POST UTME DELSU 2019 Mathematics | Objective

Are you preparing for POST UTME DELSU 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 value of x in the equation \( \frac{1}{3}x + 2 = \frac{1}{6}x - 3 \) if x is in base 10.
Correct A. 6
B. 12
C. 18
D. 24

Correct Answer: A

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Question 2
A set A contains 5 elements, and a set B contains 3 elements. If the union of sets A and B is denoted by C, and the intersection of sets A and B is denoted by D, find the number of elements in set C if set D contains 2 elements.
A. 6
Correct B. 7
C. 8
D. 9

Correct Answer: B

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Question 3
Solve the inequality \( \frac{x-2}{x+1} > 0 \) u\sing interval notation.
Correct A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (2, ∞)
C. \( -∞, 1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)

Correct Answer: A

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Question 4
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
Correct D. 30

Correct Answer: D

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Question 5
A 3x3 matrix is given as \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \). Find the determinant of the matrix.
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 6
A random sample of 25 students from a large population has a mean height of 175 cm with a s\tandard deviation of 5 cm. Calculate the probability that a randomly selected student from the same population has a height greater than 180 cm.
A. 0.25
B. 0.5
Correct C. 0.75
D. 0.9

Correct Answer: C

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Question 7
Find the derivative of the function \( f(x) = \frac{x^2}{x^2 + 1} \) u\sing the quotient rule.
A. \( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \)
B. \( f'(x) = \frac{2x^2}{\( x^2 + 1 \)^2} \)
Correct C. \( f'(x) = \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2} \)
D. \( f'(x) = \frac{2x^3}{\( x^2 + 1 \)^2} \)

Correct Answer: C

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Question 8
Solve the quadratic 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 9
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) u\sing integration.
Correct A. \( \ln(2) - \ln(1) \)
B. \( \ln(2) - \ln(2) \)
C. \( \ln(1) - \ln(2) \)
D. \( \ln(2) - \ln(2) \)

Correct Answer: A

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Question 10
Solve the trigonometric equation \( \sin^2(x) + \cos^2(x) = 1 \) u\sing trigonometric identities.
Correct A. \( \sin(x) = \pm \sqrt{\frac{1}{2}} \)
B. \( \cos(x) = \pm \sqrt{\frac{1}{2}} \)
C. \( \tan(x) = \pm \sqrt{\frac{1}{2}} \)
D. \( \cot(x) = \pm \sqrt{\frac{1}{2}} \)

Correct Answer: A

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Question 11
Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 2cm.
A. 100π cm³
B. 200π cm³
Correct C. 300π cm³
D. 400π cm³

Correct Answer: C

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Question 12
A circle passes through the points (2,3), (4,5), and (6,7). Find the equation of the circle.
Correct A. x² + y² + 2x - 6y + 5 = 0
B. x² + y² - 2x + 6y - 5 = 0
C. x² + y² + 4x - 2y - 3 = 0
D. x² + y² - 4x + 2y + 3 = 0

Correct Answer: A

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Question 13
The mean of 5 numbers is 15. If one of the numbers is 10, find the sum of the other 4 numbers.
A. 40
Correct B. 50
C. 60
D. 70

Correct Answer: B

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Question 14
Find the area under the curve y = 2x² + 3x - 4 from x = 0 to x = 2.
A. 20
B. 30
Correct C. 40
D. 50

Correct Answer: C

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Question 15
A number in base 8 is represented as 123. Find its equivalent in base 10.
A. 83
B. 93
Correct C. 103
D. 113

Correct Answer: C

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Question 16
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
Correct A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )

Correct Answer: A

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Question 17
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
Correct B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)

Correct Answer: B

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Question 18
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{4}{3} pi \)
Correct B. \( \frac{8}{3} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{32}{3} pi \)

Correct Answer: B

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Question 19
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. \( \sin x \cos x \)
D. \( \sin^2 x \)

Correct Answer: A

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Question 20
Find the area of the triangle formed by the points ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. ( 12 )
B. ( 16 )
Correct C. ( 20 )
D. ( 24 )

Correct Answer: C

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Question 21
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the height of a student is normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.5
Correct D. 0.8413

Correct Answer: D

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Question 22
Solve for x in the equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 3 \ 3 \end{bmatrix} \).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 23
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?
A. 200
B. 250
Correct C. 300
D. 350

Correct Answer: C

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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 = 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 25
Solve the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for x.
A. x = 0
Correct B. x = 90
C. x = 180
D. x = 270

Correct Answer: B

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