**QUESTIONS**

Attempt all questions in the spaces provided

- Evaluate (3mks)

-19 + (6-8) ÷ 2 x 5

16 ÷ 4 x -3 - Express the following numbers as products of their prime factors (3mks)
- 357
- 5929

- Find the GCD of 72, 96 and 300 (3mk)
- Express 0.872872872………….as a fraction (3mks)
- Show how the following calculations are performed using number line (4mks)
- -2 + (-2) + -3 + (-1)
- -7 – (-8)

- Evaluate (3mks)

4 ½ - (5^{1}/_{5}+^{4}/_{5}of^{25}/_{3}) - Charles spent ¼ of his net salary on school fees. He spent ¼ 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)
- Which of the following numbers is divisible by 11, 3, and 4 (3mks)
- 2596
- 5896
- 1052

- All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
- Write down the number formed. (1mk)
- Test whether or not the number formed in 16 (a) above is divisible by 11. (2mks)

- 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)
- Evaluate: ¼ +
^{1}/_{5}÷ ½ of^{1}/_{3}½ of (^{4}\_{5}– ¾ + ½ ) (3mks) - The sum of
^{3}/_{8},^{20}/_{3}and x is 6^{57}/_{120}. Find x. (2mks) - Evaluate without using tables or calculators. (3mks)

0.036 × 0.0049

0.07 × 0.048 - A shop keeper sells a shirt for Kshs.350 thereby making a profit of 40%. Calculate the buying price of the shirt (3mks)
- Evaluate: (3marks)

44 -(-28) - 82 × -12 - 24

12 × -2 96 ÷ -12 × 9 - ]
- A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n. (3marks)
- Reduce the following expression onto a single fraction.(3 marks)

4x - 5 - 2x - 1

2 6 - Convert 7 into a decimal (3mks)

8 - If X: Y =1:2 and Y: Z =3:5 find X: Y: Z (3mks)
- 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)
- The ratio of John’s earnings to Musa’s earnings is 5:3 if johns earning’s increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musa’s earnings if the sum of their new earnings is sh 9600. (3mks)
- Convert into percentage (3mks)
- 0.03%

- 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

- Evaluate (3mks)

-19 + (6-8) ÷ 2 x 5

16 ÷ 4 x -3**num: -19 + (-2) ÷ 2 × 5**

-19 - 2 ÷ 2 × 5

-19 - 1 × 5

- 24

Den: 16 ÷ 4 x -3

4 × -3

- 12

-24

-12

= 2 - Express the following numbers as products of their prime factors (3mks)
- 357
**3 × 7****× 17** - 5929
**7****× 3****× 29**

- 357
- Find the GCD of 72, 96 and 300 (3mk)
2 72 96 30 3 36 48 15 12 16 5 **= 2 × 3**

= 6 - Express 0.872872872………….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 - Show how the following calculations are performed using number line (4mks)
- -2 + (-2) + -3 + (-1)
**= -8** - -7 – (-8)
**= +1**

- -2 + (-2) + -3 + (-1)
- Evaluate (3mks)

4 ½ - (5^{1}/_{5}+^{4}/_{5}of^{25}/_{3}) - Charles spent ¼ of his net salary on school fees. He spent ¼ 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 × fees**

1/4 of 3/4x = bills

3/16x = bills

1/9 of 3/16x

133/144x → transport

131/144x - 3400 - Which of the following numbers is divisible by 11, 3, and 4 (3mks)
- 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 - 5896
**+(5 + 9) - (8 + 6) = 0 - divisible by 11**

5 + 8 + 9 + 6 = 28 - not divisible by 3

96 is divisible by 4 - 1052
**(1 + 5) - (10 + 2) = 4 - divisible by 11**

1 + 0 + 5 + 2 = 8 - not divisible by 3

52 - divisible by 4

- 2596
- All prime numbers between 0 and 10 are arranged in a descending order to form a whole number
- Write down the number formed. (1mk)
**7 5 3 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

- Write down the number formed. (1mk)
- 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 - Evaluate: ¼ +
^{1}/_{5}÷ ½ of^{1}/_{3}½ of (^{4}\_{5}– ¾ + ½ ) (3mks)**Num: 1/4 + 1/5 ÷ 1/2 of 1/3**

1/4 + 1/5 ÷ 1/6

1/4 + 6/5 = 1^{9}/_{20}

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

1/2 of 11/20^{11}/_{40}

1^{9}/_{20 }-^{11}/_{40}

= 1^{7}/_{40} - The sum of
^{3}/_{8},^{20}/_{3}and x is 6^{57}/_{120}. Find x. (2mks)^{3}/_{8}+^{20}/_{3}+ x = 6^{57}/_{120}^{169}/_{24}+ x = 6^{57}/_{120}-^{169}/_{24}

x = 6^{57}/_{120}-^{169}/_{24}

x =^{17}/_{30} - Evaluate without using tables or calculators. (3mks)
**0.036 × 0.0049**

0.07 × 0.048

0.036 × 0.0049 × 1000000

0.07 × 0.048 × 1000000

36 × 49

7 × 48 × 100

=^{21}/_{40} - 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 × 100

140

b.p = 250 - Evaluate: (3marks)

44 -(-28) - 82 × -12 - 24

12 × -2 96 ÷ -12 × 9**44 + 28**

-24

= 72

-24

64x - 12 - 24

= 72/-24 - 28/-72

= -^{47}/_{18} - 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 × 7 × 11 × 13 = 3003**

n = 3003 + 1 = 3004 - 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 - Convert 7 into a decimal (3mks)

8**0.875** - 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 - 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 × 396

=332640 m^{2}

G.C.D**2****840****396****2****420****198****3****210****99****70****33****12 × 12 = 144m**^{2} - The ratio of John’s earnings to Musa’s earnings is 5:3 if johns earning’s increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musa’s earnings if the sum of their new earnings is sh 9600. (3mks)
**100/112 × 5600 = 5000**

J:M = 5:3

3/5 × 5000 = 3000

musas new earnings = 9600 - 5600

= sh.4000

musa's change in earnings = 4000 - 1000

= 3000

% change = 1000 × 100

3000

=33^{1}/_{3} - Convert into percentage (3mks)
- 0.03%
**3/100 × 100 = 3%**

- 0.03%
- 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 × 5 × 10000 × 2**

6 2500 1

= 20 lorries

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