Exam Body

Year

Subject

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POST UTME CALEB UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2

Find the determinant of the matrix \\begin{bmatrix} 1 & 2 \\ 3 & 4 \\end{bmatrix}.

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 3

If f(x) = 2x^2 + 3x - 1, find f'(x) u\sing the chain rule.

Correct A. 4x + 3

B. 2x^2 + 3

C. 4x + 3x - 1

D. 2x^2 + 3x - 1

Correct Answer: A

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Question 4

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 5

Solve the system of equations \\begin{align*} x + y &= 2 \\ x - y &= 1 \\end{align*} u\sing matrices.

A. x = 1, y = 1

Correct B. x = 2, y = 0

C. x = 0, y = 2

D. x = 1, y = 2

Correct Answer: B

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Question 6

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)

Correct Answer: A

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Question 7

Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), given that \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).

Correct A. \( 5mathbf{i} - mathbf{j} \)

B. \( 2mathbf{i} + mathbf{j} \)

C. \( 3mathbf{i} + 2mathbf{j} \)

D. \( mathbf{i} - 3mathbf{j} \)

Correct Answer: A

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Question 8

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

A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

Correct C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )

Correct Answer: C

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Question 9

Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.

A. \( \frac{32}{3} pi \)

B. \( \frac{64}{3} pi \)

Correct C. \( \frac{128}{3} pi \)

D. \( \frac{256}{3} pi \)

Correct Answer: C

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Question 10

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

A. \( y = \frac{1}{2}x + 1 \)

Correct B. \( y = 2x - 1 \)

C. \( y = \frac{1}{2}x - 1 \)

D. \( y = 2x + 1 \)

Correct Answer: B

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Question 11

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 48\pi\text{ cm}^3

B. 64\pi\text{ cm}^3

Correct C. 80\pi\text{ cm}^3

D. 96\pi\text{ cm}^3

Correct Answer: C

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Question 12

A die is rolled twice. What is the probability that the sum of the two numbers shown is 7?

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

Correct D. \frac{2}{3}

Correct Answer: D

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Question 13

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. \( x-2 \)^2+\( y-3 \)^2=9

D. \( x-2 \)^2+\( y-3 \)^2=25

Correct Answer: A

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Question 14

A particle moves along the curve y=x^2+2x+1. Find the equation of the \tangent line at the point where x=1.

Correct A. y=x+3

B. y=x+2

C. y=x-1

D. y=x-2

Correct Answer: A

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Question 15

Find the area of the region bounded by the parabola y=x^2, the line y=2x, and the x-axis.

A. \frac{16}{3}

Correct B. \frac{32}{3}

C. \frac{64}{3}

D. \frac{128}{3}

Correct Answer: B

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Question 16

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 17

A circle has a radius of 5 cm. Find the area of the circle.

A. 50π

Correct B. 100π

C. 150π

D. 200π

Correct Answer: B

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Question 18

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the chain rule.

A. 6x + 2

B. 6x + 2

Correct C. 6x^2 + 4x - 10

D. 6x^2 + 4x - 10

Correct Answer: C

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Question 19

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 1/2

B. 1/3

Correct C. 2/5

D. 3/8

Correct Answer: C

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Question 20

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -3 \) ∪ (1, ∞)

D. \( -∞, -1 \) ∪ (3, ∞)

Correct Answer: A

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Question 21

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.

Correct A. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)

B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)

C. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)

D. \( egin{pmatrix} 3 \ -6 \end{pmatrix} \)

Correct Answer: A

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Question 22

Find the equation of the circle with center ( C(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 23

Find the volume of the sphere with radius ( 6 ).

Correct A. \( \frac{4}{3} pi \( 6 \ \)^3 )

B. \( \frac{4}{3} pi \( 6 \ \)^2 )

C. \( \frac{4}{3} pi \( 6 \ \) )

D. \( \frac{4}{3} pi \( 6 \ \)^2 )

Correct Answer: A

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Question 24

Find the surface area of the sphere with radius ( 6 ).

Correct A. ( 4 pi (6)^2 )

B. ( 4 pi (6) )

C. ( 2 pi (6)^2 )

D. ( 2 pi (6) )

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \( y = \frac{2}{2} x + \frac{1}{2} \)

B. \( y = \frac{2}{2} x + \frac{3}{2} \)

C. \( y = \frac{2}{2} x + \frac{5}{2} \)

D. \( y = \frac{2}{2} x + \frac{1}{2} \)

Correct Answer: A

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