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POST UTME CALEB UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME CALEB UNIVERSITY exams? Reviewing past 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.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. x > 4

B. x > 6

C. x < 4

D. x < 6

Correct Answer: A

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Question 2

Find the area under the curve $ y = \sin\( x \ $ ) 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

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 $.

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

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

Find the equation of the line pas\sing 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

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing 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

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

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

Solve the trigonometric equation $ 2 \sin^2 x + 3 \cos x - 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

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

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 12

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

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

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

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

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing 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

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing 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

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

Solve the equation $ \sin^2 x + \cos^2 x = 1 $ u\sing 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

Find the derivative of the function ( f(x) = x^3 \sin x ) u\sing 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

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. 2

D. 3

Correct Answer: B

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Question 22

A rec\tangular 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

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

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

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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