Exam Body

Year

Subject

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UTME 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?

A. 45

B. 50

Correct C. 60

D. 75

Correct Answer: C

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Question 2

The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile score.

A. 18%

Correct B. 28%

C. 36%

D. 50%

Correct Answer: B

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Question 3

5,8,6 and k occur with frequencies 3,2,4 and 1 respectively and have a mean of 5.7. Find the value of k.

A. 4

B. 3

Correct C. 2

D. 1

Correct Answer: C

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Question 4

What is the mean deviation of x, 2x, x+1 and 3x, if their mean is 2?

A. 0.5

Correct B. 1.0

C. 1.5

D. 2.0

Correct Answer: B

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Question 5

In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?

A. 15

Correct B. 28

C. 30

D. 45

Correct Answer: B

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Question 6

In how many ways can 9 people be seated if 3 chairs are available?

Correct A. 720

B. 504

C. 336

D. 210

Correct Answer: A

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Question 7

The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?

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

B. \( \frac{4}{9} \)

C. \( \frac{8}{27} \)

D. \( \frac{1}{27} \)

Correct Answer: A

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Question 8

\[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Marks} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No. of students} & 3 & 4 & 1 & 0 & 4 & 5 & 2 & 1 \\ \hline \end{array} \] The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.

A. \( \frac{3}{5} \)

B. \( \frac{2}{5} \)

Correct C. \( \frac{7}{20} \)

D. \( \frac{1}{5} \)

Correct Answer: C

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Question 9

Determine the value of x for which \( (x^{2}-1)>0 \).

Correct A. x<-1 or x>1

B. -1

C. x>0

D. x<-1

Correct Answer: A

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Question 10

Find the range of values of x for which 3x-7 ≤ 0 and x+5>0

Correct A. -5

B. -5 ≤ x ≤ \( \frac{7}{3} \)

C. -5

D. -5 ≤ x< \( \frac{7}{3} \)

Correct Answer: A

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Question 11

The sum of the first n terms of the arithmetic progression 5,11,17,23,29,35,... is

A. n(3n-0.5)

B. n(3n+2)

Correct C. n(3n+2.5)

D. n(3n+5)

Correct Answer: C

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Question 12

Find to infinity, the sum of the sequence \( 1, T,(T)^{2},(T)^{3} \),

A. 10

Correct B. 9

C. %

D. T

Correct Answer: B

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Question 13

If m*n=n-(m+2) for any real numbers m and n, find the value of 3*(-5).

A. -6

B. -8

Correct C. -10

D. -12

Correct Answer: C

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Question 14

A binary operation \( \otimes \) defined on the set of integers is such that \( m \otimes n = m + n + mn \) for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0.

Correct A. \( \frac{5}{4} \)

B. \( \frac{-5}{4} \)

C. \( \frac{5}{6} \)

D. \( \frac{-5}{6} \)

Correct Answer: A

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Question 15

If Q= \( \begin{pmatrix} 9 & -2 \\ -7 & 4\end{pmatrix} \), then |Q| is

A. -50

B. -22

Correct C. 22

D. 50

Correct Answer: C

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Question 16

If p=\( \begin{pmatrix}x+3 & x+2 \\ x+1 & x-1\end{pmatrix} \), evaluate x if |P|= -10.

Correct A. -5

B. -2

C. 2

D. 5

Correct Answer: A

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Question 17

What is the size of each interior angle of a 12 -sided regular polygon?

A. \( 120^{\circ} \)

Correct B. \( 150^{\circ} \)

C. \( 30^{\circ} \)

D. \( 180^{\circ} \)

Correct Answer: B

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Question 18

A circle of perimeter 28 cm is opened to form a square. What is the maximum possible area of the square?

A. \( 56 \mathrm{~cm}^{2} \)

Correct B. \( 49 \mathrm{~cm}^{2} \)

C. \( 98 \mathrm{~cm}^{2} \)

D. \( 28 \mathrm{~cm}^{2} \)

Correct Answer: B

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Question 19

A chord of a circle of radius 7 cm is 5 cm from the centre of the circle. What is the length of the chord?

A. \( 4 \sqrt{6} \mathrm{~cm}\)

B. \( 3 \sqrt{6} \mathrm{~cm} \)

Correct C. \( 6 \sqrt{6} \mathrm{~cm} \)

D. \( 2 \sqrt{6} \mathrm{~cm} \)

Correct Answer: C

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Question 20

A solid metal cube of side 3 cm is placed in a rectangular tank of dimensions 3,4 and 5 cm. What volume of water can the tank now hold?

A. \( 48 \mathrm{~cm}^{3} \)

Correct B. \( 33 \mathrm{~cm}^{3} \)

C. \( 60 \mathrm{~cm}^{3} \)

D. \( 27 \mathrm{~cm}^{3} \)

Correct Answer: B

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Question 21

The perpendicular bisector of a line \( \mathbf{X Y} \) is the locus of a point.

A. whose distance from X is always twice its distance from Y

B. whose distance from Y is always twice its distance from X

C. which moves on the line XY

Correct D. which is equidistant from the points X and Y

Correct Answer: D

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Question 22

The midpoint of \( P(x, y) \) and \( Q(8,6) \) is (5, 8). Find \( x \) and y.

Correct A. (2,10)

B. (2,8)

C. (2,12)

D. (2,6)

Correct Answer: A

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Question 23

Find the equation of a line perpendicular to line \( 2 y =5 x+4 \) which passes through (4,2).

A. \( 5y-2 x -18=0 \)

B. \( 5y+2 x-18=0 \)

C. \( 5y-2 x+18=0 \)

Correct D. \( 5y+2 x-2=0 \)

Correct Answer: D

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Question 24

In a right angled triangle, if \( tanq =E \). What is \( \cos q-\sin q \) ?

A. G

B. H

Correct C. F

D. I

Correct Answer: C

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Question 25

A man walks \( 100 \text{ m} \) due West from a point X to Y, and then \( 100 \text{ m} \) due North to a point Z. Find the bearing of X from Z.

Correct A. \( 195^\circ \)

B. \( 1350^\circ \)

C. \( 225^\circ \)

D. \( 045^\circ \)

Correct Answer: A

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