1.
Variation
y varies inversely as x. If y = 39 when x = 2, find y when x = 6.
Answer: B. y = k/x, so k = 39 × 2 = 78. When x = 6, y = 78 ÷ 6 = 13.
JAMB UTME Mathematics practice questions
Try 10 free Mathematics questions below, each with the answer explained. When you are ready, practise all 2,596 on a timed CBT screen.
The UTME is JAMB's computer-based entrance exam for Nigerian universities, polytechnics and colleges of education. You sit Use of English and three other subjects in 2 hours: 60 questions for Use of English and 40 for each other subject.
- 2,596 questions in our bank
- 25 topics
- Every answer explained
10 free sample questions
Tap an answer to check it and see the explanation.
2.
Statistics
Find the range of 86, 80, 40, 58, 15, 28.
Answer: A. Range = highest − lowest = 86 − 15 = 71.
3.
Percentages
A trader bought a bag for ₦18,400 and sold it for ₦21,160. Find the percentage profit.
Answer: A. Profit = 2,760; percentage profit = profit ÷ cost price × 100 = 15%.
4.
Indices
Simplify 9⁷ × 9⁵ ÷ 9⁴.
Answer: C. Same base: add powers when multiplying and subtract when dividing: 7 + 5 − 4 = 8, so 9⁸.
5.
Standard form
Express 85,700 in standard form.
Answer: B. Move the decimal point 4 places to the left: 8.57 × 10⁴.
6.
Quadratic equations
Find the roots of x² + 3x + 2 = 0.
Answer: D. Factorise: (x + 2)(x + 1) = 0, so x = -2 or x = -1.
7.
Ratio and proportion
Share ₦15,400 between Ada and Bayo in the ratio 5 : 6. Find the larger share.
Answer: D. Total parts = 11; one part = 1,400; larger share = 6 × 1,400 = ₦8,400.
8.
Coordinate geometry
Find the gradient of the line joining (1, 1) and (3, 7).
Answer: C. Gradient = (y₂ − y₁) ÷ (x₂ − x₁) = (6) ÷ (2) = 3.
9.
Simultaneous equations
Solve the simultaneous equations: x + y = 22 and x − y = 4.
Answer: D. Adding: 2x = 26, so x = 13. Then y = 22 − 13 = 9.
10.
Probability
A bag contains 5 red, 6 blue and 5 green balls. A ball is picked at random. What is the probability that it is red?
Answer: B. P(red) = number of red ÷ total = 5/16 = 5/16.
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Questions in the MyGradePrep bank for each topic.
| Topic | Questions |
|---|---|
| Mensuration | 342 |
| Statistics | 301 |
| Angles and triangles | 180 |
| Circle theorems | 171 |
| Sequences and series | 170 |
| Coordinate geometry | 141 |
| Percentages | 127 |
| Variation | 121 |
| Commercial arithmetic | 120 |
| Angles and parallel lines | 120 |
| Arithmetic | 91 |
| Linear equations | 62 |
| Indices | 61 |
| Quadratic equations | 60 |
| Number bases | 60 |
| Ratio and proportion | 60 |
| Simultaneous equations | 60 |
| Probability | 60 |
| Fractions | 60 |
| Standard form | 60 |
| Trigonometry | 56 |
| Plane geometry | 44 |
| Pythagoras | 40 |
| Logarithms | 16 |
| Polygons | 12 |