Exam Body

Year

Subject

Paper Type

UTME 2020 Mathematics | Objective

Are you preparing for UTME exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find T in terms of K, Q and S if S=\(2r\sqrt{\pi(QT+K)}\)

A. \( \frac{S^2}{2\pi r^2 Q} - \frac{K}{Q} \)

B. \( \frac{S^2}{2\pi r^2 Q} - K \)

Correct C. \( \frac{S^2}{4\pi r^2 Q} - \frac{K}{Q} \)

D. \( \frac{S^2}{2\pi r^2 Q} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2

The graph of f(x) = \( x^2 \) - 5x + 6 crosses the x-axis at the points:

A. (-6,0), (-1,0)

B. (-3,0), (-2,0)

C. (-6,0), (1,0)

Correct D. (2,0), (3,0)

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

Factorize completely the expression \( abx^2 \) + 6y - 3ax - 2byx.

Correct A. (ax - 2y)(bx - 3)

B. (bx + 3)(2y - ax)

C. (bx + 3)(ax - 2y)

D. (ax - 2y)(ax - b)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

Solve the following inequality (x-3)(x-4) ≤ 0

Correct A. 3 ≤ x ≤ 4

B. 3

C. 3 ≤ x<4

D. 3

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.

A. 175

B. 85

Correct C. 64

D. 45

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

Simplify \( \frac{x^2 -1}{ x^2 + 2x^2 - x - 2} \)

A. \( \frac{1}{x-1} \)

Correct B. \( \frac{x-1}{x+1} \)

C. \( \frac{x-1}{x+2} \)

D. \( \frac{1}{x-2} \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

Express \( \frac{5x-12}{(x-2)(x-3)} \) in partial fractions

A. \( \frac{2}{x+2} \) + \( \frac{3}{x-3} \)

Correct B. \( \frac{2}{x-2} \) + \( \frac{3}{x-3} \)

C. \( \frac{2}{x-3} \)-\( \frac{3}{x-2} \)

D. \( \frac{5}{x-3} \)-\( \frac{4}{x-2} \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

If \( (1P03)_4 = 115_{10} \) find P.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

Evaluate \( 64.764^{2} -35. 236^{2} \) correct to 3 significant figures.

A. 2960

Correct B. 2950

C. 2860

D. 2850

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

Find the value of \( (0.006)^{3} + (0.0004)^{3} \) in standard form

Correct A. \( 2.8 \times 10^{-9} \)

B. \( 2.8 \times 10^{-7} \)

C. \( 2.8 \times 10^{-5} \)

D. \( 2.8 \times 10^{-6} \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

Given that \( \log_a 2 \) = 0.693 and \( \log_a 3 \) = 1.097, find \( \log_a 13.5 \).

A. 1.404

Correct B. 1.790

C. 2.598

D. 2.790

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

Simplify \( \log_2 96 - 2\log_2 6 \)

A. \( 2 - \log_2 3 \)

Correct B. \( 3 - \log_2 3 \)

C. \( \log_2 3 - 3 \)

D. \( \log_2 3 - 2 \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

If 8=(\( 2^{2x} \))(\( 4^{x} \)), find x.

A. \( \frac{3}{8} \)

Correct B. \( \frac{3}{4} \)

C. \( \frac{4}{5} \)

D. \( \frac{5}{4} \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

TQ is tangent to circle XYTR, DYXT=\( 32^\circ \), RTQ= \( 40^\circ \). Find DYTR.

A. \( 108^\circ \)

Correct B. \( 121^\circ \)

C. \( 140^\circ \)

D. \( 148^\circ \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

A chord of a circle radius √3 cm subtends an angle of 60° on the circumference of the circle. Find the length of the chord.

A. \( \frac{ \sqrt{3} }{2} \)

B. \( \frac{3}{2} \)

C. 3

Correct D. √3 cm

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

A cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimetres. ( \(\pi\) = \( \frac{22}{7} \))

A. 12.5

Correct B. 25.0

C. 45.0

D. 50.00

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

The locus of all points at a distance 8 cm from a point N passes through points T and S. If S is equidistant from T and N, find the area of triangle STN.

A. \( 4 \sqrt{3} cm^{2} \)

Correct B. \( 16 \sqrt{3} cm^{2} \)

C. \( 32 cm^{2} \)

D. \( 64 cm^{2} \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

If the distance between the points (x, 3) and (-x, 2) is 5. Find x.

A. 6,0

B. 2,5

Correct C. \( \sqrt{6} \)

D. \( \sqrt{3} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

The sum of two numbers is twice their difference. If the difference of the numbers is p, find the larger of the two numbers.

A. \( \frac{P}{2} \)

Correct B. \( \frac{3P}{2} \)

C. \( \frac{5P}{2} \)

D. 3P

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

The first term of a geometrical progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.

A. \( \frac{8}{5} \)

B. \( \frac{8}{3} \)

C. \( \frac{72}{25} \)

Correct D. \( \frac{56}{9} \)

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

If m * n = \( \frac{n}{m} \) - \( \frac{m}{n} \) for m, n \( \in \) R, evaluate -3 * 4.

A. \( \frac{-25}{12} \)

Correct B. \( \frac{-7}{12} \)

C. \( \frac{7}{12} \)

D. \( \frac{25}{12} \)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

A binary operation * is defined by a*b=ab+a+b for any real number a and b. If the identity element is zero, find the inverse of 2 under this operation.

A. \( \frac{2}{3} \)

B. \( \frac{1}{2} \)

C. -\( \frac{1}{2} \)

Correct D. -\( \frac{2}{3} \)

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

Find the matrix T if ST=I where S= \( \begin{pmatrix}-1 & 1 \\ 0 & 1 \end{pmatrix} \) and I is the identity matrix.

A. \( \begin{pmatrix}-2 & 1 \\ 1 & 1\end{pmatrix} \)

B. \( \begin{pmatrix}-2 & -1 \\ -1 & -1\end{pmatrix} \)

Correct C. \( \begin{pmatrix}-1 & -1 \\ 0 & -1\end{pmatrix} \)

D. \( \begin{pmatrix}-1 & 1 \\ 0 & 1\end{pmatrix} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

Given that Q= \( \begin{pmatrix}6 & 0 \\ 4 & 5\end{pmatrix} \) and Q+P= \( \begin{pmatrix}7 & -2 \\ 6 & 8\end{pmatrix} \) evaluate |Q+2P|

A. 90

B. 96

C. 102

Correct D. 120

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x=0 and y=0 (where k is a constant).

A. x+y=0

Correct B. x-y=0

C. x+y+k=0

D. x-y-k=0

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support