Exam Body

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Subject

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POST UTME CALEB UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 2

If \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \overrightarrow{b} = \begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix}, find the cross product \overrightarrow{a} \times \overrightarrow{b}.

Correct A. \begin{pmatrix} 5 \ -11 \ -1 \end{pmatrix}

B. \begin{pmatrix} -5 \ 11 \ 1 \end{pmatrix}

C. \begin{pmatrix} 5 \ 11 \ 1 \end{pmatrix}

D. \begin{pmatrix} -5 \ -11 \ 1 \end{pmatrix}

Correct Answer: A

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Question 3

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

A. x = \frac{\pi}{4}

Correct B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: B

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Question 4

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

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 5

If f(x) = 2x^2 + 3x - 1, find the derivative f'(x).

Correct A. 4x + 3

B. 2x + 1

C. 4x - 3

D. 2x - 1

Correct Answer: A

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Question 6

Solve the inequality $ \frac{x-2}{x+1} > 0 $ for $ x in \( -infty, -1 \ $ cup $ -1, 2 $ cup (2, infty) ).

A. $ -\infty, -1 $ \cup $ 2, \infty $

B. $ -\infty, -1 $ \cup $ -1, 2 $

Correct C. $ -\infty, -1 $ \cup $ 2, \infty $

D. $ -\infty, -1 $ \cup $ 2, \infty $

Correct Answer: C

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Question 7

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 = 4

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

D. $ x - 2 $^2 + $ y - 3 $^2 = 9

Correct Answer: C

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Question 8

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the highest score is 90, find the number of students who scored 80.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 9

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + ldots $.

A. 1950

B. 1960

Correct C. 1970

D. 1980

Correct Answer: C

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Question 10

Solve the equation $ x^2 - 6x + 8 = 0 $.

Correct A. (2, 4)

B. (3, 2)

C. (4, 3)

D. (2, 2)

Correct Answer: A

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Question 11

Find the value of $x$ in the equation $2^x + 2^{x+1} = 3 cdot 2^{x+1}$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 12

Solve the inequality $\left| x - 2 \right| \geq 3$.

Correct A. $x \leq -1$ or $x \geq 5$

B. $x \leq 1$ or $x \geq 5$

C. $x \leq -1$ or $x \geq 2$

D. $x \leq 1$ or $x \geq 2$

Correct Answer: A

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Question 13

In the diagram below, $ABCD$ is a rec\tangle and $E$ is the midpoint of $AD$. If $AB = 6$ and $BC = 8$, find the area of triangle $ADE$.

Correct A. 24

B. 30

C. 36

D. 40

Correct Answer: A

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Question 14

Find the value of $x$ in the equation $\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}$.

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 15

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 16

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

A. 64\pi

B. 96\pi

Correct C. 128\pi

D. 192\pi

Correct Answer: C

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Question 17

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

A. 10^4

B. 10^8

Correct C. 10^{16}

D. 10^{32}

Correct Answer: C

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Question 18

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 19

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 3120

B. 3240

Correct C. 3360

D. 3480

Correct Answer: C

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Question 20

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 = 25

Correct C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: C

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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 projection of ( mathbf{b} ) onto ( mathbf{a} ).

A. $ egin{pmatrix} 0 \ 0 \end{pmatrix} $

Correct B. $ egin{pmatrix} 1 \ -\frac{1}{2} \end{pmatrix} $

C. $ egin{pmatrix} \frac{1}{2} \ -\frac{3}{2} \end{pmatrix} $

D. $ egin{pmatrix} 1 \ -1 \end{pmatrix} $

Correct Answer: B

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Question 22

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3 or 5?

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

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

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

D. $ \frac{5}{6} $

Correct Answer: C

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Question 23

Let $ A = { 1, 2, 3, 4, 5 } $ and $ B = { 2, 4, 6, 8, 10 } $. Find ( A cap B ).

A. ( { 1, 2, 3, 4, 5 } )

B. ( { 2, 4, 6, 8, 10 } )

C. ( { 1, 2, 3, 4, 5, 6, 8, 10 } )

Correct D. ( { 2, 4 } )

Correct Answer: D

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Question 24

The sum of the first 10 terms of the arithmetic progression ( 1, 3, 5, ldots ) is ( 100 ). Find the first term.

Correct A. ( 1 )

B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: A

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Question 25

Simplify $ \frac{3x^2 + 2x - 1}{2x^2 - 5x + 1} $.

Correct A. $ \frac{3x + 1}{2x - 1} $

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

C. $ \frac{3x + 1}{2x + 1} $

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

Correct Answer: A

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