JAMB Mathematics practice: free CBT questions with worked answers
UTME Mathematics covers number and numeration (number bases, indices, logarithms, surds), algebra (equations, variation, progressions, matrices), geometry and trigonometry, calculus (differentiation and integration) and statistics and probability. Speed matters: you have about the same time per question as in other subjects, but many need working.
In the UTME CBT, Mathematics is one of your three subjects besides Use of English: 40 questions, inside a 2-hour paper of 180 questions scored out of 400.
CrackIt has 476 original Mathematics questions across 25 syllabus topics (150 easy, 222 medium, 104 hard), each with an explanation in English and Pidgin.
5 free JAMB Mathematics practice questions
Original questions from our bank, written to the syllabus. Tap “Show answer” to check yourself.
Q1. Number bases
Evaluate 64₈ - 27₈, leaving your answer in base 8.
- A45₈
- B33₈
- C35₈
- D26₈
Show answer
Answer: C. 35₈
Subtract column by column in base 8. In the units column, 4 - 7 is not possible, so borrow 1 (which is 8) to make it 12 - 7 = 5. In the tens column, 5 - 2 = 3, giving 35₈.
Pidgin: Subtract for base 8. Borrow one 8 for back of 4 make e be 12, minus 7 na 5. Remaining 5 for front minus 2 na 3, so answer na 35 base 8.
Q2. Logarithms
Find x if 2log_3(x) = 4.
- A81
- B3
- C6
- D9
Show answer
Answer: D. 9
Divide both sides by 2 to get log₃(x) = 2. Then, convert to exponential form: x = 3² = 9.
Pidgin: Divide both sides by 2 first, e go remain log₃(x) = 2. Change am to index form, you go get x = 3², wey be 9.
Q3. Simple and compound interest, profit and loss
Find the compound interest on ₦200,000 for 2 years at 10% per annum, compounded annually.
- A₦45,200
- B₦40,000
- C₦42,000
- D₦44,000
Show answer
Answer: C. ₦42,000
Total amount A = 200000(1.10)² = ₦242,000. Compound Interest = Total Amount - Principal = 242000 - 200000 = ₦42,000.
Pidgin: First find di total amount using 200,000 times 1.1 squared, wey be ₦242,000. Den minus di original ₦200,000 to get ₦42,000 interest.
Q4. Quadratic equations
If alpha and beta are the roots of 4x² - 8x + 3 = 0, find the value of (alpha - beta)².
- A4
- B3/4
- C5/2
- D1
Show answer
Answer: D. 1
We know (alpha - beta)² = (alpha + beta)² - 4alpha × beta. From 4x² - 8x + 3 = 0, sum = 8/4 = 2 and product = 3/4. Thus, (2)² - 4(3/4) = 4 - 3 = 1.
Pidgin: Use identity (alpha - beta)² = (alpha + beta)² - 4alpha × beta. Sum na 2, product na 3/4. Put am inside, 4 minus 3 go give you 1.
Q5. Binary operations
If the operation × is defined on the set of integers by x × y = x + y + 3xy, find the identity element for the operation.
- A-3
- B3
- C0
- D1
Show answer
Answer: C. 0
Let e be the identity element. Then x × e = x implies x + e + 3xe = x. Solving for e: e(1 + 3x) = 0, which means e = 0 for all x.
Pidgin: Make identity element be e. If you do x × e = x, e + x + 3xe = x. When you solve am, e(1 + 3x) = 0, meaning say e = 0.
Topics covered
- Number bases (15)
- Fractions, decimals, approximations, significant figures and percentages (18)
- Indices (25)
- Logarithms (19)
- Surds (24)
- Sets and Venn diagrams (12)
- Simple and compound interest, profit and loss (19)
- Variation (22)
- Linear and simultaneous equations (12)
- Quadratic equations (17)
- Polynomials, factor and remainder theorems, change of subject (11)
- Inequalities (18)
- Arithmetic and geometric progressions (24)
- Binary operations (18)
- Matrices and determinants (17)
- Euclidean geometry: angles, triangles and polygons (18)
- Circle geometry and circle theorems (22)
- Mensuration: perimeter, area, volume and surface area (20)
- Coordinate geometry: gradient, distance, midpoint, equation of a line (23)
- Trigonometry: ratios, special angles, sine and cosine rules, bearings (17)
- Differentiation and its applications (19)
- Integration (24)
- Statistics: mean, median, mode, range, variance and standard deviation (16)
- Permutations and combinations (21)
- Probability (25)
How to score higher in Mathematics
- Learn the short methods for number bases, indices and logarithms. They appear often and can be done in under a minute each.
- Use the on-screen calculator in the CBT practice the way you will in the real exam, so you are not slowed down on the day.
- If a question takes more than two minutes, flag it, move on and come back. Every question carries the same mark.
Done with practice? See the cut-off marks for 25 universities or check your chances with the admission chance checker.
Frequently asked questions
How many questions are in JAMB UTME Mathematics?
In the UTME CBT, Mathematics is one of your three subjects besides Use of English: 40 questions, inside a 2-hour paper of 180 questions scored out of 400.
Are these real past questions?
No. CrackIt's 476 Mathematics questions are original, written to the official JAMB syllabus, and each has a worked explanation. CrackIt is not affiliated with JAMB, WAEC or NECO.
Is CrackIt free and does it work offline?
Yes. Practice by topic, timed tests and the Daily 10 are free, and once the app has loaded it works without data.
Can I read the explanations in Pidgin?
Yes. Every Mathematics explanations have a Pidgin version: tap “Pidgin” under the answer.