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POST UTME IMS U 2019 Mathematics | Objective

Prepare for your exams with POST UTME IMS U questions? Reviewing past/model 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 View Details

Solve the inequality (\(\frac{x}{x-2}\(> 1\)\) for \\((frac{x}{x-2} > 1\(x > 2\)\).

Correct A. \(x > 3 \\)

B. \(x < 3 \\)

C. \(x = 3 \\)

D. \(x = 2 \\)

Correct Answer: A

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Question 2 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

A car travels from city A to city B at an average speed of \((60km/h\)\) and returns at an average speed of \(40km/h\\((60km/h) and returns at an average speed of\). If the distance 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 View Details

Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{x^3 + 2x^2 - 5x + 1}{x^2 + 3x - 2}\)\)\) ) using 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 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\) using 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 View Details

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 View Details

Solve the system of equations \(x + y = 3\) and \(xy = 2\) using 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 View Details

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

Correct A. \(2 \(1x\)1x\)

B. \(\cos^2 x\)

C. \(\sin^2 x\)

D. \(\cos^2 x - \sin^2 x\)

Correct Answer: A

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Question 16 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 function is given by ( C(x) = \((2x^2 + 5x + 1\)\cost.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 21 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

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 View Details

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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