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POST UTME LASU 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of ( mathbf{a} cdot mathbf{b} ) if \( mathbf{a} = egin{pmatrix} 2 \ 3 \ -1 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \ 4 \end{pmatrix} \).

A. 10

Correct B. -10

C. 5

D. -5

Correct Answer: B

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Question 2

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

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 3

Solve the system of linear equations: \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y + 2z = 5 \end{cases} \).

Correct A. x = 1, y = 2, z = 3

B. x = 2, y = 3, z = 4

C. x = 3, y = 4, z = 5

D. x = 4, y = 5, z = 6

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: B

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Question 5

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

Correct A. x = -2, x = -3

B. x = -1, x = -6

C. x = 2, x = 3

D. x = 1, x = 6

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

Correct A. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

B. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

C. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

D. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )

Correct Answer: A

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Question 7

Evaluate the definite integral \( int_0^1 \( 2x^3 - 3x^2 + x - 1 \ \) dx ).

Correct A. \( left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1 \)

B. \( left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1 \)

C. \( left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1 \)

D. \( left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1 \)

Correct Answer: A

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Question 8

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

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

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

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

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

Correct Answer: A

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Question 9

Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \).

Correct A. \( left[ \frac{x^3}{3} - x^2 + x \right]_0^2 \)

B. \( left[ \frac{x^3}{3} - x^2 + x \right]_0^2 \)

C. \( left[ \frac{x^3}{3} - x^2 + x \right]_0^2 \)

D. \( left[ \frac{x^3}{3} - x^2 + x \right]_0^2 \)

Correct Answer: A

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Question 10

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

Correct A. \( x < -\frac{5}{2} \) or \( x > \frac{1}{2} \)

B. \( x < -\frac{5}{2} \) or \( x > \frac{1}{2} \)

C. \( x < -\frac{5}{2} \) or \( x > \frac{1}{2} \)

D. \( x < -\frac{5}{2} \) or \( x > \frac{1}{2} \)

Correct Answer: A

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( 32 \ \)

B. \( 64 \ \)

C. \( 96 \ \)

D. \( 128 \ \)

Correct Answer: A

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Question 12

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

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 derivative of the function ( 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{2}{\( x^2 + 1 \ \)^2} \)

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

Correct Answer: A

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Question 14

A vector \( \vec{a} \) has components \( a_x = 3 \) and \( a_y = 4 \). Find the magnitude of the vector.

Correct A. \( 5 \ \)

B. \( 10 \ \)

C. \( 15 \ \)

D. \( 20 \ \)

Correct Answer: A

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Question 15

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

Correct A. \( x = -3 \ \) or \( x = 2 \ \)

B. \( x = -2 \ \) or \( x = 3 \ \)

C. \( x = -1 \ \) or \( x = 6 \ \)

D. \( x = 1 \ \) or \( x = -6 \ \)

Correct Answer: A

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Question 16

In a triangle with sides of length 5, 12, and 13, find the area u\sing Heron's formula.

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 17

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

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 18

Find the volume of a sphere with radius 6 cm.

Correct A. 904.778

B. 904.778

C. 904.778

D. 904.778

Correct Answer: A

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Question 19

Solve the inequality \( x^2 - 4x + 4 \geq 0 \).

Correct A. \[ x \leq 2 \]

B. \[ x \geq 2 \]

C. \[ x < 2 \]

D. \[ x > 2 \]

Correct Answer: A

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Question 20

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. \[ y = x - 1 \]

D. \[ y = x + 1 \]

Correct Answer: A

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Question 21

Given that \( \tan \theta = \frac{1}{3} \), find the value of \( \sin \theta \cos \theta \) u\sing the identity \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).

Correct A. 1/6

B. 1/2

C. 2/3

D. 3/4

Correct Answer: A

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Question 22

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > -3/2

C. x < -3/2 or x > 1

D. x < 3/2 or x > -1

Correct Answer: A

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Question 23

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 24

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 25

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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