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POST UTME CALEB UNIVERSITY 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

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. $\frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4$

Correct Answer: A

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Question 2 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using the Rational Root Theorem.

A. $x = 1$

B. $x = 2$

Correct C. $x = 3$

D. $x = 4$

Correct Answer: C

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Question 3 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using the Chain Rule.

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

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

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

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

Correct Answer: A

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Question 4 View Details

Solve the system of equations using matrices:\nn$egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}$.

Correct A. $x = 2, y = 3$

B. $x = 3, y = 2$

C. $x = 4, y = 5$

D. $x = 5, y = 4$

Correct Answer: A

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Question 5 View Details

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

Correct A. $\frac{1}{2} \times 2 \times 3$

B. $\frac{1}{2} \times 3 \times 2$

C. $\frac{1}{2} \times 2 \times 4$

D. $\frac{1}{2} \times 3 \times 4$

Correct Answer: A

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Question 6 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 7 View Details

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. 120\pi

B. 150\pi

Correct C. 180\pi

D. 200\pi

Correct Answer: C

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Question 8 View Details

Solve the inequality $x^2 - 6x + 8 > 0$.

A. $x < 2$

Correct B. $x > 2$

C. $x < 4$

D. $x > 4$

Correct Answer: B

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Question 9 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 10 View Details

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

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

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

C. $x =$$\frac{3\pi}{4}$\)

D. $x =$$\frac{5\pi}{4}$\)

Correct Answer: B

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 12 View Details

Solve the equation [ \$\sin^2$ x + \$\cos^2$$(x = 1$\) \] for [ 0 \\$((x = 1)$\leq x \leq 2 \pi \].

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

B. $x =$$\frac{3\pi}{2}$\)

C. $x =$\pi

D. $x = 0$

Correct Answer: A

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Question 13 View Details

A random experiment has two independent events [ A ] and [ B \]. If [$P(A) =$$\\(] and [ B ]. If [ P(A) = \frac{1}{2}$\) \] and [$P(B) =$$\frac{1}{3}$\) \], find [ P$A \cap B$ \].

Correct A. $\frac{1}{6}$\)

B. $\frac{1}{3}$\)

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

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

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

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

Correct Answer: A

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Question 15 View Details

Find the derivative of the function [$f(x) =$$\frac{1}{x^2 + 1}$\)\) \].

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

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

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

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

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a population of 1000 students has a mean height of 170 cm with a standard deviation of 5 cm. Calculate the probability that the sample mean height of a new random sample of 20 students will be less than 165 cm.

A. 0.001

B. 0.01

C. 0.1

Correct D. 0.5

Correct Answer: D

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Question 17 View Details

Solve the following system of linear equations using matrices:

A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

Correct C. \begin{bmatrix} 5 \\ 11 \end{bmatrix}

D. \begin{bmatrix} 7 \\ 13 \end{bmatrix}

Correct Answer: C

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Question 18 View Details

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 19 View Details

Find the derivative of the function f(x) = $3x^2 + 2x - 5$.

Correct A. 6x + 2

B. $3x^2 + 2$

C. 6x - 2

D. $3x^2 - 2$

Correct Answer: A

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Question 20 View Details

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the box.

Correct A. 72

B. 48

C. 24

D. 12

Correct Answer: A

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Question 21 View Details

Solve the inequality ($\frac{\(x^2 - 4}{x + 2}$$> 0$\) for x in \$(frac{x^2 - 4}{x + 2} > 0\(-\infty, -2 \ cup -2, \infty$ )\).

A. $-2, -1$ ∪ (1, ∞)

Correct B. $-∞, -2$ \cup $-1, 1$\)∪ (1, ∞)

C. $-∞, -2$ ∪ (1, ∞)

D. $-2, -1$ ∪ (1, ∞)

Correct Answer: B

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Question 22 View Details

A matrix ( A ) is defined as $A = egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}$. Find the determinant of ( A ).

Correct A. 5

B. 3

C. 2

D. 1

Correct Answer: A

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Question 23 View Details

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 24 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using the chain rule.

Correct A. $2 \(1x$1x\)

B. $$1x$

C. $$1x$

D. $\cos^2 x$

Correct Answer: A

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Question 25 View Details

A quadratic equation is defined as $x^2 + 4x + 4 = 0$. Find the roots of the equation.

Correct A. $-2, 0$

B. $-1, 1$

C. (0, 2)

D. $-1, -1$

Correct Answer: A

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