Exam Body

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Subject

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POST UTME UNILORIN 2020 Mathematics | Objective

Are you preparing for POST UTME UNILORIN 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.

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Question 1

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 80?

Correct A. 0.9772

B. 0.6827

C. 0.3413

D. 0.1587

Correct Answer: A

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Question 2

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \)

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3

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

Correct A. 8

B. 6

C. 10

D. 12

Correct Answer: A

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Question 4

A company produces two products, A and B. The profit on product A is ₦100 per unit and the profit on product B is ₦150 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?

Correct A. ₦65,000

B. ₦70,000

C. ₦75,000

D. ₦80,000

Correct Answer: A

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Question 5

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

A. 48

Correct B. 50

C. 52

D. 54

Correct Answer: B

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Question 6

Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 4 \ \) )

B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 4 \ \) )

C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 2 cdot 4 cdot 2 \ \) )

D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 2 cdot 4 cdot 2 \ \) )

Correct Answer: A

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Question 7

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{pi}{2} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{pi}{6} \)

Correct Answer: A

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Question 8

Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.

Correct A. \( \frac{64}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{16}{3} \)

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

Correct Answer: A

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Question 9

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

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 10

Find the surface area of the sphere with radius 5 cm.

Correct A. ( 100pi )

B. ( 50pi )

C. ( 25pi )

D. ( 10pi )

Correct Answer: A

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

Solve the system of equations: \( \begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases} \).

Correct A. x = 1, y = 3

B. x = 2, y = 2

C. x = 3, y = 1

D. x = 4, y = 0

Correct Answer: A

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Question 13

A random variable ( X ) has a probability distribution given by: \( P\( X = x \ \) = \begin{cases} \frac{1}{2} & \text{if } x = 1 \ \frac{1}{4} & \text{if } x = 2 \ \frac{1}{4} & \text{if } x = 3 \ \end{cases} ). Find the probability that ( X ) takes a value greater than 2.

A. \frac{1}{2}

B. \frac{1}{4}

Correct C. \frac{3}{4}

D. \frac{1}{8}

Correct Answer: C

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Question 14

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 15

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

A. \frac{1}{4}

B. \frac{1}{2}

C. \frac{3}{4}

Correct D. \frac{2}{3}

Correct Answer: D

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Question 16

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{pmatrix} ].

A. 13

Correct B. -13

C. 0

D. 1

Correct Answer: B

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Question 17

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 18

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 2x - 3

D. y = 2x + 3

Correct Answer: A

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Question 19

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 20

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

A. 3

Correct B. 6

C. 9

D. 12

Correct Answer: B

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Question 21

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 22

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 23

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \( x + 2 \)² + \( y - 3 \)² = 16

B. \( x - 2 \)² + \( y + 3 \)² = 16

C. \( x + 2 \)² + \( y + 3 \)² = 16

D. \( x - 2 \)² + \( y - 3 \)² = 16

Correct Answer: A

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Question 24

A die is rolled twice. Find the probability that the sum of the two numbers is 7.

A. 1/6

Correct B. 1/12

C. 1/36

D. 1/24

Correct Answer: B

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Question 25

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = -2x + 7

D. y = 2x - 7

Correct Answer: A

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