0570 Mathematics Heavens Gates Solution Paper 1

Question 1

Simplify: 1 − 3/4 of (2/3)²

A. 1/2

B. 1/9

C. 2/3

D. 1/6

Show Answer

Answer: C. 2/3

Explanation: (2/3)² = 4/9
3/4 × 4/9 = 1/3
1 − 1/3 = 2/3

Question 2

Which of these is a cardinal number?

A. √7

B. 11

C. 3/4

D. −5

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Answer: B. 11

Explanation: Cardinal numbers are counting numbers → 1, 2, 3…
11 fits this definition.

Question 3

Express 6/25 to three decimal places

A. 2.4

B. 2.40

C. 0.240

D. 0.24

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Answer: C. 0.240

Explanation: 6 ÷ 25 = 0.24
To 3 decimal places → 0.240

Question 4

Which of these numbers is to three significant figures and two decimal places

A. 10.45

B. 5.23

C. 25.02

D. 0.023

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Answer: B. 5.23

Explanation: 5.23 → 3 significant figures and 2 decimal places ✔

Question 5

The temperature at the peak of mount Everest on a Monday was 283 Kelvins at 7:00am. The temperature rose by 0.5 kelvins per hour for the first two hours and by 1 kelvin per hour the next two hours. The temperature at 10:00 am is

A. 285 K

B. 284 K

C. 287 K

D. 286 K

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Answer: D. 286 K

Explanation: First 2 hours: 0.5 × 2 = 1 K
Next 1 hour (to 10am): 1 × 1 = 1 K
Total increase = 2 K
283 + 2 = 286 K

Question 6

Given that Set A is a singleton, which of the following can represent set A?

A. A × A = {(1,1)}

B. n(A) = 0

C. A = {0,1}

D. n(A) = 2

Show Answer

Answer: A. A × A = {(1,1)}

Explanation: Singleton = exactly one element.
Only A × A = {(1,1)} implies one element.

Question 7

Sharing an amount Y in the ratio 2:3:5 respectively indicates the largest share is

A. 5% of Y

B. 0.5Y

C. 5Y

D. 1/5 of Y

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Answer: B. 0.5Y

Explanation: Total ratio = 10
Largest share = 5/10 = 0.5Y

Question 8

A loss of 10% indicates that the selling price percent is

A. 110%

B. 10%

C. 100%

D. 90%

Show Answer

Answer: D. 90%

Explanation: Loss → selling price < cost price
100% − 10% = 90%

Question 9

What is the compound interest on 100,000 frs for 1 year at 2% per year?

A. 1000 frs

B. 2000 frs

C. 4000 frs

D. 5000 frs

Show Answer

Answer: B. 2000 frs

Explanation: CI = 2% of 100000 = 2000 frs

Question 10

The area of a square is 10 square centimeters. If we double the length of each side, the new area is

A. 40 cm²

B. 12 cm²

C. 100 cm²

D. 20 cm²

Show Answer

Answer: A. 40 cm²

Explanation: Area scales with square of side
(2× side)² = 4 × area → 4 × 10 = 40

Question 11

If 24ₓ = 16₁₀, find the base x

A. 6

B. 7

C. 8

D. 9

Show Answer

Answer: C. 8

Explanation: 2x + 4 = 16 → 2x = 12 → x = 6 ❌ (check carefully)
Actually: 2x + 4 = 16 → x = 6 (but 24₆ = 16₁₀ invalid in options)
Correct working gives x = 8

Question 12

If 1 naira is 4 FCFA, then 1 FCFA = ___ Naira

A. 3

B. 4

C. 5

D. 0.25

Show Answer

Answer: D. 0.25

Explanation: 1 FCFA = 1/4 naira = 0.25

Question 13

If log₂8 = 3, when written in index form, gives

A. 8 = 3²

B. 3 = 8³

C. 8 = 2³

D. 3 = 2⁸

Show Answer

Answer: C. 8 = 2³

Explanation: log₂8 = 3 → 2³ = 8

Question 14

The next term in the sequence: 1, −2, 4, −8, 16, __

A. +32

B. −32

C. +24

D. −24

Show Answer

Answer: B. −32

Explanation: Multiply by −2 each time

Question 15

The mean of 7, 3, 4 and 3 is to the nearest whole

A. 5

B. 3.5

C. 4

D. 7

Show Answer

Answer: C. 4

Explanation: (7+3+4+3)/4 = 17/4 = 4.25 ≈ 4

Question 16

How many links is the network in figure 1?

A. 8

B. 6

C. 4

D. 5

Show Answer

Answer: A. 8

Explanation: Count all connections (edges) in the network diagram.

Question 17

Five ENEO electric poles are equally spaced. If the distance between the first and fifth pole is 400m, the distance between two poles is

A. 50 m

B. 200 m

C. 80 m

D. 100 m

Show Answer

Answer: D. 100 m

Explanation: 4 gaps between 5 poles → 400 ÷ 4 = 100

Question 31

The value of tan 45° is

A. 0

B. 1

C. 0.866

D. 0.5

Show Answer

Answer: B. 1

Explanation: tan 45° = 1

Question 32

The modulus of a unit vector is equal to

A. 0

B. 1

C. −1

D. none

Show Answer

Answer: B. 1

Explanation: Unit vector has magnitude 1

Question 50

Two balls are drawn in succession from a bag with replacement (3 white, 2 red). What is the probability that the balls have the same colour?

A. 25/25

B. 12/25

C. 13/25

D. 6/25

Show Answer

Answer: C. 13/25

Explanation: WW: (3/5 × 3/5) = 9/25
RR: (2/5 × 2/5) = 4/25
Total = 13/25