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POST UTME LASU 2025 Mathematics | Objective

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Question 1

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

A. \( \frac{1}{2} \sqrt{1 - x^2} \)

B. \( \frac{x}{\( 1 - x^2 \ \)^{3/2}} )

Correct C. \( \frac{1}{\( 1 - x^2 \ \)^{3/2}} )

D. \( \frac{1}{2} \( 1 - x^2 \ \)^{-3/2} )

Correct Answer: C

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Question 2

A box with a square base has a volume of 27 cubic meters. If the height of the box is 3 meters, find the length of each side of the base.

A. 3 meters

Correct B. 4 meters

C. 5 meters

D. 6 meters

Correct Answer: B

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Question 3

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the die is rolled again. If the number rolled is odd, the die is rolled three more times. What is the probability that the number rolled is greater than 4?

A. 1/2

B. 1/3

C. 2/3

Correct D. 3/4

Correct Answer: D

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Question 4

A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 70 and 90.

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 5

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 1 \ 4 & 3 & 2 \ 1 & 2 & 3 \end{bmatrix} \).

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 6

Determine the equation of the line pas\sing through the points (2,3) and (4,5).

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = x + 2

D. y = x - 2

Correct Answer: B

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Question 7

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

A. x = 10^2

Correct B. x = 10^4

C. x = 10^{-2}

D. x = 10^{-4}

Correct Answer: B

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Question 8

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 9

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ \( -3, ∞ \)

D. \( -∞, 1 \) ∪ \( -3, ∞ \)

Correct Answer: A

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Question 10

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366

B. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366

Correct Answer: A

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Question 11

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

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

B. \( \frac{5\pi}{6} \ \)

C. \( \frac{7\pi}{6} \ \)

D. \( \frac{11\pi}{6} \ \)

Correct Answer: A

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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 area of the triangle with vertices ( A(2,3) ), ( B(4,5) ), and ( C(6,7) ).

Correct A. \( 10 \ \)

B. \( 15 \ \)

C. \( 20 \ \)

D. \( 25 \ \)

Correct Answer: A

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Question 14

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. \( 6x + 2 \ \)

B. \( 6x - 2 \ \)

C. \( 6x + 1 \ \)

D. \( 6x - 1 \ \)

Correct Answer: A

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Question 15

Find the volume of the cylinder with radius 4 and height 6.

Correct A. \( 96\pi \ \)

B. \( 192\pi \ \)

C. \( 288\pi \ \)

D. \( 384\pi \ \)

Correct Answer: A

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Question 16

In the diagram below, the equation of the circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (h, k) = (2, 3) ) and the radius is \( r = 4 \), find the equation of the circle.

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )

D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 17

Solve the inequality \( \frac{x}{2} - 3 > 7 \) for ( x ).

Correct A. \( x > 24 \)

B. \( x < -24 \)

C. \( x > 20 \)

D. \( x < 20 \)

Correct Answer: A

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Question 18

Find the volume of the cylinder with radius \( r = 6 \) and height \( h = 10 \).

Correct A. ( 1800pi )

B. ( 1200pi )

C. ( 900pi )

D. ( 600pi )

Correct Answer: A

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Question 19

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \)

B. \( x = -3 \)

C. \( x = 2 \)

D. \( x = 3 \)

Correct Answer: A

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Question 20

Find the area of the triangle with base \( b = 8 \) and height \( h = 12 \).

Correct A. ( 48 )

B. ( 60 )

C. ( 72 )

D. ( 80 )

Correct Answer: A

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Question 21

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).

A. \( x = \frac{pi}{2} \)

Correct B. \( x = \frac{pi}{4} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: B

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Question 22

Find the surface area of the sphere with radius \( r = 5 \).

Correct A. ( 100pi )

B. ( 50pi )

C. ( 25pi )

D. ( 10pi )

Correct Answer: A

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Question 23

Solve the system of linear equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).

A. \( x = 2, y = 2 \)

B. \( x = 1, y = 3 \)

C. \( x = 3, y = 1 \)

D. \( x = 4, y = 0 \)

Correct Answer: VIEW ANSWER

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Question 24

Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 25

Solve the equation \frac{1}{x^2} + \frac{1}{\( x+1 \)^2} = \frac{1}{4} for x.

A. -2

Correct B. -1

C. 1

D. 2

Correct Answer: B

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