هذه المجموعة متاحة بلغتها الأصلية.
JAMB Mathematics CBT practice: past-question style questions
Twenty objective questions in the style of the JAMB UTME Mathematics CBT: number bases, indices, logarithms, surds, sequences, sets, matrices, calculus, statistics, probability, trigonometry and mensuration. Use the timed CBT mode, then read the worked solutions.
أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان JAMB UTME. ليست أسئلة رسمية.
Timed mode
20 questions in 14 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
الموضوع: Number bases
1. Convert 101101₂ to base ten.
الحل
C. 45
- 101101₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰.
- = 32 + 0 + 8 + 4 + 0 + 1 = 45.
الموضوع: Indices
2. Evaluate 25^(−3/2).
الحل
B. 1/125
- A negative power means a reciprocal: 25^(−3/2) = 1 ÷ 25^(3/2).
- 25^(1/2) = 5, so 25^(3/2) = 5³ = 125.
- The answer is 1/125.
الموضوع: Logarithms
3. Simplify log₂8 + log₂4 − log₂2.
الحل
A. 4
- log₂8 = 3, log₂4 = 2 and log₂2 = 1.
- 3 + 2 − 1 = 4.
الموضوع: Indices
4. Solve 2^(x + 1) = 32.
الحل
D. x = 4
- Write 32 as a power of 2: 32 = 2⁵.
- So x + 1 = 5, which gives x = 4.
الموضوع: Surds
5. Simplify √12 + √27.
الحل
C. 5√3
- √12 = √(4 × 3) = 2√3.
- √27 = √(9 × 3) = 3√3.
- 2√3 + 3√3 = 5√3.
الموضوع: Modular arithmetic
6. Evaluate 5 × 4 (mod 7).
الحل
B. 6
- 5 × 4 = 20.
- 20 ÷ 7 = 2 remainder 6, so 20 ≡ 6 (mod 7).
الموضوع: Simple interest
7. Find the simple interest on ₦20,000 at 5% per annum for 3 years.
الحل
A. ₦3,000
- Simple interest = PRT ÷ 100.
- = 20,000 × 5 × 3 ÷ 100 = ₦3,000.
الموضوع: Quadratic equations
8. If α and β are the roots of 2x² − 7x + 3 = 0, find α + β.
الحل
D. 7/2
- For ax² + bx + c = 0, the sum of the roots is −b/a.
- Here a = 2 and b = −7, so α + β = 7/2.
الموضوع: Simultaneous equations
9. Solve x + y = 7 and x − y = 1.
الحل
C. x = 4, y = 3
- Add the equations: 2x = 8, so x = 4.
- Substitute: 4 + y = 7, so y = 3.
الموضوع: Variation
10. y varies inversely as x, and y = 6 when x = 4. Find y when x = 8.
الحل
B. 3
- Inverse variation: y = k/x.
- 6 = k/4, so k = 24.
- When x = 8, y = 24/8 = 3.
الموضوع: Sequences
11. Find the 5th term of the arithmetic progression 3, 7, 11, ...
الحل
A. 19
- The first term a = 3 and the common difference d = 4.
- Tₙ = a + (n − 1)d, so T₅ = 3 + 4 × 4 = 19.
الموضوع: Sequences
12. Find the sum of the first 4 terms of the geometric progression 2, 6, 18, ...
الحل
D. 80
- a = 2 and r = 3.
- Sₙ = a(rⁿ − 1)/(r − 1) = 2(3⁴ − 1)/(3 − 1).
- = 2 × 80 ÷ 2 = 80.
الموضوع: Sets
13. n(A) = 12, n(B) = 9 and n(A ∩ B) = 4. Find n(A ∪ B).
الحل
C. 17
- n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- = 12 + 9 − 4 = 17.
الموضوع: Matrices
14. Find the determinant of the matrix with rows (3, 2) and (1, 4).
الحل
B. 10
- For rows (a, b) and (c, d), the determinant is ad − bc.
- = 3 × 4 − 2 × 1 = 12 − 2 = 10.
الموضوع: Differentiation
15. Find the gradient of the curve y = 3x² − 4x + 1 at x = 2.
الحل
A. 8
- dy/dx = 6x − 4.
- At x = 2: 6 × 2 − 4 = 8.
الموضوع: Integration
16. Find ∫(4x³ + 2x) dx.
الحل
D. x⁴ + x² + c
- Raise each power by 1 and divide by the new power.
- ∫4x³ dx = x⁴ and ∫2x dx = x².
- Add the constant: x⁴ + x² + c.
الموضوع: Statistics
17. Find the median of 3, 8, 5, 9, 4, 7.
الحل
C. 6
- Arrange in order: 3, 4, 5, 7, 8, 9.
- There are 6 numbers, so the median is the mean of the 3rd and 4th: (5 + 7) ÷ 2 = 6.
الموضوع: Probability
18. A bag holds 5 red and 3 blue balls. Two balls are picked one after the other without replacement. Find the probability that both are red.
الحل
B. 5/14
- P(first red) = 5/8.
- One red ball is gone, so P(second red) = 4/7.
- 5/8 × 4/7 = 20/56 = 5/14.
الموضوع: Trigonometry
19. If sin θ = 3/5 and θ is acute, find tan θ.
الحل
A. 3/4
- Draw a right-angled triangle with opposite = 3 and hypotenuse = 5.
- Adjacent = √(5² − 3²) = 4.
- tan θ = opposite ÷ adjacent = 3/4.
الموضوع: Mensuration
20. Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7.)
الحل
D. 1540 cm³
- V = πr²h.
- = 22/7 × 7 × 7 × 10 = 22 × 7 × 10 = 1540 cm³.