CHECK THE QUESTIONS HERE
END TERM 3 – 2022
FORM 1
MATHEMATICS.
MARKING SCHEME
Instructions.
Answer all questions in the spaces provided.
- Express the following numbers in words. (2mks)
- 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 (7/3 – 3/7 ) 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 | 30 | 35 | 50 |
| 5 | 15 | 35 | 25 |
| 3 | 3 | 7 | 5 |
| 5 | 1 | 7 | 5 |
| 7 | 1 | 7 | 1 |
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
- 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
- ax – ay + bx –by (2mks)
a+b
a(x-y) + b (x – y)
a+b
(a+b) (x-y) = x-y
a+b
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Find a if a2 = b2 + c2 given that b=2 c=3.5. (2mks)
a2= 22 + 3.52
a2 = 16.25
a= 4.031
- 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 | 10.30am | 10.40 am |
| C | 11.00 am | 11.05 am |
| D | 11.20am |
- 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
- A rectangular plot measures 100m by 200m. Determine:
- 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
