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POST UTME COVENANT UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Solve for 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 2 View Details

Find the value of $\sin^2 60^\circ \$ + \$\cos^2$ $60^\circ$ ).

Correct A. 1

B. 0

C. 2

D. 3

Correct Answer: A

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Question 3 View Details

A particle moves in a straight line with an initial velocity of 5 $(m/s$\). If it decelerates uniformly at a rate of 2 $m/s\\((m/s). If it decelerates uniformly at a rate of 2 \^2$, find its velocity after 4 seconds.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 4 View Details

In the diagram below, ( ABC ) is a right-angled triangle with angle (B = 90\)^\circ. If \$(B = 90)^\(AB = 3$ cm and $BC = 4$ cm, find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 5 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $-\infty, -1$ \cup $3, \infty$

B. $-\infty, 1$ \cup $3, \infty$

C. $-\infty, -1$ \cup $1, \infty$

D. $-\infty, 1$ \cup $1, \infty$

Correct Answer: A

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Question 6 View Details

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

A. 24

B. 30

Correct C. 36

D. 42

Correct Answer: C

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Question 7 View Details

Solve for ( x ) in the equation $\log_{10} x^2 \$$= 4 ).$

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 8 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 9 View Details

A particle moves in a straight line with an initial velocity of (5 , \text{$m/s$}\) and an acceleration of \$(5 , text{m/s}\(2 , \text{m/s}^2$. Find its velocity after ( 3 ) seconds.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 10 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x > \frac{3}{2}$

D. $x > -1$ or $x < \frac{3}{2}$

Correct Answer: A

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Question 11 View Details

A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

Correct A. 512\pi

B. 256\pi

C. 1024\pi

D. 2048\pi

Correct Answer: A

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Question 12 View Details

Solve for 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 13 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 14 View Details

A vector ($\vec{a}$\) has a magnitude of 6 units and makes an angle of 30\$(vec{a}\circ with the positive x-axis. Find the x and y components of \(\vec{a}$.

Correct A. 3\hat{i} + 3\hat{j}

B. 6\hat{i} + 3\hat{j}

C. 3\hat{i} + 6\hat{j}

D. 6\hat{i} + 6\hat{j}

Correct Answer: A

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Question 15 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. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 2$^2 + $y - 4$^$2 = 16$

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = x\^2 + 2x - 3$ from $x = 0$ to $x = 4$.

A. 120

B. 140

Correct C. 160

D. 180

Correct Answer: C

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Question 17 View Details

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 18 View Details

Find the value of x in the equation $x^3$ - \$(2x^2 - 5x + 6$$= 0.$\)

A. 1

B. -2

Correct C. 3

D. -3

Correct Answer: C

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Question 19 View Details

Solve the equation \$(x^2 + 4x - 5$$= 0$\) using the quadratic formula.

Correct A. $x = -5$, $x = 1$

B. $x = -1$, $x = 5$

C. $x = 1$,$x = -5$

D. $x = -5$,$x = -1$

Correct Answer: A

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Question 20 View Details

Find the area under the curve $y = x\^3 - 2x^2 + x + 1$ from $x = 0$ to $x = 2$.

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 21 View Details

Determine the value of $\int_0^1 x^2 \sin^2 x \, dx$.

Correct A. $\frac{1}{3}$\)

B. $\frac{1}{2}$\)

C. $\frac{2}{3}$\)

D. $\frac{1}{4}$\)

Correct Answer: A

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Question 22 View Details

Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$.

Correct A. $-\infty, -2$ \cup $2, \infty$

B. $-\infty, -2$ \cup $-2, 2$ \cup $2, \infty$

C. $-\infty, -2$ \cup $2, \infty$

D. $-\infty, 2$ \cup $2, \infty$

Correct Answer: A

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Question 23 View Details

Find the area under the curve $y = $1x$ from $x = 0$ to $x = \pi$.

Correct A. 2

B. 1

C. 0

D. -1

Correct Answer: A

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Question 24 View Details

Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.

Correct A. (1, 1)

B. (2, 0)

C. $-1, 3$

D. (0, 2)

Correct Answer: A

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Question 25 View Details

Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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