Exam Body

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POST UTME OAU 2018 Mathematics | Objective

Are you preparing for POST UTME OAU 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

In a survey of 100 students, the mean height of the students is 175 cm. If the s\tandard deviation of the heights is 5 cm, what is the probability that a randomly selected student will have a height between 170 cm and 180 cm?

Correct A. 0.6915

B. 0.3085

C. 0.5

D. 0.8413

Correct Answer: A

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Question 2

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 3

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 4

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?

A. 48

Correct B. 50

C. 52

D. 54

Correct Answer: B

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Question 5

A basket contains 5 red apples and 3 green apples. If 2 apples are drawn at random, what is the probability that both apples are red?

Correct A. 0.25

B. 0.5

C. 0.75

D. 0.9

Correct Answer: A

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Question 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The frustum is cut off by a plane parallel to the base of the cone.

Correct A. 48\pi cm^3

B. 64\pi cm^3

C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: A

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Question 7

Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 8

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

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 6x + 1

D. f'(x) = 6x - 1

Correct Answer: A

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Question 9

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. What is the mean score of the class?

Correct A. 11.2

B. 12.1

C. 13.5

D. 14.8

Correct Answer: A

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Question 10

Find the determinant of the matrix \[ \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \] u\sing the formula for 2x2 matrices.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 11

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 12

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 13

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

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 14

A vector ( mathbf{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. 3, 4

B. 4, 3

C. 5, 5

D. 6, 6

Correct Answer: A

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Question 15

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

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 16

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 17

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

A. 40

Correct B. 50

C. 60

D. 70

Correct Answer: B

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Question 18

Find the derivative of the function [ f(x) = \frac{1}{x^2} \] u\sing the chain rule.

A. \frac{-2}{x^3}

Correct B. \frac{2}{x^3}

C. \frac{-1}{x^3}

D. \frac{1}{x^3}

Correct Answer: B

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Question 19

Solve the inequality [ 2x^2 + 5x - 3 \geq 0 \].

Correct A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)

B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)

D. \left\( -\infty, \frac{3}{2} \right \) \cup \left\( -\frac{1}{2}, \infty \right \)

Correct Answer: A

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Question 20

Find the value of [ \log_{10} (1000) \].

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 21

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 22

A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. What is the probability that a randomly selected number from this set is greater than 25?

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 23

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -3 \) ∪ (1, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 24

Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ... ).

Correct A. 1950

B. 1960

C. 1970

D. 1980

Correct Answer: A

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Question 25

A polynomial function has a degree of 4 and has roots at x = -2, x = 1, x = 3, and x = 4. What is the polynomial function?

Correct A. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x - 4 \)

B. \( x - 2 \)\( x + 1 \)\( x + 3 \)\( x + 4 \)

C. \( x + 2 \)\( x - 1 \)\( x + 3 \)\( x - 4 \)

D. \( x - 2 \)\( x + 1 \)\( x - 3 \)\( x + 4 \)

Correct Answer: A

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