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POST UTME LASU 2023 Mathematics | Objective

Are you preparing for POST UTME LASU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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 2

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

Correct A. \( x in \( -infty, -3 \ \) cup (2, infty) )

B. \( x in \( -infty, -3 \ \) cup (3, infty) )

C. \( x in \( -infty, -2 \ \) cup (2, infty) )

D. \( x in \( -infty, -2 \ \) cup (3, infty) )

Correct Answer: A

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Question 3

A die is rolled twice. Find the probability that the sum of the two numbers is 7.

A. \( \frac{1}{6} \)

B. \( \frac{1}{12} \)

Correct C. \( \frac{1}{36} \)

D. \( \frac{1}{24} \)

Correct Answer: C

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Question 4

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

Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )

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

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

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

Correct Answer: A

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Question 5

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

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 6

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

A. 2x

B. -2x

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

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

Correct Answer: C

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Question 7

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

A. x < -1

B. x > -1

Correct C. x < 1

D. x > 1

Correct Answer: C

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Question 8

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{2}

Correct B. \frac{2}{3}

C. \frac{3}{4}

D. \frac{4}{5}

Correct Answer: B

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Question 9

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

Correct A. x = 2

B. x = -2

C. x = 1

D. x = -1

Correct Answer: A

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Question 10

Find the derivative of the function ( f(x) = x^3 \sin x ) u\sing the product rule.

A. 3x^2 \sin x + x^3 \cos x

B. x^3 \cos x - 3x^2 \sin x

C. x^2 \sin x + 3x^2 \cos x

Correct D. x^3 \cos x + 3x^2 \sin x

Correct Answer: D

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Question 11

Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( AB ) if it exists.

Correct A. \( egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix} \)

B. \( egin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix} \)

C. \( egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix} \)

D. \( egin{bmatrix} 23 & 26 \ 49 & 56 \end{bmatrix} \)

Correct Answer: A

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Question 12

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

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

B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )

C. \( \frac{x}{\( x^2 + 1 \ \)^2} )

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

Correct Answer: A

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Question 13

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 90.

Correct A. \( \frac{1}{2} \)

B. \( \frac{1}{4} \)

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

D. \( \frac{1}{3} \)

Correct Answer: A

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Question 14

Solve the equation \( \log_2 \( x^2 + 1 \ \) = 3 ) for ( x ).

Correct A. \( x = 7 \)

B. \( x = -7 \)

C. \( x = 5 \)

D. \( x = -5 \)

Correct Answer: A

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Question 15

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 16

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find P\( X + Y < 1 \).

Correct A. 1/2

B. 1/3

C. 2/3

D. 3/4

Correct Answer: A

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Question 17

Find the derivative of the function f(x) = \( 2x^2 + 1 \) / \( x^2 - 4 \) u\sing the chain rule.

Correct A. \frac{4x}{\( x^2 - 4 \)^2}

B. \frac{2x}{\( x^2 - 4 \)^2}

C. \frac{4x}{\( x^2 - 4 \)^2} + \frac{2x}{\( x^2 - 4 \)^2}

D. \frac{4x}{\( x^2 - 4 \)^2} - \frac{2x}{\( x^2 - 4 \)^2}

Correct Answer: A

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Question 18

Simplify the expression \sqrt{64x^6y^4} u\sing the properties of radicals.

Correct A. 8x^3y^2

B. 2^3x^3y^2

C. 2^6x^6y^4

D. 4x^3y^2

Correct Answer: A

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Question 19

Find the equation of the circle with center (2, 3) and radius 4.

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

B. \( x - 3 \)^2 + \( y - 2 \)^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 20

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} u\sing the formula for 3x3 matrices.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 21

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 23

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 24

Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \).

Correct A. {(1, 1)}

B. {\( 1, -1 \)}

C. {\( -1, 1 \)}

D. {\( -1, -1 \)}

Correct Answer: A

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Question 25

Find the value of x in the equation \( \frac{x}{2} + 3 = 7 \).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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