Exam Body

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Subject

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POST UTME ELIZADE UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME ELIZADE 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.

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Question 1

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pi\text{ cm}^3

Correct B. 300\pi\text{ cm}^3

C. 400\pi\text{ cm}^3

D. 500\pi\text{ cm}^3

Correct Answer: B

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Question 2

Solve for x in the equation \( \frac{1}{x+1} + \frac{1}{x-2} = \frac{3}{x^2-3x-2}\ \).

A. x = 1

B. x = -1

Correct C. x = 2

D. x = -2

Correct Answer: C

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Question 3

A set of 5 consecutive integers has a median of 10. What is the sum of the integers?

A. 250

B. 260

Correct C. 270

D. 280

Correct Answer: C

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Question 4

A bakery sells 480 loaves of bread per day. If they make a profit of ₦2.50 per loaf, how much profit do they make in a day?

Correct A. ₦1200

B. ₦1200.00

C. ₦1200.00

D. ₦1200.00

Correct Answer: A

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Question 5

Find the surface area of the sphere with a radius of 6 cm.

Correct A. 288\pi\text{ cm}^2

B. 288\pi\text{ cm}^2

C. 288\pi\text{ cm}^2

D. 288\pi\text{ cm}^2

Correct Answer: A

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Question 6

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} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).

A. 0

Correct B. \begin{pmatrix} \frac{4}{13} \\ \frac{6}{13} \end{pmatrix}

C. \begin{pmatrix} \frac{2}{13} \\ \frac{3}{13} \end{pmatrix}

D. \begin{pmatrix} \frac{1}{13} \\ \frac{-2}{13} \end{pmatrix}

Correct Answer: B

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Question 7

A fair six-sided die is rolled. What is the probability that the number appearing on the die is even?

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 8

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

A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)

B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)

Correct C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)

D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)

Correct Answer: C

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Question 9

Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \) u\sing the definite integral.

Correct A. \frac{20}{3}

B. \frac{22}{3}

C. \frac{24}{3}

D. \frac{26}{3}

Correct Answer: A

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Question 10

A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the sum of the first 5 terms of the sequence.

A. 63

Correct B. 65

C. 67

D. 69

Correct Answer: B

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Question 11

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

Correct A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16

B. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16

C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16

D. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 12

Solve the system of linear equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - y &= 3 \end{align*}

Correct A. \text{Solution: } x = 2, y = 2

B. \text{Solution: } x = 1, y = 3

C. \text{Solution: } x = 3, y = 1

D. \text{Solution: } x = 4, y = 0

Correct Answer: A

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Question 13

Find the volume of the sphere with radius 6.

Correct A. 904.778

B. 904.778

C. 904.778

D. 904.778

Correct Answer: A

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Question 14

Solve the quadratic equation: \begin{align*} x^2 + 5x + 6 &= 0 \end{align*}

Correct A. \text{Solution: } x = -2, x = -3

B. \text{Solution: } x = 2, x = 3

C. \text{Solution: } x = -1, x = -6

D. \text{Solution: } x = 1, x = 6

Correct Answer: A

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Question 15

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

Correct A. \text{Equation: } y = 2x - 1

B. \text{Equation: } y = 2x + 1

C. \text{Equation: } y = -2x + 1

D. \text{Equation: } y = -2x - 1

Correct Answer: A

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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 random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.

Correct A. 1.5

B. 2

C. 2.5

D. 3

Correct Answer: A

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Question 18

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

Correct A. 2\sin x \cos x

B. \cos^2 x

C. \sin^2 x

D. \tan x

Correct Answer: A

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Question 19

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 70.

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 20

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.

A. 0

B. \frac{\pi}{2}

Correct C. \frac{\pi}{4}

D. \frac{3\pi}{4}

Correct Answer: C

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Question 21

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 22

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 23

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores are above 60, what is the value of the lower limit of the interval?

A. 50

Correct B. 55

C. 60

D. 65

Correct Answer: B

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Question 24

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

A. 16

Correct B. 32

C. 64

D. 128

Correct Answer: B

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Question 25

A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who prefer only Mathematics?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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