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POST UTME UI 2020 Mathematics | Objective

Are you preparing for POST UTME UI 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

A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. Find the volume of water in the \tank.

Correct A. 490π m³

B. 4900π m³

C. 49000π m³

D. 490000π m³

Correct Answer: A

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Question 2

Solve for x in the equation: 2x^2 + 5x - 3 = 0

A. x = -1

Correct B. x = 1

C. x = -3

D. x = 3

Correct Answer: B

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Question 3

In a right-angled triangle, the length of the hypotenuse is 10cm and one of the other sides is 6cm. Find the length of the third side.

A. 8cm

Correct B. 12cm

C. 14cm

D. 16cm

Correct Answer: B

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Question 4

A car travels from city A to city B at an average speed of 60km/h and returns at an average speed of 40km/h. What is the average speed for the round trip?

A. 45km/h

B. 50km/h

Correct C. 55km/h

D. 60km/h

Correct Answer: C

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Question 5

A set of 5 coins contains 2 nickels and 3 dimes. If a coin is selected at random, what is the probability that it is a nickel?

A. 0.2

Correct B. 0.3

C. 0.4

D. 0.5

Correct Answer: B

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Question 6

Find the value of x in the equation $ 2x^2 + 5x - 3 = 0 $.

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 7

Solve for y in the equation $ \frac{y}{2} + 3 = 7 $.

Correct A. 8

B. 10

C. 12

D. 14

Correct Answer: A

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Question 8

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24

Correct B. 100.48

C. 200.96

D. 251.2

Correct Answer: B

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Question 9

A line passes through the points (2, 3) and (4, 5). Find the equation of the line.

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 3x - 1

D. y = 3x + 1

Correct Answer: A

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Question 10

A random experiment has two possible outcomes: heads or tails. If the probability of getting heads is 0.4, find the probability of getting tails.

Correct A. 0.3

B. 0.4

C. 0.5

D. 0.6

Correct Answer: A

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Question 11

Solve the inequality $ \frac{x}{x-2} > 1 $ for $ x > 2 $.

A. x > 2

Correct B. x > 4

C. x < 2

D. x < 4

Correct Answer: B

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Question 12

Find the derivative of the function ( f(x) = 3x^2 \sin x ) u\sing the product rule.

Correct A. 6x \sin x + 3x^2 \cos x

B. 6x \cos x + 3x^2 \sin x

C. 6x \sin x - 3x^2 \cos x

D. 6x \cos x - 3x^2 \sin x

Correct Answer: A

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Question 13

A random variable X has a probability distribution given by $ P\( X = 1 \ $ = \frac{1}{3} ) and $ P\( X = 2 \ $ = \frac{2}{3} ). Find the probability that X is greater than 1.

A. \frac{1}{3}

Correct B. \frac{2}{3}

C. \frac{1}{2}

D. 1

Correct Answer: B

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Question 14

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 15

Solve the system of equations u\sing matrices: \[ \begin{array}{ccc} x + y + z & = & 6 2x + 3y + z & = & 11 x + 2y + 3z & = & 7 \end{array} \]

Correct A. \begin{array}{ccc} x & = & 1 \ y & = & 2 \ z & = & 3 \end{array}

B. \begin{array}{ccc} x & = & 2 \ y & = & 1 \ z & = & 3 \end{array}

C. \begin{array}{ccc} x & = & 1 \ y & = & 3 \ z & = & 2 \end{array}

D. \begin{array}{ccc} x & = & 3 \ y & = & 2 \ z & = & 1 \end{array}

Correct Answer: A

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Question 16

Determine the number of terms in the series $ sum_{n=1}^{infty} \frac{1}{n\( n+1 \ $} ) that satisfy $ \frac{1}{n\( n+1 \ $} < \frac{1}{100} ).

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 17

Find the value of $ lim_{x \to 0} \frac{\sin x}{x} $ u\sing L'Hopital's rule.

Correct A. 1

B. 0

C. -1

D. ∞

Correct Answer: A

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Question 18

Solve the matrix equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $ for ( x ) and ( y ).

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 3 $

C. $ x = 3, y = 4 $

D. $ x = 4, y = 5 $

Correct Answer: A

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Question 19

A binary operation ( ast ) is defined as $ a ast b = a^2 + b^2 $. Find the value of ( 2 ast 3 ).

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 20

Find the area of the region bounded by the curves $ y = x^2 $ and $ y = 4x $.

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 21

In a base 8 number system, what is the value of the digit $x$ in the number $x_{8} = 105_{10}$?

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 22

Let $S$ be the set of all positive integers $n$ such that $n$ is divisible by $5$ and $n$ is a perfect square. What is the sum of the elements of $S$?

A. 50

Correct B. 100

C. 150

D. 200

Correct Answer: B

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Question 23

Find the sum of the infinite geometric series $\sum_{n=1}^\infty \frac{2}{3^n}$.

A. \frac{2}{3}

Correct B. \frac{4}{9}

C. \frac{6}{9}

D. \frac{8}{9}

Correct Answer: B

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Question 24

Find the volume of the solid formed by revolving the region bounded by the curve $y = x^2$ and the line $y = 2x$ about the $x$-axis.

A. \frac{16}{3}\pi

Correct B. \frac{32}{3}\pi

C. \frac{64}{3}\pi

D. \frac{128}{3}\pi

Correct Answer: B

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Question 25

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ u\sing the chain rule.

Correct A. -\frac{2x}{$ x^2 + 1 $^2}

B. -\frac{2x}{$ x^2 + 1 $^2} + \frac{2}{x^2 + 1}

C. \frac{2x}{$ x^2 + 1 $^2}

D. \frac{2}{x^2 + 1}

Correct Answer: A

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