# FORM 1 END OF TERM 3 2022 Exam-MATHEMATICS And Answers

Nov 1, 2022

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END TERM 3 – 2022

FORM 1

MATHEMATICS.

MARKING SCHEME

Instructions.

Answer all questions in the spaces provided.

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

Fourteen million six hundred and thirty three thousand and one.

• 30000010

Thirty million and ten.

• 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

• 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.

• 1120043

( 1 + 2 + 0 + 4 ) – ( 1 + 0 + 4)

7 – 5 = 2

Not divisible

• Use Bodmas to evaluate.                                                                                            (3mks)

½        3/5 + ¼  (7/33/7 ) of 1 ½ ÷ 5

3 5/7

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÷ 35/7

13/35 x 7/26

=1/10

• 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

• Using mathematical tables evaluate.
• 73402                                                                                                               (1mk)

7.340 x 103

53.88 x 106

5.388 x 107

• 14.52 + 0.7142                                                                                                 (2mks)

7.14 x 10-10 = 50.98 x10-2

210.3 + 0.5098

= 210.8098

• Given that a:b = 1:2 and b:c = 3:4. Find a:b:c                                                            (1mk)

a:b:c                            (1×3)                (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 x 5 x 3 x 5 x 3 = 450 mins

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 πr2

360

4.8 = Ѳ x 22/7 x 3.52

360

Ѳ = 44.88O

1.  Express the following as a single fraction.
1. 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

• ax – ay + bx –by                                                                                             (2mks)

a+b

a(x-y) + b (x – y)

a+b

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

a+b

1. 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                                           8                                              8

24                                           10                                           ?

15x 8 x 8

24 x10

= 4 days

1. Use factor tree to decompose 256 into prime factors.                                                (2mks)

256 = 2×128                        2 x 8

2 x 64                         2 x 4

2 x 32                         2 x 2

2 x 16                           2x 2 x2 x 2 x 2 x 2 x2

= 27

1. 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

1. Use bodmas to evaluate:                                                                                             (4mks)

5×6-76÷4+27÷3

4-2×4+36÷4

30 – 19 + 9                          4 – 8 + 9

20                                       5

= 20/5

= 4

1. A Kenyan bank buys and sells foreign currency as shown in the table below.

A tourist arrived in Kenya with 15000 pounds which he converted in kshs.

1. How much kshs did he receive?                                                                                 (2mks)

15000 x 124.65

= 1869750

• 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

1. 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

= 512cm3

Length = 3√512

= 8 cm

1.  Find a if a2 = b2 + c2 given that b=2 c=3.5.                                                               (2mks)

a2= 22 + 3.52

a2 = 16.25

a= 4.031

1. Below is a travel timetable for a vehicle operating between towns A and D 70 km apart.
1. 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

• 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

1. A rectangular plot measures 100m by 200m. Determine:
2. Its perimeter in km.                                                                                         (2mks)

= 2 (100+200)

1000

= 0.6 km

• Its area in m2.                                                                                                  (2mks)

= 100 x 200

= 20,000m2

• Its area in ha.                                                                                                   (2mks)

20000  = 2ha

10000

• 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

• If the cost of 1 tile is sh. 25. How much money will be spent on tiles.          (2mks)

20,000 x 25

= 500,000