## Questions

Instructions.

- Answer all questions in the spaces provided.

- Express the following numbers in words. (2mks)
- 14633001
- 30000010

- A matatu charges sh. 120 as fare from town A to town B. It has a capacity of 18 passangers. How much money does it make in one day covering 10 trips with full capacity. (3mks)
- Use the divisibility test of 11 to check whether the following numbers are divisible by 11. (2mks)
- 1048564
- 1120043

- Use Bodmas to evaluate. (3mks)

½ (3/5 + ¼ (7/3 – 3/7 ) of 1 ½ ÷ 5)

3^{5}/_{7} - Victoria spent ¼ of his net January salary on school fees. She spent ¼ of the remainder on electricity and water bills. She then spent 1/9 of what was left on transport. If she finally had sh. 3400. What was her net January salary. (3mks)
- Using mathematical tables evaluate.
- 7340
^{2}(1mk) - 14.5
^{2}+ 0.714^{2}(2mks)

- 7340
- Given that a:b = 1:2 and b:c = 3:4. Find a:b:c (1mk
- Three bells ring at intervals 30mins, 35mins and 50 mins. If they ring together at 11:25 p.m on Monday at what time and day will they next ring together? (3mks)
- The length of minute hand of a clock is 3.5cm. Find the angle it turns through if it sweeps an area of 4.8cm2. (take π=
^{22}/_{7}) (3mks) - Express the following as a single fraction.
- x-1 + x+2 + x (3mks)

2 4 5 - ax – ay + bx –by (2mks)

a+b

- x-1 + x+2 + x (3mks)
- Fifteen tractors each working eight hours a day takes eight days to plough a piece of land. How long would it take 24 tractors each working 10 hours a day to plough the same piece of land. (3mks)
- Use factor tree to decompose 256 into prime factors. (2mks)
- Juma, Ali and Hassan share the profit of their business in the ratios 3:7:9 respectively. If Juma receives sh. 6000. How much profit did the business yield. (3mks)
- Use bodmas to evaluate: (4mks)

5x6-76÷4+27÷3

4-2x4+36÷4 - A Kenyan bank buys and sells foreign currency as shown in the table below.
Buying (ksh) Selling (ksh) 1 us dollar 95.34 95.87 1 uk pound 124.65 125.13 - How much kshs did he receive? (2mks)
- He later spend sh. 125340 while in Kenya. He converted the remainder in dollars. How many dollars did he receive? (3mks)

- A metallic cuboid measuring 16cm by 8cm by 4cm was melted. The material was used to make a cube. What is the length of the cube. (3mks)
- Find a if a
^{2}= b^{2}+ c^{2}given that b=2 c=3.5. (2mks) - Below is a travel timetable for a vehicle operating between towns A and D 70 km apart.
Town Arrival Departure A 10.10 am B 10.30 am 10.40 am C 11.00 am 11.05 am D 11.20 am - At what time does the vehicle depart from town A? (1mk)
- How long does it take to travel from town A to town B? (1mk)
- For how long does it stay in town B? (1mk)
- At what time does it arrive in town D? (1mk)
- What is the average speed of the whole journey? (3mks)
- A football match lasts 90 minutes with a break of 15 minutes at half time. If a referee allows five minutes extra for injuries and stoppages, what time does a match which kicks off at 4:30 pm end? (3mks)

- A rectangular plot measures 100m by 200m. Determine:
- Its perimeter in km. (2mks)
- Its area in m
^{2}. (2mks) - Its area in ha. (2mks)
- Square tiles of 100cm by 100cm are used to cover the floor. How many tiles are used? (2mks)
- If the cost of 1 tile is sh. 25. How much money will be spent on tiles. (2mks)

## Marking Scheme

- Express the following numbers in words. (2mks)
- 14633001
- Fourteen million six hundred and thirty three thousand and one.

- 30000010
- Thirty million and ten.

- 14633001
- A matatu charges sh. 120 as fare from town A to town B. It has a capacity of 18 passangers. How much money does it make in one day covering 10 trips with full capacity. (3mks)
- 120 x 18 = 2160

1 trip = 2160

10 trips = 2160 x 10

= shs. 21,600

- 120 x 18 = 2160
- Use the divisibility test of 11 to check whether the following numbers are divisible by 11. (2mks)
- 1048564
- ( 1 + 4 + 5 + 4 ) – (0 + 8 + 6)

14 – 14 = 0

Divisible.

- ( 1 + 4 + 5 + 4 ) – (0 + 8 + 6)
- 1120043
- ( 1 + 2 + 0 + 4 ) – ( 1 + 0 + 4)

7 – 5 = 2

Not divisible

- ( 1 + 2 + 0 + 4 ) – ( 1 + 0 + 4)

- 1048564
- Use Bodmas to evaluate. (3mks)
- ½(
^{3}/_{5}+ ¼ (^{7}/_{3}–^{3}/_{7}) of 1 ½ ÷ 5)

½ (^{3}/_{5}+ (^{40}/_{21}) of 1 ½ ÷ 5)

½ (^{3}/_{5}+^{10}/_{21}x^{3}/_{2}x^{1}/_{5})

½ (^{3}/_{5}+^{1}/_{7})

½ (^{26}/_{35}) =^{13}/_{35}^{13}/_{35 }÷ 3^{5}/_{7}^{13}/_{35}x^{ 7}/_{26}

=^{1}/_{10}

- ½(
- Victoria spent ¼ of his net January salary on school fees. She spent ¼ of the remainder on electricity and water bills. She then spent 1/9 of what was left on transport. If she finally had sh. 3400. What was her net January salary. (3mks)
- School fees= ¼

Electricity = ¼ x ¾ = 3/16

Transport = 1/9 x 9/16=1/16

Total = ½

½ = 3400

Total salary = shs. 6800

- School fees= ¼
- Using mathematical tables evaluate.
- 7340
^{2}(1mk)- 7.340 x 103

53.88 x 106

5.388 x 107

- 7.340 x 103
- 14.5
^{2}+ 0.714^{2}(2mks)- 7.14 x 10-10 = 50.98 x10-2

210.3 + 0.5098

= 210.8098

- 7.14 x 10-10 = 50.98 x10-2

- 7340
- Given that a:b = 1:2 and b:c = 3:4. Find a:b:c (1mk)
a:b:c (1x3) (2 x 3) (2 x 4) 1:2 a: b: c: 3:4 3 6 8 - Three bells ring at intervals 30mins, 35mins and 50 mins. If they ring together at 11:25 p.m on Monday at what time and day will they next ring together. (3mks)
2 3

03

55

05 1

53

52

53 3 7 5 5 1 7 5 7 1 7 1

7hr 30mins

2325 6:50 a.m

730

2050 Tuesday - The length of minute hand of a clock is 3.5cm. Find the angle it turns through if it sweeps an area of 4.8cm2. (take π=22/7) (3mks)
- A= Ѳ x πr
^{2}

360

4.8 = Ѳ x^{22}/_{7}x 3.5^{2}

360

Ѳ = 44.88^{O}

- A= Ѳ x πr
- Express the following as a single fraction.
- x- 1 + x + 2 + x (3mks)

2 4 5- 10 (x – 1) + 5 (x +2) + 4 (x)

20

10x – 0 + 5x + 10 + 4x

20

19/20x

- 10 (x – 1) + 5 (x +2) + 4 (x)
- ax – ay + bx –by (2mks)

a+b- a(x-y) + b (x – y)

a+b

(a+b) (x-y) = x-y

a+b

- a(x-y) + b (x – y)

- x- 1 + x + 2 + x (3mks)
- Fifteen tractors each working eight hours a day takes eight days to plough a piece of land. How long would it take 24 tractors each working 10 hours a day to plough the same piece of land. (3mks)
Tractors hours Days 15

248

108

?15x 8 x 8

24 x10

= 4 days - Use factor tree to decompose 256 into prime factors. (2mks)
- 256 = 2x128 2 x 8

2 x 64 2 x 4

2 x 32 2 x 2

2 x 16 2 x 2 x2 x 2 x 2 x 2 x2 = 2^{7}

- 256 = 2x128 2 x 8
- Juma, Ali and Hassan share the profit of their business in the ratios 3:7:9 respectively. If Juma receives sh. 6000. How much profit did the business yield. (3mks)
- 3=6000

19 = ?

=19 x 6000

3

= shs 38000

- 3=6000
- Use bodmas to evaluate: (4mks)
- 5 x 6 - 76 ÷ 4 + 27 ÷ 3

4-2x4+36÷4

30 – 19 + 9 4 – 8 + 9

20 5

= 20/5

= 4

- 5 x 6 - 76 ÷ 4 + 27 ÷ 3
- A Kenyan bank buys and sells foreign currency as shown in the table below.
Buying (ksh) Selling (ksh) 1 us dollar 95.34 95.87 1 uk pound 124.65 125.13

A tourist arrived in Kenya with 15000 pounds which he converted in kshs.- How much kshs did he receive? (2mks)
- 15000 x 124.65

= 1869750

- 15000 x 124.65
- He later spend sh. 125340 while in Kenya. He converted the remainder in dollars. How many dollars did he receive? (3mks)
- 1867950

-125340

1,744,410

= 1744410

125.13

= 13940.78 dollars

- 1867950

- How much kshs did he receive? (2mks)
- A metallic cuboid measuring 16cm by 8cm by 4cm was melted. The material was used to make a cube. What is the length of the cube? (3mks)
- V = L x W x h

= 18 x 8 x 4

= 512

Volume cube = L x L x L

= 512cm^{3}

Length = 3√512

= 8 cm

- V = L x W x h
- Find a if a
^{2}= b^{2}+ c^{2}given that b=2 c=3.5. (2mks)- a
^{2}= 2^{2}+ 3.5^{2}a^{2}= 16.25

a= 4.031

- a
- Below is a travel timetable for a vehicle operating between towns A and D 70 km apart.
Town Arrival Departure A 10.10 am B 10.30 am 10.40 am C 11.00 am 11.05 am D 11.20 am - At what time does the vehicle depart from town A? (1mk)
- 10.10 am

- How long does it take to travel from town A to town B? (1mk)
- 20 mins

- For how long does it stay in town B? (1mk)
- 10 mins

- At what time does it arrive in town D? (1mk)
- 11:20 a.m

- What is the average speed of the whole journey? (1mk)
- S= D = 70

T 1^{1}/_{6}

= 60km/hr

- S= D = 70
- A football match lasts 90 minutes with a break of 15 minutes at half time. If a referee allows five minutes extra for injuries and stoppages, what time does a match which kicks off at 4:30 pm end? (3mks)
- 90 + 15 + 5 = 1 hr 50 mins

16:30

1 :50

14:40 hrs

2:40p.m

- 90 + 15 + 5 = 1 hr 50 mins

- At what time does the vehicle depart from town A? (1mk)
- A rectangular plot measures 100m by 200m. Determine:
- Its perimeter in km. (2mks)
- = 2 (100+200)

1000

= 0.6 km

- = 2 (100+200)
- Its area in m2. (2mks)
- = 100 x 200

= 20,000m2

- = 100 x 200
- Its area in ha. (2mks)
- 20000 = 2ha

10000

- 20000 = 2ha
- Square tiles of 100cm by 100cm are use to cover the floor. How many tiles are used? (2mks)
- = 10000 x 20000

100 100

= 100 x 200

= 20,000 tiles

- = 10000 x 20000
- If the cost of 1 tile is sh. 25. How much money will be spent on tiles. (2mks)
- 20,000 x 25

= 500,000

- 20,000 x 25

- Its perimeter in km. (2mks)

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