## QUESTIONS Attempt all questions in the spaces provided

1. Evaluate (3mks)
-19 + (6-8) Ã· 2 x 5
16 Ã· 4 x -3
2. Express the following numbers as products of their prime factors (3mks)
1. 357
2. 5929
3. Find the GCD of 72, 96 and 300 (3mk)
4. Express 0.872872872â¦â¦â¦â¦.as a fraction (3mks)
5. Show how the following calculations are performed using number line (4mks)
1. -2 + (-2) + -3 + (-1)
2. -7 â (-8)
6. Evaluate (3mks)
4 Â½ - (5 1/5 + 4/5 of 25/3)
7. Charles spent Â¼ of his net salary on school fees. He spent Â¼ of the remainder on electricity and water bills. He then spent 1/9 of what was left on transport. If he finally had sh 3400, what was his net January salary (3mks)
8. Which of the following numbers is divisible by 11, 3, and 4 (3mks)
1. 2596
2. 5896
3. 1052
9. All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
1. Write down the number formed. (1mk)
2. Test whether or not the number formed in 16 (a) above is divisible by 11. (2mks)
10. A man is x years old now. In 10 years time, he will be twice as old as he was 5 years ago. How old will he be in 10 years time? (3mks)
11. Evaluate: Â¼ + 1/5 Ã· Â½ of 1/3
Â½ of ( 4\5 â Â¾ + Â½ )                   (3mks)
12. The sum of 3/8, 20/3 and x is 657/120. Find x. (2mks)
13. Evaluate without using tables or calculators. (3mks)
0.036 Ã 0.0049
0.07 Ã 0.048
14.
15.
16. A shop keeper sells a shirt for Kshs.350 thereby making a profit of 40%. Calculate the buying price of the shirt (3mks)
17. Evaluate:     (3marks)
44 -(-28)  -  82 Ã -12 - 24
12 Ã -2        96 Ã· -12 Ã 9
18.                      ]
19. A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n. (3marks)
20. Reduce the following expression onto a single fraction.(3 marks)
4x - 5  - 2x - 1
2            6
21.
22. Convert 7 into a decimal (3mks)
8
23. If X: Y =1:2 and Y: Z =3:5 find X: Y: Z (3mks)
24. A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes. Find the maximum area of one plot. (4marks)
25. The ratio of Johnâs earnings to Musaâs earnings is 5:3 if johns earningâs increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musaâs earnings if the sum of their new earnings is sh 9600. (3mks)
26. Convert into percentage (3mks)
1. 0.03%
27. Three Lorries, each making five trips per day, transport 2500 crates from a factory to a distributor in two days. How many Lorries, each making six trips a day, are needed to transport 10000 such crates in a day? (3mks)

## MARKING SCHEME Attempt all questions in the spaces provided

1. Evaluate (3mks)
-19 + (6-8) Ã· 2 x 5
16 Ã· 4 x -3
num: -19 + (-2) Ã· 2 Ã 5
-19 - 2  Ã· 2 Ã 5
-19 - 1 Ã 5
- 24

Den: 16 Ã· 4 x -3
4  Ã  -3
- 12

-24
-12
= 2
2. Express the following numbers as products of their prime factors (3mks)
1. 357 3 Ã 7 Ã 17
2. 5929 7 Ã 3 Ã 29
3. Find the GCD of 72, 96 and 300 (3mk)
 2 72 96 30 3 36 48 15 12 16 5
= 2 Ã 3
= 6
4. Express 0.872872872â¦â¦â¦â¦.as a fraction (3mks)
r = 0.8728
10r = 8.72828
-100r = 87.2828
1000r = 872.828
10000r = 8728.28
100r = 87.28
9900r
=  8641   r = 8641
9900       9900         9900
5. Show how the following calculations are performed using number line (4mks)
1. -2 + (-2) + -3 + (-1) = -8
2. -7 â (-8) = +1
6. Evaluate (3mks)
4 Â½ - (5 1/5 + 4/5 of 25/3) 7. Charles spent Â¼ of his net salary on school fees. He spent Â¼ of the remainder on electricity and water bills. He then spent 1/9 of what was left on transport. If he finally had sh 3400, what was his net January salary (3mks)
1/x Ã fees
1/4 of 3/4x = bills
3/16x = bills
1/9 of 3/16x
133/144x â transport
131/144x - 3400
8. Which of the following numbers is divisible by 11, 3, and 4 (3mks)
1. 2596
+(2 + 9) - (5 + 6) = 0 it is divisible by 11
2 + 5 + 9 + 6 = 22 - not divisible by 3
96/4 = 15 - divisible by 4
2. 5896
+(5 + 9) - (8 + 6) = 0 - divisible by 11
5 + 8 + 9 + 6 = 28 - not divisible by 3
96 is divisible by 4
3. 1052
(1 + 5) - (10 + 2) = 4 - divisible by 11
1 + 0 + 5 + 2 = 8 - not divisible by 3
52 - divisible by 4
9. All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
1. Write down the number formed. (1mk)
7 5 3 2
2. Test whether or not the number formed in 16 (a) above is divisible by 11. (2mks)
(7 + 3) - (5 + 2) = 3
not divisible by 11
10. A man is x years old now. In 10 years time, he will be twice as old as he was 5 years ago. How old will he be in 10 years time? (3mks)
 now 5 years ago 10 years time man x (x - 5) 2(x - 5)
x + 10 = 2x - 5
x - 2x = -5 - 10
-x = -15
x = 15

10 years time
- x + 10 = 15 + 10
= 25
11. Evaluate: Â¼ + 1/5 Ã· Â½ of 1/3
Â½ of ( 4\5 â Â¾ + Â½ )                   (3mks)
Num: 1/4 + 1/5 Ã· 1/2 of 1/3
1/4 + 1/5  Ã· 1/6
1/4 + 6/5 = 19/20

Den: 1/2 of (4/5 - 3/4 + 1/2)
1/2 of 11/20
11/40

19/20 - 11/40
= 17/40
12. The sum of 3/8, 20/3 and x is 657/120. Find x. (2mks)
3/820/3 + x = 657/120
169/24 + x = 657/120169/24
x = 657/120169/24
x = 17/30
13. Evaluate without using tables or calculators. (3mks)
0.036 Ã 0.0049
0.07 Ã 0.048
0.036 Ã 0.0049   Ã 1000000
0.07 Ã 0.048    Ã 1000000
36 Ã 49
7 Ã 48 Ã 100
= 21/40
14.
15.
16. A shop keeper sells a shirt for Kshs.350 thereby making a profit of 40%. Calculate the buying price of the shirt (3mks)
sp = 350
350 - 140%
- 100%
350 Ã 100
140
b.p = 250
17. Evaluate:     (3marks)
44 -(-28)  -  82 Ã -12 - 24
12 Ã -2        96 Ã· -12 Ã 9
44 + 28
-24
= 72
-24
64x - 12 - 24
= 72/-24 - 28/-72
= -47/18
18.
19. A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n. (3marks)
 3 3 7 11 13 7 1 7 11 13 11 1 1 11 13 15 1 1 1 13 1 1 1 1
3 Ã 7 Ã 11 Ã 13 = 3003
n = 3003 + 1 = 3004
20. Reduce the following expression onto a single fraction.(3 marks)
4x - 5  - 2x - 1
2            6
3(4x - 5) - (2x - 1) = (12x - 15) - (2x - 1)
2            6               6
= 12x - 15 - 2x + 1
6
= 12x - 2x - 15 + 1
6
= 10x - 14
6
21.
22. Convert 7 into a decimal (3mks)
8
0.875
23. If X: Y =1:2 and Y: Z =3:5 find X: Y: Z (3mks)
X Y Z
1:2
3: 5
3:6:10
24. A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes. Find the maximum area of one plot. (4marks) = 840 Ã 396
=332640 m2
G.C.D
 2 840 396 2 420 198 3 210 99 70 33
12 Ã 12 = 144m2
25. The ratio of Johnâs earnings to Musaâs earnings is 5:3 if johns earningâs increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musaâs earnings if the sum of their new earnings is sh 9600. (3mks)
100/112 Ã 5600 = 5000
J:M = 5:3
3/5 Ã 5000 = 3000
musas new earnings = 9600 - 5600
= sh.4000
musa's change in earnings = 4000 - 1000
= 3000
% change = 1000 Ã 100
3000
=331/3
26. Convert into percentage (3mks)
1. 0.03%
3/100 Ã 100 = 3%
27. Three Lorries, each making five trips per day, transport 2500 crates from a factory to a distributor in two days. How many Lorries, each making six trips a day, are needed to transport 10000 such crates in a day? (3mks)
3 Ã 5 Ã 10000 Ã 2
6         2500    1
= 20 lorries