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POST UTME UNIBEN 2018 Mathematics | Objective

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Question 1 View Details

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 View Details

Solve the matrix equation (AX = B\), where A = \begin{bmatrix} 1 & 2 \\$((AX = B)$, where A = \\ 3 & 4 \end{bmatrix},$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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$ using 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 View Details

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 View Details

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 View Details

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 View Details

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

Correct A. $x > 4$

B. $x > 2$

C. $x < 2$

D. $x < 4$

Correct Answer: A

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Question 12 View Details

A rectangular 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 View Details

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 View Details

A company produces two products, A and B. The profit from product A is 10 per unit, and the profit from product B is15 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 View Details

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 $km/h\\((km/h). On the return trip, the car travels at an average speed of 40$. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard 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 View Details

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 View Details

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

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 View Details

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 View Details

Solve the system of equations $\begin{align*} x + y & = 4 \ 2x - 3y & = 5 \end{align*}$ using 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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