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POST UTME CALEB UNIVERSITY 2017 Mathematics | Objective

Prepare for your exams with POST UTME CALEB UNIVERSITY questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

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

Correct A. $x > 4$

B. $x > 6$

C. $x < 4$

D. $x < 6$

Correct Answer: A

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Question 2 View Details

Find the area under the curve $y = $1x \$ ) from $x = 0$ to $x = \frac{\pi}{2}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 3 View Details

A particle moves in a straight line with its position given by ( s(t) = $(2t^3 - 5t^2 + 3t + 1$\) ). Find the velocity and acceleration at time $t = 1\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity and acceleration at time$.

Correct A. $v(1) = 5$,$a(1) = -3$

B. $v(1) = 3$,$a(1) = 5$

C. $v(1) = -3$,$a(1) = 5$

D. $v(1) = 5$,$a(1) = -5$

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 6 View Details

Find the derivative of the function ( f(x) = $\frac{1}{2x^2 + 3x - 1}$\)\) ) using the quotient rule.

Correct A. f'$(x) =$$\frac{-4x + 3}{2x^2 + 3x - 1$ ^2}\)\)

B. f'$(x) =$$\frac{4x + 3}{2x^2 + 3x - 1$ ^2}\)\)

C. f'$(x) =$$\frac{2x^2 + 3x - 1}{$ $2x^2 + 3x - 1$ ^2}\)\)

D. f'$(x) =$$\frac{-2x^2 - 3x + 1}{$ $2x^2 + 3x - 1$ ^2}\)\)

Correct Answer: A

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Question 7 View Details

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

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 8 View Details

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. \text{Area of triangle}$= 2.5$

B. \text{Area of triangle}$= 3.5$

C. \text{Area of triangle}$= 4.5$

D. \text{Area of triangle}$= 5.5$

Correct Answer: A

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Question 9 View Details

Solve the trigonometric equation $2 \sin^2 x + 3 $1x - 1 = 0$.

Correct A. \$sin x =$$\frac{1}{2}$\)

B. \$cos x =$$\frac{1}{2}$\)

C. \$sin x =$$\frac{1}{3}$\)

D. \$cos x =$$\frac{1}{3}$\)

Correct Answer: A

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Question 10 View Details

Find the value of ( x ) in the equation $x^3 - 6x^2 + 11x - 6 = 0$.

Correct A. $x = 1$

B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: A

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Question 11 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 12 View Details

Find the determinant of the matrix [ egin{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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Question 13 View Details

Solve the inequality [ \$(2x^2 + 3x - 1$$> 0$\) ].

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

B. $-\infty, 0$ \cup $1, \infty$

C. $-\infty, -1$ \cup (0, 1)

D. $-\infty, 1$

Correct Answer: A

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Question 14 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 + $y - 3$^$2 = 4$

C. $x - 3$^2 + $y - 2$^$2 = 16$

D. $x - 3$^2 + $y - 2$^$2 = 4$

Correct Answer: A

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Question 15 View Details

Solve the trigonometric equation [ 2 \$\sin^2$ x + 3 \cos $x - 1 = 0$ ].

A. $x =$$\frac{\pi}{6}$\)

B. $x =$$\frac{\pi}{4}$\)

Correct C. $x =$$\frac{\pi}{3}$\)

D. $x =$$\frac{\pi}{2}$\)

Correct Answer: C

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Question 16 View Details

Find the derivative of the function ( f(x) = $\frac{1}${\sqrt{1 - $x^2}}$\) ) using the chain rule.

Correct A. f'$(x) =$$\frac{x}${ 1 - $x^2$ \)^{$3/2$}}\)

B. f'$(x) =$$\frac{-x}${ 1 - $x^2$ \)^{$3/2$}}\)

C. f'$(x) =$$\frac{1}${ 1 - $x^2$ \)^{$3/2$}}\)

D. f'$(x) =$$\frac{2x}${ 1 - $x^2$ \)^{$3/2$}}\)

Correct Answer: A

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Question 17 View Details

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

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 18 View Details

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 19 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$ using trigonometric identities.

Correct A. \$\sin^2$$x =$\$\cos^2$ x

B. \$\sin^2$$x =$\$\cos^2$ x + 1

C. \$\sin^2$$x =$\$\cos^2$ x - 1

D. \$\sin^2$$x =$\$\cos^2$ x + 2

Correct Answer: A

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Question 20 View Details

Find the derivative of the function ( f(x) = $x^3$ \sin x ) using the product rule.

Correct A. f'$(x) =$$3x^2$ \sin x + $x^3$ \cos x

B. f'$(x) =$$3x^2$ \sin x - $x^3$ \cos x

C. f'$(x) =$$3x^2$ \cos x + $x^3$ \sin x

D. f'$(x) =$$3x^2$ \cos x - $x^3$ \sin x

Correct Answer: A

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Question 21 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. 2

D. 3

Correct Answer: B

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Question 22 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is its volume?

A. 400 $cm^3$

B. 500 $cm^3$

Correct C. 600 $cm^3$

D. 800 $cm^3$

Correct Answer: C

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Question 23 View Details

Solve the system of linear equations $\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$. What is the value of ( x )?

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 24 View Details

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 50.24 $cm^2$

B. 50.27 $cm^2$

C. 50.29 $cm^2$

D. 50.31 $cm^2$

Correct Answer: A

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Question 25 View Details

A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg?

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 12 cm

Correct Answer: C

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