 0.4
=400 + (1.35 x 0.4)
=400 + 0.54
=400.54
Incorrect
Using BODMAS, we would start with the division first, then multiplication and finally addition last.
(8 ? 0.02) + 1.35 x 0.4
=400 + (1.35 x 0.4)
=400 + 0.54
=400.54
-
Question 7 of 50
7. Question
2 pointsThe marked price of a blouse was Sh. 750. Halima bought five such blouses after being given a 10% discount. How much did she pay for the five blouses?
Correct
After discount, purchase price was 90% of the marked price.
Thus, purchase price of 1 blouse = 90% x 750 = Sh.675
Cost of 5 blouses = 5 x 675 = Sh.3375
Incorrect
After discount, purchase price was 90% of the marked price.
Thus, purchase price of 1 blouse = 90% x 750 = Sh.675
Cost of 5 blouses = 5 x 675 = Sh.3375
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Question 8 of 50
8. Question
2 pointsKatua bought the following items from a kiosk:
2kg of rice for Sh. 152
1.5kg of meat @ Sh. 160
2 loaves of bread @ Sh. 23
What balance did he receive if he paid for the items using a Sh. 1000 note?
Correct
Total cost for rice = 152
Total cost for meat = 1kg = 160, Thus 1.5kg = 1.5 x 160 = 240
Total cost of bread = 1 loaf=Sh. 23, Thus 2 loaves = 2 x 23 = 46
Total cost of all items = 152 + 240 + 46 = Sh.438
Balance = 1000 – 438 = Sh. 562
Incorrect
Total cost for rice = 152
Total cost for meat = 1kg = 160, Thus 1.5kg = 1.5 x 160 = 240
Total cost of bread = 1 loaf=Sh. 23, Thus 2 loaves = 2 x 23 = 46
Total cost of all items = 152 + 240 + 46 = Sh.438
Balance = 1000 – 438 = Sh. 562
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Question 9 of 50
9. Question
2 pointsIn the figure below, RPQ is a triangle. Point O is inside the triangle. Join RO, PO and QO.
What is the size of the obtuse angle POQ?
Correct
Incorrect
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Question 10 of 50
10. Question
2 pointsThe ages, in years, of 10 pupils in a class are: 16, 18, 15, 14, 17, 16, 14, 13, 19 and 14. What is the median age of the pupils?
Correct
To find the median age, we arrange all the numbers in ascending order and look for the middle number. i.e.
13, 14, 14, 14, 15, 16, 16, 17, 18, 19
The middle number here lies between 15 and 16, indicated in bold above.
Thus, median = (15 + 16) / 2 = 15.5
Incorrect
To find the median age, we arrange all the numbers in ascending order and look for the middle number. i.e.
13, 14, 14, 14, 15, 16, 16, 17, 18, 19
The middle number here lies between 15 and 16, indicated in bold above.
Thus, median = (15 + 16) / 2 = 15.5
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Question 11 of 50
11. Question
2 pointsWhich one of the following statements is true about all quadrilaterals?
Correct
Incorrect
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Question 12 of 50
12. Question
2 pointsA container of volume 1 cubic metre is full of juice. The juice is then poured into five litre containers. How many such containers are used?
Correct
1 cubic metre = 1000 litres
Thus, number of containers = 1000 ? 5
=200 containers
Incorrect
1 cubic metre = 1000 litres
Thus, number of containers = 1000 ? 5
=200 containers
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Question 13 of 50
13. Question
2 pointsA road is represented by a length of 3.2cm on a map. What is the actual length of the road in kilometres if the scale used is 1:50000?
Correct
1km = 100000cm
Thus, scale of 1:50000 means 1cm rep 50000/100000 = 0.5km
Thus 3.2cm = 3.2 x 0.5 = 1.6km
Incorrect
1km = 100000cm
Thus, scale of 1:50000 means 1cm rep 50000/100000 = 0.5km
Thus 3.2cm = 3.2 x 0.5 = 1.6km
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Question 14 of 50
14. Question
2 pointsIn the triangle KLM drawn below, construct the perpendicular bisector of line KM to cut line KM at N and line KL at P.
What is the size of the acute angle KPN?
Correct
Incorrect
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Question 15 of 50
15. Question
2 pointsWhat is the value of x in 3(2x + 1) + 5(x + 4) = 61?
Correct
First we open the brackets by multiplying what is inside the brackets and what is out
3(2x + 1) + 5(x + 4) = 61? becomes? 6x + 3 + 5x + 20 = 61
Thus we have 11x + 23 = 61
11x = 61 – 23
11x = 38
Dividing both sides by 11 we obtain x = 38/11
38/11 written as a mixed fraction becomes 3 5/11
Incorrect
First we open the brackets by multiplying what is inside the brackets and what is out
3(2x + 1) + 5(x + 4) = 61? becomes? 6x + 3 + 5x + 20 = 61
Thus we have 11x + 23 = 61
11x = 61 – 23
11x = 38
Dividing both sides by 11 we obtain x = 38/11
38/11 written as a mixed fraction becomes 3 5/11
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Question 16 of 50
16. Question
2 pointsWhich one of the following is the correct net for an open cube?
Correct
Incorrect
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Question 17 of 50
17. Question
2 pointsSixteen workers can dig a field in 12 days. How many more workers are required so as to do the work in 8 days?
Correct
16 workers = 12 days
Therefore, 8 days = (12/8) x 16
= 24 workers
More workers = 24 – 16 = 8 more workers
Incorrect
16 workers = 12 days
Therefore, 8 days = (12/8) x 16
= 24 workers
More workers = 24 – 16 = 8 more workers
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Question 18 of 50
18. Question
2 pointsThe top of a ladder, 26 metres long, leans on a vertical wall. The ladder touches the wall at a height of 10 metres. What is the horizontal distance from the bottom of the ladder to the wall?
Correct
We first begin by drawing the sketch below
From the triangle so obtained and by Pythagoras’ Theorem,
Hypotenuse2 = Base2 + Height2
Thus (26 x 26) = Base2 + (10 x 10)
Base2 = 676 – 100 = 576
Base = ?576? = 24 m
Incorrect
We first begin by drawing the sketch below
From the triangle so obtained and by Pythagoras’ Theorem,
Hypotenuse2 = Base2 + Height2
Thus (26 x 26) = Base2 + (10 x 10)
Base2 = 676 – 100 = 576
Base = ?576? = 24 m
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Question 19 of 50
19. Question
2 pointsThe table below represents the sales of milk in litres by a vendor in five days. The sale for Thursday is not shown.
DAYS MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
NUMBER OF LITRES 25
19
23
22
One litre of milk was sold for Sh.25. The vendor got a total of Sh.2925 for the sale of milk during the five days. How many more litres of milk did the vendor sell on Thursday than on Tuesday?
Correct
To obtain total quantity of milk sold we divide total sales by the cost per litre. i.e.
2925 ? 25 = 117 litres
To obtain quantity sold on Thursday, we subtract the total minus the sum of the quantity sold on Mon, Tue, Wed and Fri.
= 117 – (25 +19 + 23 +22)
=117 – 89
=28 litres
The question is however asking for ‘how many more litres’ which is the difference between the quantities of the two days i.e.
=28 – 19
=9 litres
Incorrect
To obtain total quantity of milk sold we divide total sales by the cost per litre. i.e.
2925 ? 25 = 117 litres
To obtain quantity sold on Thursday, we subtract the total minus the sum of the quantity sold on Mon, Tue, Wed and Fri.
= 117 – (25 +19 + 23 +22)
=117 – 89
=28 litres
The question is however asking for ‘how many more litres’ which is the difference between the quantities of the two days i.e.
=28 – 19
=9 litres
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Question 20 of 50
20. Question
2 pointsThe table below shows the postal rates for sending a money order.
VALUE OF ORDER (in sh)
COMMISSION
Not exceeding 500
Sh 42
501 – 1000
Sh 114
1001 – 3000
Sh 174
3001 – 5000
Sh 209
5001 – 10000
Sh 295
10001 – 20000
Sh 441
20001 – 30000
Sh 617
School fees for two children in the same school was sh. 9,400 and sh.11,800. The father bought one money order to pay the total amount of fees. How much more would he have spent had he bought two separate money orders for the fees?
Correct
Buying separate orders, the cost would have been 295 + 441 = Sh 736
Buying one order would be the cost of an order worth (9400+11800) = cost of an order for 21,200 = 617
Increased cost would have been = 736 – 617 = 119
Incorrect
Buying separate orders, the cost would have been 295 + 441 = Sh 736
Buying one order would be the cost of an order worth (9400+11800) = cost of an order for 21,200 = 617
Increased cost would have been = 736 – 617 = 119
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Question 21 of 50
21. Question
2 pointsWhat is the next number in the pattern 1, 3, 7, 15,….?
Correct
We first begin by subtracting to get the difference between every two successive numbers
i.e. 3-1 = 2 and 7 – 3 = 4 and 15 – 7 = 8
Thus the difference appears as 2, 4, 8,…
From this pattern we can see that the next number is just a multiplication by 2 of the previous number and so the next difference should be = 8 x 2 = 16
So the next number in the series should be = 15 + 16 = 31
Incorrect
We first begin by subtracting to get the difference between every two successive numbers
i.e. 3-1 = 2 and 7 – 3 = 4 and 15 – 7 = 8
Thus the difference appears as 2, 4, 8,…
From this pattern we can see that the next number is just a multiplication by 2 of the previous number and so the next difference should be = 8 x 2 = 16
So the next number in the series should be = 15 + 16 = 31
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Question 22 of 50
22. Question
2 pointsThe table below shows Sagana – Nanyuki train fares for adults.
STATION NANYUKI
NARO MORU
KIGANJO
KARATINA
SAGANA
NANYUKI –
20
35
55
70
NARO MORU 20
–
20
35
50
KIGANJO 35
20
–
20
35
KARATINA 55
35
20
–
20
SAGANA 70
50
35
20
–
The fare for children is half that of adults. Taipei and his two children travelled from Nanyuki to Sagana. On their return journey they first paid the fare to Karatina. They later paid the fare to Nanyuki. How much more money did they spend on travel for their return journey?
Correct
Incorrect
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Question 23 of 50
23. Question
2 pointsThe figure below is a trapezium. Lines HG = 11cm, GF = 5cm, EF = 15cm and HE = 3cm. Line EF is parallel to HG and angle FEH = angle EHG = 90?
What is the area of the figure?
Correct
Incorrect
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Question 24 of 50
24. Question
2 pointsA rectangular container 45cm long and 25cm wide was full of water. After removing 22.5 litres of the water, the level of water became 4cm high. What was the height of the container?
Correct
Capacity of the tank is given by its volume (45 cm = 0.45 m), (25 cm = 0.25 m)
1 cubic metre = 1000 litres
When 22.5litres are removed, this represents h1 = h – 4
Thus, Vol = [0.45 x 0.25 x (h-0.04)] x 1000 = 22.5
[0.1125(h – 0.04)] 1000 = 22.5
112.5 (h – 0.04) = 22.5
112.5h – 4.5 = 22.5
112.5h = 22.5+4.5
112.5h = 27
Thus h = 27 / 112.5
h = 0.24 m? = 24 cm
Incorrect
Capacity of the tank is given by its volume (45 cm = 0.45 m), (25 cm = 0.25 m)
1 cubic metre = 1000 litres
When 22.5litres are removed, this represents h1 = h – 4
Thus, Vol = [0.45 x 0.25 x (h-0.04)] x 1000 = 22.5
[0.1125(h – 0.04)] 1000 = 22.5
112.5 (h – 0.04) = 22.5
112.5h – 4.5 = 22.5
112.5h = 22.5+4.5
112.5h = 27
Thus h = 27 / 112.5
h = 0.24 m? = 24 cm
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Question 25 of 50
25. Question
2 pointsNekesa has p pencils. Rhoda has 3 more pencils than Nekesa. Karani has two pencils less than the total number that Nekesa and Rhoda have. How many pencils do they have altogether?
Correct
Nekesa = p
Rhoda = p + 3
Karani = p + p + 3 – 2 = 2p + 1
Thus total = p + p + 3 + 2p + 1
= 4p + 4
Incorrect
Nekesa = p
Rhoda = p + 3
Karani = p + p + 3 – 2 = 2p + 1
Thus total = p + p + 3 + 2p + 1
= 4p + 4
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Question 26 of 50
26. Question
2 pointsCherono spent sh 8100 on food in May. In the month of June, she spent 10% less on food than in May. How much money did she spend on food in June?
Correct
Spending 10% less means she spent = 100% – 10% = 90%
Thus, money spent = 90% x 8100 = Sh 7290
Incorrect
Spending 10% less means she spent = 100% – 10% = 90%
Thus, money spent = 90% x 8100 = Sh 7290
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Question 27 of 50
27. Question
2 pointsAmina shared money among her three children. The first got 1/3 while the second got 1/4 of the money. The third got 1/2 of what remained. Amina was left with sh 1500. How much money had she before it was shared?
Correct
Total for first and second children, we find the LCM of 4 and 3 and add
= 1/3 + 1/4 = (4+3)/12 = 7/12
Remainder = 1 – 7/12 = 5/12
Third got = 1/2 x 5/12 = 5/24
Total = 7/12 + 5/24 = (14+5)/24
=19/24
Remainder = 1 – 19/24 = 5/25 = Sh 1500
Thus 1 = 24/24 = 24/5 x 1500
= Sh 7200
Incorrect
Total for first and second children, we find the LCM of 4 and 3 and add
= 1/3 + 1/4 = (4+3)/12 = 7/12
Remainder = 1 – 7/12 = 5/12
Third got = 1/2 x 5/12 = 5/24
Total = 7/12 + 5/24 = (14+5)/24
=19/24
Remainder = 1 – 19/24 = 5/25 = Sh 1500
Thus 1 = 24/24 = 24/5 x 1500
= Sh 7200
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Question 28 of 50
28. Question
2 pointsA motorist travelling at an average speed of 84km/h took 2 hours and 30 minutes to travel from town M to town N. She then took 3 hours and 20 minutes to travel back to town M. What was the average speed for the whole journey?
Correct
Distance from Town M to N = speed x Time
= 84 km/h x 2 1/2 hours = 84 x 5/2 = 210km
Total time taken for the whole journey = 2 30/60 + 3 20/60
= 2 1/2 + 3 1/3
=5 + (1/2 + 1/3)
=5 5/6 hours = 35/6 hours
Average speed = (Total Distance from M to N and back) / Total time
=(210 + 210) ? 35/6
=420 ? 35/6
= 420 x 6/35
= 72 km/h
Incorrect
Distance from Town M to N = speed x Time
= 84 km/h x 2 1/2 hours = 84 x 5/2 = 210km
Total time taken for the whole journey = 2 30/60 + 3 20/60
= 2 1/2 + 3 1/3
=5 + (1/2 + 1/3)
=5 5/6 hours = 35/6 hours
Average speed = (Total Distance from M to N and back) / Total time
=(210 + 210) ? 35/6
=420 ? 35/6
= 420 x 6/35
= 72 km/h
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Question 29 of 50
29. Question
2 pointsIn the figure below, line PQ is parallel to line SR and QT is equal to TR. Angle QPT = 31? and angle TSR = 57?
What is the size of angle PQR?
Correct
Incorrect
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Question 30 of 50
30. Question
2 pointsThe charges for sending a telegram were as follows:
The first 10 words or less Sh 15.
Any additional words sh 1.50 each.
Abbreviations and punctuationmarks are counted as words.
A tax of 20% is charged on the amount.
The total amount to be paid is rounded off to the nearest 50 cents. What was the cost of sending the following telegram?
JOHN MLAMA P.O. BOX 360 NYERI GOING TO KISUMU AFTER THE EXAMINATION KOIGI
Correct
Incorrect
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Question 31 of 50
31. Question
2 pointsBelow is a travel graph showing the journey of a motorist travelling from town L to town K and back, and that of a cyclist travelling from town L to town K.
How far from town L was the cyclist when he met the motorist travelling back to town L?
Correct
Incorrect
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Question 32 of 50
32. Question
2 pointsWhat is the value of 1/3(2x + 4y2) + 5p – 8 when 1/3 when p = 6, x = 2p and y = 1/2x – 1?
Correct
Incorrect
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Question 33 of 50
33. Question
2 pointsA machine packs 250 two-kilogram packets of sugar while another packs 375 one-kilogram packets each day. How many tonnes of sugar altogether, do the two machines pack in five days?
Correct
Incorrect
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Question 34 of 50
34. Question
2 pointsA square of side 2 cm is cut from each corner of a rectangular paper measuring 8 cm by 12 cm. Which one of the following statements is true?
Correct
Incorrect
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Question 35 of 50
35. Question
2 pointsA salesman is paid a salary of sh 1,500 per month plus a commission of 2 1/2% on the sale of goods above sh 10,000. In one month he was paid a total of sh 1,800. How much was the sale of the goods?
Correct
Total commission paid = 1,800 – 1,500 = sh 300
Assuming total sale of goods = x
2 1/2% of x = 300
0.025 x x = 300
Thus x = 300 ? 0.025
x = 12,000
Since this commission sale is for goods above 10,000 then
Total sale = 12,000 + 10,000
= sh 22,000
Incorrect
Total commission paid = 1,800 – 1,500 = sh 300
Assuming total sale of goods = x
2 1/2% of x = 300
0.025 x x = 300
Thus x = 300 ? 0.025
x = 12,000
Since this commission sale is for goods above 10,000 then
Total sale = 12,000 + 10,000
= sh 22,000
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Question 36 of 50
36. Question
2 pointsIn a group of 126 spectators the ratio of men to women was 3:4. What is the new ratio if 2 more men and 8 more women joined the group of spectators?
Correct
Number of men originally = 3/(3+4) x 126
=3/7 x 126 = 54
Number of women = 126 – 54 = 72
New number of men = 54 + 2 = 56
New number of women = 72 + 8 = 80
New ratio = 56:80 which on simplifying becomes = 7:10
Incorrect
Number of men originally = 3/(3+4) x 126
=3/7 x 126 = 54
Number of women = 126 – 54 = 72
New number of men = 54 + 2 = 56
New number of women = 72 + 8 = 80
New ratio = 56:80 which on simplifying becomes = 7:10
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Question 37 of 50
37. Question
2 pointsA clock was set on Monday at 8.30am. On Tuesday, the following day, the clock showed 8.45pm when the correct time was 8.30pm. How many minutes was the clock gaining in every 24 hours?
Correct
From Monday 8.30am to Tuesday 8.30pm = 36 hours
Time gained = 8.45 – 8.30 = 0.15 = 15 minutes
Thus, if 36 hours = 15 min gained,
24 hours = 24/36 x 15
= 10 minutes
Incorrect
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Question 38 of 50
38. Question
2 pointsThe base of a closed cuboid measures 4 cm by 5 cm and the height is 7 cm. The base and the top parts of the cuboid are painted. What is the total surface area of the parts which are not painted?
Correct
Total surface area not painted = Area of all sides = 2(7 x 4) + 2(7 x 5)
= (2 x 28) + (2 x 35)
= 56 + 70
= 126 cm2
Incorrect
Total surface area not painted = Area of all sides = 2(7 x 4) + 2(7 x 5)
= (2 x 28) + (2 x 35)
= 56 + 70
= 126 cm2
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Question 39 of 50
39. Question
2 pointsDuring an election the winning candidate got 0.425 of the votes cast while the other two candidates got 0.39 and 0.183 respectively. There were 48 spoilt votes. How many votes did the winning candidate get?
Correct
Total of the fractions = 0.425 + 0.39 + 0.183 = 0.998
Ratio of spoilt votes = 1 – 0.998 = 0.002
If 0.002 represents 48 votes,
Then winning votes = 0.425/0.002 x 48
=10,200 votes
Incorrect
Total of the fractions = 0.425 + 0.39 + 0.183 = 0.998
Ratio of spoilt votes = 1 – 0.998 = 0.002
If 0.002 represents 48 votes,
Then winning votes = 0.425/0.002 x 48
=10,200 votes
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Question 40 of 50
40. Question
2 pointsA motorist started on a journey of 250 km at 6.30 am. travelling at an average speed of 100km/h. After travelling for 150km, the car got a puncture and it took him 30 minutes to change the wheel. He then continued with the rest of the journey at an average speed of 80km/h. At what time did he reach his destination?
Correct
Time for first part of journey = Distance ? Speed
= 150 ? 100
=1.5 hours = 1 hour 30min
Time for second part of journey = Distance ? Speed
= (250 – 150) ? 80
= 100 ? 80
=1.25 hours = 1 hour and 15 minutes
Total time taken for journey = 1 1/2 + 1/2 + 1 1/4
=3 1/4 hours
Arrival time = 06.30 + 3.15 = 09.45 am.
Incorrect
Time for first part of journey = Distance ? Speed
= 150 ? 100
=1.5 hours = 1 hour 30min
Time for second part of journey = Distance ? Speed
= (250 – 150) ? 80
= 100 ? 80
=1.25 hours = 1 hour and 15 minutes
Total time taken for journey = 1 1/2 + 1/2 + 1 1/4
=3 1/4 hours
Arrival time = 06.30 + 3.15 = 09.45 am.
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Question 41 of 50
41. Question
2 pointsFour children bought 53 oranges altogether. Nekoye bought x oranges and Kamau bought 9 oranges more than Nekoye. Fatuma bought twice as many oranges as Nekoye. Atieno bought as many oranges as both Kamau and Fatuma bought. Which one of the following equations can be used to find the number of oranges Nekoye bought?
Correct
Nekoye = x
Kamau = x + 9
Fatuma = 2 x
Atieno = x + 9 + 2x = 3x + 9
Total = 53 Oranges
Equation = x + x + 9 + 2x + 3x + 9 = 53
which becomes 7x + 18 = 53
Incorrect
Nekoye = x
Kamau = x + 9
Fatuma = 2 x
Atieno = x + 9 + 2x = 3x + 9
Total = 53 Oranges
Equation = x + x + 9 + 2x + 3x + 9 = 53
which becomes 7x + 18 = 53
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Question 42 of 50
42. Question
2 pointsWaithera borrowed sh 10 000 for a period of two years. She was charged compound interest at the rate of 15% per year. How much interest did she pay altogether?
Correct
Sum after one year = (100 + 15)% = 115% x 10,000
= 11,500
Sum after second year = 115% x 11,500
= 13,225
Total interest paid = 13,225 – 10,000
= sh 3,225
Incorrect
Sum after one year = (100 + 15)% = 115% x 10,000
= 11,500
Sum after second year = 115% x 11,500
= 13,225
Total interest paid = 13,225 – 10,000
= sh 3,225
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Question 43 of 50
43. Question
2 pointsThe figure below represents a table mat made up of a rectangle and four semi-circles. the rectangle measures 14 cm by 7 cm.
What is the area of the table mat? (Take ? =? 22/7)
Correct
Here we add the area of the rectangle and that of the four semi-circles.
If you observe keenly, we can have the two semicircles of 14 cm diameter join to form a full circle and the two semicircles of 7 cm diameter join to form a full circle too.
Thus we look for the area of one rectangle and two circles of diameter 7 cm (radius is 3.5 cm) and 14 cm (radius is 7 cm)
Area =(L x W) + ? r?12 + ? r 22
= (7 x 14) + (22/7 x 3.5 x 3.5) + (22/7 x 7 x 7)
= 98 + 38.5 + 154
=290.5 cm2
Incorrect
Here we add the area of the rectangle and that of the four semi-circles.
If you observe keenly, we can have the two semicircles of 14 cm diameter join to form a full circle and the two semicircles of 7 cm diameter join to form a full circle too.
Thus we look for the area of one rectangle and two circles of diameter 7 cm (radius is 3.5 cm) and 14 cm (radius is 7 cm)
Area =(L x W) + ? r?12 + ? r 22
= (7 x 14) + (22/7 x 3.5 x 3.5) + (22/7 x 7 x 7)
= 98 + 38.5 + 154
=290.5 cm2
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Question 44 of 50
44. Question
2 pointsThe cash price of a tractor is 1.8 million shillings. Rotich bought it on hire purchase terms. The total amount he paid was 30% more than the cash price. He paid a deposit of 660 000 and the remainder in 24 equal monthly installments. How much was each installment?
Correct
Price paid on Hire Purchase = 130% x 1,800,000 = sh 2,340,000
Hire Purchase price – Deposit = Total for installments
2,340,000 – 660,000 = 1,680,000
Monthly installment = Total installments?? Number of months
= 1,680,000 ? 24
= sh 70,000
Incorrect
Price paid on Hire Purchase = 130% x 1,800,000 = sh 2,340,000
Hire Purchase price – Deposit = Total for installments
2,340,000 – 660,000 = 1,680,000
Monthly installment = Total installments?? Number of months
= 1,680,000 ? 24
= sh 70,000
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Question 45 of 50
45. Question
2 pointsOmala and Mwite had packets of tea to be packed into cartons. Each carton holds 46 packets. Omala packed 63 cartons and remained with 24 packets while Mwite packed 54 cartons and remained with 19 packets. How many more packets of tea had Omala than Mwite?
Correct
Omala had = (63 x 46) + 24 = 2922 packets
Mwite had = (54 x 46) + 19 =2503 packets
Number of packets more = 2922 – 2503 = 419 packets
Incorrect
Omala had = (63 x 46) + 24 = 2922 packets
Mwite had = (54 x 46) + 19 =2503 packets
Number of packets more = 2922 – 2503 = 419 packets
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Question 46 of 50
46. Question
2 pointsThe figure shown below, is formed by two right-angled triangles ABD and BCD.
What is the area of the triangle BCD?
Correct
Incorrect
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Question 47 of 50
47. Question
2 pointsThe population of a village is represented by the pie chart below:
If there were 300 girls, how many more boys than men were there?
Correct
Fraction for girls = 360? – (80? +40? + 90?)
= 360? – 210? = 150?
If 150? = 300 girls,
Then boys = 90/150 x 300 = 180 boys
Men = 40/150 x 300 = 80 men
Thus difference = 180 – 80
=100 boys
Incorrect
Fraction for girls = 360? – (80? +40? + 90?)
= 360? – 210? = 150?
If 150? = 300 girls,
Then boys = 90/150 x 300 = 180 boys
Men = 40/150 x 300 = 80 men
Thus difference = 180 – 80
=100 boys
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Question 48 of 50
48. Question
2 pointsComplete the construction of a parallelogram PQRS, where line PR is a diagonal.
What is the length of line QS?
Correct
A parallellogram has opposite sides equal and opposite angles equal.
Connect point S to R and draw a line parallel to PQ , having the same length as PQ. This will give point S and the whole parallelogram can then be drawn and QS measured.
Incorrect
A parallellogram has opposite sides equal and opposite angles equal.
Connect point S to R and draw a line parallel to PQ , having the same length as PQ. This will give point S and the whole parallelogram can then be drawn and QS measured.
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Question 49 of 50
49. Question
2 pointsWhich is the correct order of writing the fractions 3/4, 7/9, 4/5 and 9/11 from the largest to the smallest?
Correct
First, find the L.C.M. of the base numbers i.e. 4, 9, 5 and 11 which in this case would be 1980
Putting all the numbers under the LCM number we get
3/4 = 1485/1980
7/9 = 1540/1980
4/5 = 1584/1980
9/11 = 1620/1980
Arranging these number in order from largest to smallest would be
1620/1980, 1584/1980, 1540/1980 and then 1485/1980
which translates to 9/11, 4/5, 7/9, 3/4
Incorrect
First, find the L.C.M. of the base numbers i.e. 4, 9, 5 and 11 which in this case would be 1980
Putting all the numbers under the LCM number we get
3/4 = 1485/1980
7/9 = 1540/1980
4/5 = 1584/1980
9/11 = 1620/1980
Arranging these number in order from largest to smallest would be
1620/1980, 1584/1980, 1540/1980 and then 1485/1980
which translates to 9/11, 4/5, 7/9, 3/4
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Question 50 of 50
50. Question
2 points
Which one of the shapes below would fit in the dotted space in the pattern above?
Correct
To correctly answer this, look at the number of triangles that are increasing as you move downwards i.e. first line has one triangle, second line has three, third has five, fourth has seven. Since we keep increasing successive triangles by two, the next line should have nine and this is only in option D.
Incorrect
To correctly answer this, look at the number of triangles that are increasing as you move downwards i.e. first line has one triangle, second line has three, third has five, fourth has seven. Since we keep increasing successive triangles by two, the next line should have nine and this is only in option D.