IJMB Mathematics
Past Questions
20+ verified Mathematics past questions for IJMB. Step-by-step worked answers in 5 Nigerian languages.
Mathematics topics (2)
Sample Mathematics past questions
1. If f(x) = 2x + 3, f(4) = ?
- A. 8
- B. 11
- C. 14
- D. 20
Answer: B
AI Explanation
**The reasoning** This is about **function evaluation** — simply substitute the given value into the function. Given: f(x) = 2x + 3, and we need f(4) Replace every "x" with 4: - f(4) = 2(4) + 3 - f(4) = 8 + 3 - f(4) = **11** Think of a function as a machine: you feed it a number (input), it follows its rule, and gives you back an answer (output). Here, the rule is "multiply by 2, then add 3." **Why the wrong options tempt you** - **A) 8** — You stopped after 2(4) and forgot to add 3. The function has *two* operations! - **C) 14** — You might have added incorrectly (2+4+3 = 9, not 14) or multiplied 2×4 then doubled it somehow. Stay organized! - **D) 20** — Perhaps you did 4×3 + 8, mixing up the operations. Always follow BODMAS strictly. **Quick takeaway** Function notation f(x) means "what you do *to* x" — so f(4) means do everything in the formula *to* 4, step by step. Substitute, then calculate carefully!
2. Sum of an AP a=1, d=2, n=5.
- A. 11
- B. 15
- C. 25
- D. 30
Answer: C
AI Explanation
**The reasoning** In an Arithmetic Progression (AP), we find the sum using the formula: **Sₙ = n/2 × [2a + (n-1)d]** Given: a = 1 (first term), d = 2 (common difference), n = 5 (number of terms) Let's substitute: S₅ = 5/2 × [2(1) + (5-1)(2)] S₅ = 5/2 × [2 + 4(2)] S₅ = 5/2 × [2 + 8] S₅ = 5/2 × 10 S₅ = **25** You can verify: the sequence is 1, 3, 5, 7, 9 → sum = 25 ✓ **Why the wrong options tempt you** **A) 11** — You might've added just a and d incorrectly or confused it with the last term calculation. **B) 15** — Common error: using n = 3 instead of n = 5, or miscalculating (n-1)d. **D) 30** — You probably multiplied n × (a + d) = 5 × 6, forgetting the proper AP sum formula. **Quick takeaway** For AP sums, always use **Sₙ = n/2 × [2a + (n-1)d]** — think of it as "number of terms times the average of first and last term."
3. If f(x)=2x²,then f(3)=
- A. 6
- B. 12
- C. 18
- D. 36
Answer: C
4. The roots of x²−5x+6=0 are:
- A. 1 and 6
- B. 2 and 3
- C. −2 and −3
- D. 1 and 5
Answer: B
5. cos 0° equals:
- A. 0
- B. 1
- C. −1
- D. 0.5
Answer: B
6. The sum of the first 5 natural numbers is:
- A. 10
- B. 15
- C. 20
- D. 25
Answer: B
7. If log x = 2 (base 10), x =
- A. 20
- B. 100
- C. 200
- D. 1000
Answer: B
8. tan 45° equals:
- A. 0
- B. 1
- C. 0.5
- D. undefined
Answer: B
9. Solve: 2x + 5 = 11
- A. x = 2
- B. x = 3
- C. x = 4
- D. x = 6
Answer: B
AI Explanation
2x = 6 → x = 3.
10. Differentiate: y = 4x² + 3
- A. 8x
- B. 4x
- C. 8x + 3
- D. 4x + 3
Answer: A
AI Explanation
dy/dx of 4x² = 8x; constant 3 differentiates to 0.
11. Integrate: ∫ 3x² dx
- A. x³ + C
- B. 6x + C
- C. 3x + C
- D. x²+ C
Answer: A
AI Explanation
∫ 3x² dx = 3 · x³/3 + C = x³ + C.
12. Solve: x² − 25 = 0
- A. x = 5 only
- B. x = −5 only
- C. x = ±5
- D. No solution
Answer: C
AI Explanation
x² = 25 → x = ±5.
13. log₁₀ 1 =
- A. 0
- B. 1
- C. 10
- D. Undefined
Answer: A
AI Explanation
log of 1 in any base = 0 (since b⁰ = 1).
14. Find the roots of x² − 6x + 8 = 0:
- A. x = 2, 4
- B. x = 1, 8
- C. x = −2, −4
- D. x = 4, 8
Answer: A
AI Explanation
(x − 2)(x − 4) = 0 → x = 2 or 4.
15. If sin θ = 1, θ =
- A. 0°
- B. 45°
- C. 90°
- D. 180°
Answer: C
AI Explanation
sin 90° = 1.
16. Mean of 5, 10, 15, 20, 25:
- A. 10
- B. 15
- C. 20
- D. 25
Answer: B
AI Explanation
Sum = 75; ÷ 5 = 15.
17. Probability of rolling a 3 on a fair die:
- A. 1/2
- B. 1/3
- C. 1/6
- D. 1/12
Answer: C
AI Explanation
Six outcomes; favourable = 1 → 1/6.
18. Area of a circle with radius 7 (π = 22/7):
- A. 44
- B. 154
- C. 49
- D. 22
Answer: B
AI Explanation
Area = πr² = 22/7 × 49 = 154.
19. Solve: 3x = 27
- A. x = 3
- B. x = 6
- C. x = 9
- D. x = 12
Answer: C
AI Explanation
x = 27 ÷ 3 = 9.
20. What is the value of 5!?
- A. 20
- B. 60
- C. 120
- D. 150
Answer: C
AI Explanation
5! = 5 × 4 × 3 × 2 × 1 = 120.
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