Mathematics Questions and Answers - Form 2 Term 1 Opener Exams 2023

INSTRUCTIONS;

ATTEMPT ALL QUESTIONS

Evaluate without using mathematical tables or calculator (3 mks)
¾ + ²/₅ ÷ ³/₅ of 1²/₃
(1 ¾ - ⁵/₈) × ²/₉
A number n is such that when it is divided by 27 and 30 or 45, the remainder is always 3. Find the smallest value of n. (3 mks)
A tourist arrived in Kenya with US Dollars 3000 which he exchanged into Kenya shillings. He spent Ksh. 75000 on hotel accommodation and Ksh.42500 on travel and other expenses. He changed the remaining money into sterling pounds. Calculate how much money in sterling pounds that he remained with using the following rates. (Leave your answer to the nearest 1£) [3mks]

Buying(Kshs) Selling(Kshs)

1 US dollar($) 78.45 78.95

1 Sterling pound(£) 120.27 121.04
Given the ratios A;B is 3;4 and B;C Is 2;3 express the ratio A;B;C in the simplest form. [3mks]
Three cisterns flush after intervals of 24 minutes, 30minutes and 40 minutes respectively. The cisterns flash together at 10.00pm.what time will they flush together again [ 3mks]
Convert 0.375 into a decimal (3mks)
Use tables of squares to evaluate; (4mks)
6250² ÷ 0.1750²
Find the length of a square whose area is 0.0081m². (3mks)
A foreign government donated sh. 67.9 billion while the Kenya Government contributed sh. 200 million towards the project. Of the total amount sh. 10.8 million was used to pay experts, sh. 670,000 for the purchase of stationery and sh. 12.8 million for the acquisition of machinery. How much money remained unused ? (Express your answer in words). (4mks)
Solve the following simultaneous equations. [4mks]
3x + y = 10
x + 6 y = 5
Simon earned sh. 400 as a commission for a sale of goods worth sh. 16,000. What would be his earnings for a total sale of sh. 7,000? (4mks)
A right-angled triangular prism has length 3m, breadth 2m and height 2.5m. If the mass of the prism is 3.4kg, find its density. (4mks)
The ratio of John’s earnings to Musa’s earning is 5:3. If John’s earnings increase by 12%, his new figure becomes sh. 5600. Find the corresponding percentage change in Musa’s earnings if the sum of the new earnings is sh. 9600. (3mks)
A man earns x shillings while his wife earns ¹/₃ of this. After spending a third of their combined income, they have sh. 2,400 left. How much money does the man earn? (4mks)
Below is a travel timetable for a vehicle operating between towns A and D seventykilometers apart. (5mks)

Town Arrival Departure

A 10.10 a.m

B 10.30 a.m 10.40 a.m

C 11.00 a.m 11.05 a.m

D 11.20 a.m
1. At what time does the vehicle depart from town A ?
2. How long does it take to travel from town A to town B.
3. For how long does it stay in town B ?
4. At what time does it arrive in town D ?
5. What is the average speed for the whole journey ?
The table below shows measurements of a farm in a field’s book. XY = 2000m

F 200

C 150

A 200

Y
1800
1600
1200
900
600
300
100
X
G 100

E 300
D 100

B 200
1. Using a scale 1cm rep 100m. Sketch the map of the farm (2mks)
2. Calculate the area of the farm in hectares (8mks)
Four towns R,T,K and G are such that T is 84km directly to the north of R and K is on bearing of 295° from R at a distance of 60km. G is on a bearing of 340° from K and at a distance of 30km.
1. Using the scale of 1cm to represent 10km make an accurate scale drawing to show the relative positions of the towns. (3mks)
2. Find:-
  1. The distance and the bearing of T from K (2mks)
  2. The distance and the bearing of G from T. (2mks)

MARKING SCHEME

Evaluate without using mathematical tables or calculator (3 mks)
¾ + ²/₅ ÷ ³/₅ of 1²/₃
(1 ¾ - ⁵/₈) × ²/₉
Numerator
¾ + ²/₅ ÷ 1 = 15 + 8
20
= ²³/₂₀
Denominator
⁷/₄ − ⁵/₈ = 14− 5
8
⇒ ⁹/₈ × ²/₉
=¼
²³/₂₀÷ ¼ = 4³/₅
A number n is such that when it is divided by 27 and 30 or 45, the remainder is always 3. Find the smallest value of n. (3 mks)

3 × 3 × 3 × 5 × 2
= 270
270 + 3
= 273
A tourist arrived in Kenya with US Dollars 3000 which he exchanged into Kenya shillings. He spent Ksh. 75000 on hotel accommodation and Ksh.42500 on travel and other expenses. He changed the remaining money into sterling pounds. Calculate how much money in sterling pounds that he remained with using the following rates. (Leave your answer to the nearest 1£) [3mks]

Buying(Kshs) Selling(Kshs)

1 US dollar($) 78.45 78.95

1 Sterling pound(£) 120.27 121.04

1 Us dollar = Ksh 78.45
3000 = ?
3000 × 78.45
1
- Sh. 235350
235350 − 117500
= Sh 117850
1£ = Ksh 121.04
? = Sh 117850
117850
121.04
= £ 973.65
Given the ratios A;B is 3;4 and B;C Is 2;3 express the ratio A;B;C in the simplest form. [3mks]
Three cisterns flush after intervals of 24 minutes, 30minutes and 40 minutes respectively. The cisterns flash together at 10.00pm.what time will they flush together again [ 3mks]

2 × 3 × 5 × 4 = 120
¹²⁰/₆₀ = 2hrs
10.00 + 2
= 12.00 p.m
Convert 0.375 into a decimal (3mks)
375
1000
⁷⁵/₅₀₀
= ³/₂₀
Use tables of squares to evaluate; (4mks)
6250² ÷ 0.1750²
(6.250 × 10³)²
6.25² × 10⁶
39.063 × 10⁶
0.1750²
(1.750 × 10⁻¹)²
1.750² × 10⁻²
3.0625 × 10⁻²
39.063 × 10⁶
3.0625 × 10⁻²
12.76 × 10⁸
1.276 × 10⁹
Find the length of a square whose area is 0.0081m². (3mks)
√(81 × 10⁻⁴)
81^½ × 10⁻²
9 × 10⁻²
= 0.09
A foreign government donated sh. 67.9 billion while the Kenya Government contributed sh. 200 million towards the project. Of the total amount sh. 10.8 million was used to pay experts, sh. 670,000 for the purchase of stationery and sh. 12.8 million for the acquisition of machinery. How much money remained unused ? (Express your answer in words). (4mks)
679 × 10⁸
200000000
681 × 10⁸
10.8
12.8
23.6
23.6 × 10⁶
0.6
24.2 × 10⁶
681 × 10⁸ − 24.2 × 10⁶
(681.000 − 0.242) × 10⁶
= 680.758 × 10⁶
= Ksh 680758000
Solve the following simultaneous equations. [4mks]
3x + y = 10
x + 6 y = 5
x = 5 − 6y
3x + y = 10
3(5 − 6y) + y = 10
15 − 18y + y = 10
15 − 17y = 10
− 17y = − 5
y = ⁵/₁₇
x = 5 − 6(⁵/₁₇)
= 5 − ³⁰/₁₇
⇒ 5 − 1¹³/₁₇
= 4 ¹³/₁₇
Simon earned sh. 400 as a commission for a sale of goods worth sh. 16,000. What would be his earnings for a total sale of sh. 7,000? (4mks)
400 = 16000
? = 7000
400 × 7000
16000
= Ksh 175
A right-angled triangular prism has length 3m, breadth 2m and height 2.5m. If the mass of the prism is 3.4kg, find its density. (4mks)

V = ½ × 2 × 2.5 × 3
= 7.5 m³
D = ^m/_v = 3.4 kg
7.5m³
= 0.4533 kg/m³
The ratio of John’s earnings to Musa’s earning is 5:3. If John’s earnings increase by 12%, his new figure becomes sh. 5600. Find the corresponding percentage change in Musa’s earnings if the sum of the new earnings is sh. 9600. (3mks)
5600 = 112
100
5600 × 100
112
= 5000
John : Musa
5 : 3
5000 : 3000
5000 × ³/₅
=Ksh 3000
9600 − 5600
= Sh. 4000
Increase
1000 × 100
3000
= 33.3%
A man earns x shillings while his wife earns ¹/₃ of this. After spending a third of their combined income, they have sh. 2,400 left. How much money does the man earn? (4mks)
x + ¹/₃x = ⁴/₃x
¹/₃(⁴/₃x) = ⁴/₉x
⁵/₉x = 2400
x = 2400 × 9
5
= Sh. 4320
Below is a travel timetable for a vehicle operating between towns A and D seventykilometers apart. (5mks)

Town Arrival Departure

A 10.10 a.m

B 10.30 a.m 10.40 a.m

C 11.00 a.m 11.05 a.m

D 11.20 a.m
1. At what time does the vehicle depart from town A ?
  - 10.10 a.m
2. How long does it take to travel from town A to town B.
  10.30a.m − 10.10a.m = 20 minutes
3. For how long does it stay in town B ?
  10.40 a.m − 10.30a.m = 10minutes
4. At what time does it arrive in town D ?
  - 11.20 a.m
5. What is the average speed for the whole journey ?
  TD = 70 = 70 ÷ ⁷/₆ = 60km/hr
  T.T 1¹/₆
The table below shows measurements of a farm in a field’s book. XY = 2000m

F 200

C 150

A 200

Y
1800
1600
1200
900
600
300
100
X
G 100

E 300
D 100

B 200
1. Using a scale 1cm rep 100m. Sketch the map of the farm (2mks)
2. Calculate the area of the farm in hectares (8mks)
  1. ½ × 100 × 200
    = 10000
  2. ½(200+150) × 500
    = 87500
  3. ½(200+150) × 1000
    = 175000
  4. ½(400) × 200
    = 40000
  5. ½(300 × 200)
    = 30000
  6. ½(200+100) × 600
    = 90000
  7. ½(300+100) × 300
    = 60000
  8. ½(100+300) × 600
    = 120000
  9. ½(200) × 100
    = 10000
    10000 + 87500 + 175000 + 40000 + 30000 + 90000 + 60000 + 120000 + 10000 = 622500
    ⇒ 62.25ha
Four towns R,T,K and G are such that T is 84km directly to the north of R and K is on bearing of 295° from R at a distance of 60km. G is on a bearing of 340° from K and at a distance of 30km.
1. Using the scale of 1cm to represent 10km make an accurate scale drawing to show the relative positions of the towns. (3mks)
2. Find:-
  1. The distance and the bearing of T from K (2mks)
    Location of T
    Location of K
    Location of G
    Distance TK = 80 ± km
    Bearing of T from K: 047°±1
  2. The distance and the bearing of G from T. (2mks)
    Distance GT = 72 ± 2km
    Bearing of G from T : 245°± 2°