POST UTME IMS U 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
Correct A. \( x > 3 \ \)
B. \( x < 3 \ \)
C. \( x = 3 \ \)
D. \( x = 2 \ \)

Correct Answer: A

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Question 2
A cylindrical \tank with a radius of 4m and height of 10m is filled with water. Find the volume of water in the \tank.
A. \( 1600 \pi \text{ m}^3 \ \)
Correct B. \( 3200 \pi \text{ m}^3 \ \)
C. \( 4000 \pi \text{ m}^3 \ \)
D. \( 8000 \pi \text{ m}^3 \ \)

Correct Answer: B

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Question 3
A bakery sells 250 loaves of bread per day at ₦200 each. Calculate the total daily revenue.
Correct A. ₦50,000
B. ₦45,000
C. ₦40,000
D. ₦35,000

Correct Answer: A

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Question 4
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
Correct A. \( y = 2x - 1 \ \)
B. \( y = 2x + 1 \ \)
C. \( y = x + 2 \ \)
D. \( y = x - 2 \ \)

Correct Answer: A

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Question 5
A car travels from city A to city B at an average speed of 60km/h and returns at an average speed of 40km/h. If the dis\tance between the two cities is 240km, find the average speed for the round trip.
A. \( 48 \text{ km/h} \ \)
Correct B. \( 50 \text{ km/h} \ \)
C. \( 52 \text{ km/h} \ \)
D. \( 55 \text{ km/h} \ \)

Correct Answer: B

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Question 6
Solve the inequality \( \frac{x-2}{x+1} > 0 \) for \( x in \( -infty, -1 \ \) cup \( -1, 2 \) cup (2, infty) ).
A. \( -\infty, -1 \) \cup \( 2, \infty \)
Correct B. \( -\infty, -1 \) \cup \( -1, 2 \) \cup \( 2, \infty \)
C. \( -\infty, -1 \) \cup \( -1, 2 \)
D. \( -\infty, -1 \) \cup \( 2, \infty \)

Correct Answer: B

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Question 7
Find the value of ( x ) in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).
Correct A. -3
B. -2
C. -1
D. 0

Correct Answer: A

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Question 8
A set ( S ) contains the elements ( {1, 2, 3, 4, 5, 6} ). Find the number of subsets of ( S ) that contain exactly three elements.
A. 10
Correct B. 15
C. 20
D. 25

Correct Answer: B

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Question 9
In the diagram below, ( ABC ) is a triangle with \( AB = 5 \) cm, \( BC = 6 \) cm, and \( AC = 7 \) cm. Find the length of the altitude from ( A ) to ( BC ).
A. 3
B. 4
Correct C. 5
D. 6

Correct Answer: C

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Question 10
The mean of five numbers is 20. If one of the numbers is 15, find the sum of the other four numbers.
Correct A. 75
B. 80
C. 85
D. 90

Correct Answer: A

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Question 11
Find the derivative of the function ( f(x) = \frac{x^3 + 2x^2 - 5x + 1}{x^2 + 3x - 2} ) u\sing the quotient rule.
A. \( \frac{3x^2 + 4x - 5}{\( x^2 + 3x - 2 \ \)^2} )
Correct B. \( \frac{3x^2 + 4x - 5}{\( x^2 + 3x - 2 \ \)^2} - \frac{2\( x^2 + 3x - 2 \)}{\( x^2 + 3x - 2 \)^2} )
C. \( \frac{3x^2 + 4x - 5}{\( x^2 + 3x - 2 \ \)^2} + \frac{2\( x^2 + 3x - 2 \)}{\( x^2 + 3x - 2 \)^2} )
D. \( \frac{3x^2 + 4x - 5}{\( x^2 + 3x - 2 \ \)^2} - \frac{2\( x^2 + 3x - 2 \)}{\( x^2 + 3x - 2 \)^2} + \frac{3x^2 + 4x - 5}{\( x^2 + 3x - 2 \)^2} )

Correct Answer: B

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Question 12
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) u\sing interval notation.
Correct A. \( -infty, -3 \ \) cup \( -3, -1 \) cup (1, infty) )
B. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )
C. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )
D. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )

Correct Answer: A

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Question 13
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(5, 6) ).
A. 10
B. 20
Correct C. 30
D. 40

Correct Answer: C

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Question 14
Solve the system of equations \( x + y = 3 \) and \( xy = 2 \) u\sing substitution.
Correct A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)

Correct Answer: A

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Question 15
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. \( \cos^2 x - \sin^2 x \)

Correct Answer: A

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Question 16
Solve for 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
Find the value of \( \frac{d}{dx} \( x^3 - 6x^2 + 11x - 6 \ \) ).
Correct A. 3x^2 - 12x + 11
B. 3x^2 - 12x + 6
C. 3x^2 - 12x - 6
D. 3x^2 + 12x - 6

Correct Answer: A

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Question 18
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 19
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 20
A company produces x units of a product, where the \cost function is given by ( C(x) = 2x^2 + 5x + 1 ). Find the value of x that minimizes the \cost.
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 21
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. 24\pi cm^3
B. 48\pi cm^3
Correct C. 72\pi cm^3
D. 96\pi cm^3

Correct Answer: C

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Question 22
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.
Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 23
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. \frac{1}{4}
Correct B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}

Correct Answer: B

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Question 24
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. -1
D. 2

Correct Answer: A

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Question 25
Solve the polynomial equation \begin{align*} x^3 + 2x^2 - 7x - 12 = 0. \end{align*}
A. x = -3
B. x = -1
Correct C. x = 3
D. x = 4

Correct Answer: C

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