JAMB Mathematics CBT Practice Test

Practise UTME Mathematics on a computer-based test that works like the real one: timed questions, a navigator to jump between them, and a full review with the correct answer and an explanation for every question.

About these JAMB Mathematics questions

There are 45 questions in this mathematics bank, written by StudentToolsNG to the topics in the JAMB UTME Mathematics syllabus and at the level of the exam. They are original practice questions, not copies of JAMB past papers, so you can practise without memorising old answers.

Each test picks questions at random and shuffles the options, so the answer to a question is not always in the same position. You get 40 seconds a question, the same pace as the UTME, where 180 questions are answered in 2 hours.

Topics covered

The questions cover 23 topics from the syllabus:

• Number bases (2 questions)
• Fractions and percentages (3 questions)
• Indices (2 questions)
• Logarithms (2 questions)
• Surds (2 questions)
• Sets (1 question)
• Polynomials (2 questions)
• Quadratic equations (1 question)
• Linear equations (1 question)
• Variation (1 question)
• Inequalities (1 question)
• Sequences and series (3 questions)
• Binary operations (1 question)
• Matrices and determinants (2 questions)
• Geometry (2 questions)
• Mensuration (2 questions)
• Trigonometry (3 questions)
• Coordinate geometry (3 questions)
• Differentiation (3 questions)
• Integration (2 questions)
• Statistics (3 questions)
• Permutations and combinations (1 question)
• Probability (2 questions)

Tips for JAMB Mathematics

• Learn the formulas that come up every year: the nth term and sum of an AP and GP, sum to infinity, the remainder theorem, areas and volumes, and the distance and gradient formulas.
• Check an answer by substituting it back. For equations, inequalities and factorisation questions this is often faster than solving from scratch.
• Watch the wording: percentage profit is on the cost price, "without replacement" changes the second probability, and order matters for permutations but not combinations.
• Do the short questions first. Flag long statistics or mensuration questions and come back once the quick marks are safe.

Sample JAMB Mathematics questions with answers

Question 1: Convert 1011₂ to base ten.

A. 11 B. 13 C. 9 D. 22

Answer: A (11). 1011₂ = 1×2³ + 0×2² + 1×2 + 1 = 8 + 0 + 2 + 1 = 11.

Question 2: A trader buys a bag for ₦4,000 and sells it for ₦5,000. What is the percentage profit?

A. 20% B. 25% C. 10% D. 30%

Answer: B (25%). Profit = ₦5,000 − ₦4,000 = ₦1,000. Percentage profit is worked on the cost price: 1,000 ÷ 4,000 × 100 = 25%. (20% is the profit as a share of the selling price, a common mistake.)

Question 3: Evaluate log₂8 + log₃9 − log₅1.

A. 6 B. 5 C. 4 D. 1

Answer: B (5). log₂8 = 3 (2³ = 8), log₃9 = 2 (3² = 9) and log₅1 = 0 (any base to power 0 is 1). 3 + 2 − 0 = 5.

Question 4: In a class of 40 students, 25 offer Physics, 20 offer Chemistry and 8 offer both. How many offer neither subject?

A. 3 B. 5 C. 13 D. 8

Answer: A (3). n(P ∪ C) = n(P) + n(C) − n(P ∩ C) = 25 + 20 − 8 = 37. Neither = 40 − 37 = 3.

Question 5: Solve the simultaneous equations 2x + y = 7 and x − y = 2.

A. x = 2, y = 3 B. x = 3, y = 1 C. x = 1, y = 5 D. x = 4, y = −1

Answer: B (x = 3, y = 1). Add the equations: 3x = 9, so x = 3. Then 3 − y = 2 gives y = 1. (x = 4, y = −1 fits the first equation only.)

Question 6: Find the 10th term of the arithmetic progression 3, 7, 11, …

A. 43 B. 40 C. 39 D. 35

Answer: C (39). a = 3, d = 4. Tₙ = a + (n − 1)d = 3 + 9 × 4 = 39.

Question 7: Find the determinant of the matrix with rows (3, 2) and (1, 4).

A. 14 B. 10 C. −10 D. 11

Answer: B (10). For rows (a, b) and (c, d) the determinant is ad − bc = 3 × 4 − 2 × 1 = 12 − 2 = 10.

Question 8: Find the area of a sector of a circle of radius 7 cm whose angle is 90°. (Take π = 22/7.)

A. 154 cm² B. 77 cm² C. 38.5 cm² D. 11 cm²

Answer: C (38.5 cm²). Area = θ/360 × πr² = 90/360 × 22/7 × 49 = 1/4 × 154 = 38.5 cm².

Question 9: From a point on level ground 20 m from the foot of a tower, the angle of elevation of the top is 45°. How tall is the tower?

A. 10 m B. 20√2 m C. 40 m D. 20 m

Answer: D (20 m). tan 45° = height ÷ 20. tan 45° = 1, so the height is 20 m.

Question 10: Find the equation of the line with gradient 2 that passes through (1, 3).

A. y = 2x + 3 B. y = 2x − 1 C. y = x + 2 D. y = 2x + 1

Answer: D (y = 2x + 1). y − 3 = 2(x − 1), so y = 2x − 2 + 3 = 2x + 1.

Question 11: Find ∫(4x³ + 2x) dx.

A. 12x² + 2 + c B. x⁴ + x² + c C. 4x⁴ + 2x² + c D. x⁴ + 2x² + c

Answer: B (x⁴ + x² + c). Raise each power by one and divide by the new power: 4x⁴/4 + 2x²/2 + c = x⁴ + x² + c. 12x² + 2 is the derivative, not the integral.

Question 12: Taking 1, 2, 3, 4, 5 as the whole population, find the variance.

A. 2.5 B. 2 C. √2 D. 3

Answer: B (2). Mean = 3. Squared deviations: 4, 1, 0, 1, 4, total 10. Population variance = 10 ÷ 5 = 2. (Dividing by n − 1 = 4 gives the sample variance 2.5.)

Frequently Asked Questions

Are these JAMB Mathematics past questions?

No. They are original questions written to the JAMB Mathematics syllabus in the same style and at the same level as the UTME. Practising on new questions shows whether you understand a topic rather than whether you remember an old answer.

How many questions are in the JAMB Mathematics paper?

Each of your three other subjects has 40 questions in the UTME, and Use of English has 60, making 180 questions in 2 hours. That is about 40 seconds a question, which is the pace this practice test uses.

How is JAMB Mathematics scored?

Each subject is scored out of 100 and the four subjects add up to your UTME score out of 400. The percentage you get in this practice test is a rough guide to your score out of 100 in mathematics.

Can I practise without a time limit?

Yes. Choose Study mode to see the correct answer and the explanation as soon as you pick an option, with no timer. Switch to the timed test once you are ready to practise at exam pace.

Other subjects

JAMB Physics CBT practice · JAMB Chemistry CBT practice · JAMB Biology CBT practice