Exam Body

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POST UTME IMS U 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. ( 12 )

B. ( 20 )

C. ( 30 )

D. ( 40 )

Correct Answer: A

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Question 2

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

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 3

Find the vector ( mathbf{a} ) given that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = egin{pmatrix} 2 \ 1 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix} \).

Correct A. \( egin{pmatrix} 3 \ 2 \end{pmatrix} \)

B. \( egin{pmatrix} 2 \ 3 \end{pmatrix} \)

C. \( egin{pmatrix} 1 \ 1 \end{pmatrix} \)

D. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)

Correct Answer: A

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Question 4

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

Correct A. ( 3094 )

B. ( 3095 )

C. ( 3096 )

D. ( 3097 )

Correct Answer: A

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Question 5

Solve the equation \( x^3 + 2x^2 - 7x + 12 = 0 \).

Correct A. \( x = -3 \)

B. \( x = -1 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: A

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Question 6

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).

Correct A. \( \frac{4}{5} \)

B. \( \frac{3}{4} \)

C. \( \frac{5}{4} \)

D. \( \frac{4}{3} \)

Correct Answer: A

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Question 7

A cylindrical \tank with a radius of 5m and height of 10m is filled with water. Find the volume of water in the \tank.

A. \( 785.4 , \text{m}^3 \)

Correct B. \( 1570.8 , \text{m}^3 \)

C. \( 3141.6 , \text{m}^3 \)

D. \( 6283.2 , \text{m}^3 \)

Correct Answer: B

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Question 8

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

Correct A. ( f'(x) = \cos(2x) cdot 2 )

B. ( f'(x) = \sin(2x) cdot 2 )

C. ( f'(x) = \cos(2x) cdot 4 )

D. ( f'(x) = \sin(2x) cdot 4 )

Correct Answer: A

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Question 9

A set of exam scores has a mean of 80 and a s\tandard deviation of 10. What is the z-score of a score of 90?

A. \( z = 0.5 \)

Correct B. \( z = 1.0 \)

C. \( z = 1.5 \)

D. \( z = 2.0 \)

Correct Answer: B

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Question 10

Simplify the expression \( \frac{2^3 cdot 3^2}{2^2 cdot 3} \).

Correct A. \( 2 cdot 3 = 6 \)

B. \( 2^3 cdot 3^2 = 72 \)

C. \( 2^2 cdot 3 = 12 \)

D. \( \frac{2^3 cdot 3^2}{2^2 cdot 3} = 4 \)

Correct Answer: A

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Question 11

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find \( lim_{x \to 2} f\( x \ \) ) u\sing the chain rule.

A. \( \frac{0}{0} \ \)

B. \( 4 \ \)

Correct C. \( 2 \ \)

D. \( \frac{4}{2} \ \)

Correct Answer: C

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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 5 terms of the geometric series \( 2 + 6 + 18 + \ldots \).

A. \( 62 \ \)

Correct B. \( 64 \ \)

C. \( 66 \ \)

D. \( 68 \ \)

Correct Answer: B

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Question 14

Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Find the number of subsets of S that contain exactly 3 elements.

Correct A. \( 120 \ \)

B. \( 126 \ \)

C. \( 132 \ \)

D. \( 140 \ \)

Correct Answer: A

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Question 15

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

Correct A. \( x = -2 \ \)

B. \( x = -1 \ \)

C. \( x = 0 \ \)

D. \( x = 1 \ \)

Correct Answer: A

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Question 16

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi cm^3

B. 64\pi cm^3

Correct C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: C

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Question 17

Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 4x + 3} > 0.

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

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

C. \left\( -\infty, 1\right \) \cup \left\( 3, \infty\right \)

D. \left\( -\infty, -1\right \) \cup \left\( 1, \infty\right \)

Correct Answer: A

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Question 18

A firm produces two products, A and B. The profit function is given by \pi(x, y) = 2x + 3y - 0.5x^2 - 2y^2, where x and y are the quantities of products A and B, respectively. Find the critical points of the profit function.

Correct A. \left\( 4, 2\right \)

B. \left\( 2, 4\right \)

C. \left\( 1, 3\right \)

D. \left\( 3, 1\right \)

Correct Answer: A

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Question 19

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 20

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 21

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).

Correct A. \( \frac{4pi}{3} \)

B. \( \frac{5pi}{3} \)

C. \( \frac{2pi}{3} \)

D. \( \frac{pi}{3} \)

Correct Answer: A

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Question 22

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

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

Correct Answer: A

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Question 23

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

Correct A. \( x = \frac{-5 pm \sqrt{109}}{4} \)

B. \( x = \frac{5 pm \sqrt{109}}{4} \)

C. \( x = \frac{-5 pm \sqrt{109}}{2} \)

D. \( x = \frac{5 pm \sqrt{109}}{2} \)

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 = 25 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 49 )

Correct Answer: A

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Question 25

Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).

Correct A. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} \)

B. \( mathbf{v} = 4mathbf{i} + 3mathbf{j} \)

C. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} \)

D. \( mathbf{v} = 4mathbf{i} - 3mathbf{j} \)

Correct Answer: A

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