UI Post-UTME Mathematics 2024 (Model questions) past questions and answers

Solve the equation: log₂(x² − 5x + 6) = 1

1. A.x = 1 or 2
2. B.x = 1 or 4
3. C.x = 2 or −3
4. D.x = −1 or 3

Let a = √5 + √3. Find the value of a² − 2√15

1. A.8
2. B.16
3. C.10
4. D.12

Find the remainder when x⁴ + 3x³ − 5x² + x − 6 is divided by x − 2

1. A.14
2. B.6
3. C.16
4. D.−3

A sector of a circle with radius 7cm has an angle of 60°. Find the area of the sector

1. A.50/7 πcm²
2. B.160/7 πcm²
3. C.49/6 πcm²
4. D.14πcm²

A cone has a height of 12cm and a base radius of 5cm. Find the total surface area

1. A.283cm²
2. B.204.23cm²
3. C.78.77cm²
4. D.142cm²

Solve for x in the interval 0° ≤ x ≤ 360°, 2 sin x = √3

1. A.60° only
2. B.60°, 120°
3. C.60°, 240°
4. D.50°, 150°

If y = e^2x sin x, find dy/dx

1. A.e^2x cos x
2. B.2e^2x sin x
3. C.e^x cos x
4. D.e^2x(2 sin x + cos x)

The mean of five numbers is 12. Four of them are 10, 15, 8 and 14. What is the fifth number?

1. A.20
2. B.60
3. C.13
4. D.17

How many integers between 1 and 500 are divisible by both 3 and 7?

1. A.23
2. B.32
3. C.14
4. D.17

The 5^th term of an arithmetic progression is 20 and the 10^th term is 40. What is the first term?

1. A.5
2. B.4
3. C.2
4. D.6

If a = 3i + 4j, find the magnitude of a

1. A.1
2. B.7
3. C.25
4. D.5

A committee of 3 is to be formed from 7 people. How many different committees are possible?

1. A.35
2. B.42
3. C.63
4. D.22

Find the discriminant of the equation x² + 2x − 3 = 0

1. A.4
2. B.12
3. C.16
4. D.8

integrate ∫(2x + 1)dx

1. A.x² + x + c
2. B.x² − x + c
3. C.x² + 2x + c
4. D.x² − 2x + c

If y varies directly as x and inversely as z and when x = 2 and z = 3, y = 4, find y when x = 3 and z = 2

1. A.6
2. B.12
3. C.15
4. D.9

The angle subtended by a diameter at the circumference of a circle is

1. A.180°
2. B.90°
3. C.60°
4. D.120°

For what value of x is (x⁴ + 3x³ − 4x² + 6)/(x − 5) undefined?

1. A.15
2. B.3
3. C.5
4. D.1/2

If α and β are the solutions to x² + 3x − 10 = 0, find 1/α + 1/β

1. A.−3/10
2. B.3/10
3. C.−10/3
4. D.10/3

At what value of x is the function y = x² − 2x − 3 minimum and what is the minimum value of the function?

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

In the figure below |PQ| = |PR| = |PS| and SR̂T = 68°, find QP̂S

1. A.68°
2. B.112°
3. C.136°
4. D.56°

Find x from the equation 27^{3x + 1/2} = 9^{5x − 1/4}

1. A.3/4
2. B.2
3. C.4
4. D.1/2