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POST UTME COAL CITY UNIVERSITY 2024 Mathematics | Objective

Are you preparing for POST UTME COAL CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 173.1 cm, 177.9 cm

B. 174.5 cm, 176.5 cm

C. 172.9 cm, 178.1 cm

D. 171.7 cm, 179.3 cm

Correct Answer: A

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Question 2

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

A. 10^4

Correct B. 10^8

C. 10^12

D. 10^16

Correct Answer: B

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Question 3

A quadratic equation is given by \(x^2 + 4x + 4 = 0\). Solve for x u\sing the quadratic formula.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 4

A circle has an equation of \(x^2 + y^2 = 16\). Find the equation of the \tangent line to the circle at the point (4, 0).

Correct A. y = -x + 4

B. y = x + 4

C. y = x - 4

D. y = -x - 4

Correct Answer: A

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Question 5

A function f(x) is defined as \(f(x) = 2x^2 + 3x - 1\). Find the derivative of f(x) u\sing the power rule.

Correct A. 4x + 3

B. 2x + 3

C. 4x - 3

D. 2x - 3

Correct Answer: A

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Question 6

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 6 & 8 & 3 \end{pmatrix} ].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7

Solve for x in the equation [ 2x^2 + 5x - 3 = 0 ].

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 8

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

B. \( x + 3 \)^2 + \( y + 4 \)^2 = 16

C. \( x - 3 \)^2 + \( y + 4 \)^2 = 16

D. \( x + 3 \)^2 + \( y - 4 \)^2 = 16

Correct Answer: A

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Question 9

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 10

Find the volume of the cylinder with radius 6 and height 8.

Correct A. 288\pi

B. 288\pi^2

C. 288\pi^3

D. 288\pi^4

Correct Answer: A

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Question 11

Determine the value of x in the equation \( \tan^2 x + 1 = sec^2 x \) for \( 0 leq x leq \frac{pi}{2} \).

Correct A. \( \frac{\pi}{4} \)

B. \( \frac{\pi}{2} \)

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

D. \( \frac{\pi}{6} \)

Correct Answer: A

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Question 12

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 13

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).

Correct A. \( 3094 \ \)

B. \( 3095 \ \)

C. \( 3096 \ \)

D. \( 3097 \ \)

Correct Answer: A

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Question 14

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

Correct A. \( x = 1, y = 1 \ \)

B. \( x = 2, y = 1 \ \)

C. \( x = 1, y = 2 \ \)

D. \( x = 2, y = 2 \ \)

Correct Answer: A

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Question 15

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

Correct A. \( 0 \ \)

B. \( 1 \ \)

C. \( 2 \ \)

D. \( 3 \ \)

Correct Answer: A

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Question 16

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].

Correct A. -1

B. 1

C. 0

D. 2

Correct Answer: A

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Question 17

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

A. \frac{-2x}{\( x^2 + 1 \)^2}

Correct B. \frac{2x}{\( x^2 + 1 \)^2}

C. \frac{-2}{\( x^2 + 1 \)^2}

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

Correct Answer: B

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Question 18

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

A. \frac{\pi}{6}

B. \frac{\pi}{4}

Correct C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: C

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Question 19

Find the mean of the data set \[ 2, 4, 6, 8, 10 \].

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 20

Solve the system of equations \[ x + y = 2 \] and \[ x - y = 1 \].

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 21

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

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

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

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

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

Correct Answer: A

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Question 22

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue, given that it is not red?

A. \frac{1}{2}

Correct B. \frac{2}{5}

C. \frac{3}{8}

D. \frac{5}{7}

Correct Answer: B

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Question 23

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

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

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

D. \( -\infty, 3 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 24

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 25

A line passes through the points (1, 2) and (4, 6). Find the equation of the line in slope-intercept form.

Correct A. y = 2x - 2

B. y = 2x + 2

C. y = -2x + 2

D. y = -2x - 2

Correct Answer: A

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