Exam Body

Year

Subject

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POST UTME UNIBEN 2018 Mathematics | Objective

Are you preparing for POST UTME UNIBEN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 2

Solve the matrix equation AX = B, where A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, X = \begin{bmatrix} x \\ y \end{bmatrix}, and B = \begin{bmatrix} 5 \\ 6 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 3

A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the value of a_5.

A. 33

B. 35

Correct C. 37

D. 39

Correct Answer: C

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Question 4

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly two elements.

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 5

A binary operation * is defined on the set of integers as follows: a * b = a^2 + b^2. Find the value of 2 * 3.

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 6

Determine the mean of the data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 7

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $ u\sing the quadratic formula. What is the value of x?

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 8

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

A. 32

B. 64

Correct C. 96

D. 128

Correct Answer: C

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Question 9

Solve the system of linear equations: $ 2x + 3y = 7 $ and $ x - 2y = -3 $.

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 determinant of the matrix $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $.

A. -2

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 11

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

Correct A. x > 4

B. x > 2

C. x < 2

D. x < 4

Correct Answer: A

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Question 12

A rec\tangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the surface area of the box.

A. 120 cm^2

Correct B. 150 cm^2

C. 180 cm^2

D. 200 cm^2

Correct Answer: B

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Question 13

If $ x^2 + 4x + 4 = 0 $, find the value of ( x ).

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 14

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 15

A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed for the entire trip?

A. 50 km/h

B. 55 km/h

Correct C. 60 km/h

D. 65 km/h

Correct Answer: C

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Question 16

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17

Solve the inequality $ x^2 - 6x + 8 > 0 $.

Correct A. x < 2 or x > 4

B. x < 4 or x > 2

C. x < 2 and x > 4

D. x > 2 and x < 4

Correct Answer: A

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Question 18

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

Correct A. $ x - 2 $^2 + $ y - 3 $^2 = 16

B. $ x - 3 $^2 + $ y - 2 $^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 19

A survey of 100 students found that 60% of them preferred pizza, 20% preferred burgers, and 20% preferred sandwiches. If 10 students preferred pizza and burgers, and 5 students preferred burgers and sandwiches, how many students preferred all three?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 20

Solve the system of equations $ x + y = 4 $ and $ xy = 5 $.

Correct A. x = 2, y = 2

B. x = 3, y = 1

C. x = 1, y = 3

D. x = 2, y = 3

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the population mean.

A. 170.3 cm, 180.7 cm

Correct B. 173.1 cm, 177.9 cm

C. 175.5 cm, 185.5 cm

D. 168.1 cm, 182.9 cm

Correct Answer: B

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Question 22

Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.

A. 120\pi cm^3

Correct B. 150\pi cm^3

C. 180\pi cm^3

D. 200\pi cm^3

Correct Answer: B

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Question 23

Solve the equation $\sin^2 x + \cos^2 x = 1$ for $x$ in the interval $[0, 2\pi)$.

Correct A. \[x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\]

B. \[x = \frac{\pi}{2}, \frac{3\pi}{2}\]

C. \[x = \frac{\pi}{4}, \frac{3\pi}{4}\]

D. \[x = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{4}, \frac{7\pi}{4}\]

Correct Answer: A

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Question 24

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 25

Solve the system of equations \[\begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}\] u\sing matrices.

Correct A. \[x = 2, y = 2\]

B. \[x = 1, y = 3\]

C. \[x = 3, y = 1\]

D. \[x = 4, y = 0\]

Correct Answer: A

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