Exam Body

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POST UTME IMS U 2017 Mathematics | Objective

Are you preparing for POST UTME IMS U exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the value of $\frac{d}{dx} \left$ \frac{1}{x^2 + 1} \right $$ u\sing the quotient rule.

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

B. \frac{2x}{$ x^2 + 1 $^2}

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

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 2

Solve the inequality $|2x - 1| \geq 3$.

Correct A. $x \leq -1$ or $x \geq 2$

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

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

D. $x \leq -1$ or $x \geq 3$

Correct Answer: A

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Question 3

Find the area of the triangle with vertices $(0, 0), (3, 0),$ and $(0, 2)$.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 4

Solve the system of equations $x + y = 2$ and $x - y = 1$.

Correct A. $x = 1.5, y = 0.5$

B. $x = 0.5, y = 1.5$

C. $x = 1, y = 1$

D. $x = 2, y = 0$

Correct Answer: A

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Question 5

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ u\sing the quotient rule.

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

B. $\frac{2x}{$ x^2 + 1 $^2}$

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

D. $\frac{2}{$ x^2 + 1 $^2}$

Correct Answer: A

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Question 6

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 7

Evaluate the integral $ int_{0}^{1} x^2 \sin x , dx $.

Correct A. $ -\cos x^2 + 2x \sin x + 2 \cos x $

B. $ -\cos x^2 - 2x \sin x - 2 \cos x $

C. $ \cos x^2 - 2x \sin x + 2 \cos x $

D. $ \cos x^2 + 2x \sin x - 2 \cos x $

Correct Answer: A

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Question 8

Solve the inequality $ \frac{x}{x - 1} > 1 $.

Correct A. $ x < -1 $ or $ x > 1 $

B. $ x < 0 $ or $ x > 1 $

C. $ x < 0 $ or $ x > 2 $

D. $ x < -1 $ or $ x > 2 $

Correct Answer: A

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Question 9

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 10

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 11

Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 12

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 13

Solve the equation \\tan x + \\cot x = 3.

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

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

C. \\frac{\pi}{2}

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

Correct Answer: B

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Question 14

Let a, b, and c be positive real numbers such that a^2 + b^2 + c^2 = 1. Find the maximum value of a^2b^2.

A. \\frac{1}{4}

B. \\frac{1}{2}

Correct C. \\frac{3}{4}

D. 1

Correct Answer: C

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Question 15

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 16

A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

B. 512\pi

Correct C. 768\pi

D. 1024\pi

Correct Answer: C

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Question 17

A die is rolled twice. What is the probability that the sum of the two numbers shown on the dice is 7?

Correct A. \frac{1}{6}

B. \frac{1}{12}

C. \frac{1}{36}

D. \frac{1}{24}

Correct Answer: A

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Question 18

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

Correct A. \left$ -2, \ 0 \right $

B. \left$ 0, \ -2 \right $

C. \left$ -2, \ -2 \right $

D. \left$ 2, \ 0 \right $

Correct Answer: A

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Question 19

Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, ...

A. 55

B. 65

Correct C. 75

D. 85

Correct Answer: C

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Question 20

A circle has a diameter of 14 cm. Find the area of the circle in square centimeters.

A. 154\pi

Correct B. 196\pi

C. 245\pi

D. 308\pi

Correct Answer: B

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Question 21

Determine the value of $x$ in the equation $\left| 2x - 3 \right| + 2 = 7$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22

A histogram of exam scores is shown below. If the mean score is 75, what is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 23

Solve the equation $\frac{1}{2} \log_{10} $ x^2 $ = 4$ for $x$.

A. 10

B. 20

C. 40

Correct D. 80

Correct Answer: D

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Question 24

In the diagram below, what is the value of $x$?

A. 30

B. 45

Correct C. 60

D. 90

Correct Answer: C

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Question 25

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30

B. 50

Correct C. 60

D. 70

Correct Answer: C

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