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POST UTME LASU 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. \( \frac{16}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{64}{3} \)

D. \( \frac{128}{3} \)

Correct Answer: A

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Question 2

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

Correct A. \( y = \frac{1}{2}x + 1 \)

B. \( y = \frac{1}{2}x - 1 \)

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

D. \( y = \frac{1}{2}x - 2 \)

Correct Answer: A

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Question 3

Solve the system of equations: \( egin{cases} x + y = 4 \ xy = 5 \end{cases} \).

Correct A. \( x = 1, y = 3 \)

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

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

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

Correct Answer: A

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Question 4

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 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )

Correct Answer: A

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Question 5

Find the mean and s\tandard deviation of the data set: ( { 2, 4, 6, 8, 10 } ).

Correct A. Mean: 6, S\tandard Deviation: 2

B. Mean: 6, S\tandard Deviation: 4

C. Mean: 6, S\tandard Deviation: 6

D. Mean: 6, S\tandard Deviation: 8

Correct Answer: A

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Question 6

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

Correct A. 10^4

B. 10^2

C. 10

D. 10^8

Correct Answer: A

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Question 7

A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity at time t = 2 seconds.

Correct A. 4t^2 - 10t + 3

B. 6t^2 - 10t + 2

C. 2t^2 - 5t + 1

D. t^2 - 5t + 2

Correct Answer: A

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Question 8

A quadratic equation has roots at x = 2 and x = -3. Write the equation in factored form.

Correct A. \( x - 2 \)\( x + 3 \)

B. \( x + 2 \)\( x - 3 \)

C. \( x - 3 \)\( x + 2 \)

D. \( x + 3 \)\( x - 2 \)

Correct Answer: A

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Question 9

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both balls are blue?

Correct A. 1/8

B. 1/7

C. 1/6

D. 1/5

Correct Answer: A

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Question 10

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 11

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value between 0.5 and 1.

A. \frac{1}{2}

Correct B. \frac{3}{4}

C. \frac{7}{8}

D. \frac{5}{6}

Correct Answer: B

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Question 12

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

Correct A. \left\( - \infty, - \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

B. \left\( - \infty, - \frac{3}{2} \right \) \cap \left\( \frac{3}{2}, \infty \right \)

C. \left\( - \infty, \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)

D. \left\( - \infty, \frac{3}{2} \right \) \cap \left\( \frac{3}{2}, \infty \right \)

Correct Answer: A

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Question 13

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{32 \pi}{3}

B. \frac{64 \pi}{3}

Correct C. \frac{128 \pi}{3}

D. \frac{256 \pi}{3}

Correct Answer: C

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Question 14

A vector ( mathbf{a} ) has magnitude 5 and direction \( 30 \degree \) counterclockwise from the positive x-axis. Find the vector ( mathbf{a} ).

Correct A. \begin{pmatrix} 4.33 \ 2.50 \end{pmatrix}

B. \begin{pmatrix} 2.50 \ 4.33 \end{pmatrix}

C. \begin{pmatrix} 3.54 \ 3.54 \end{pmatrix}

D. \begin{pmatrix} 5.00 \ 0.00 \end{pmatrix}

Correct Answer: A

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Question 15

Find the sum of the first 5 terms of the geometric series \( 2x^2 + 3x + 1 \).

Correct A. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

B. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

C. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

D. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

Correct Answer: A

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Question 16

Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).

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

B. \( \frac{3pi}{4} \)

C. \( \frac{5pi}{4} \)

D. \( \frac{7pi}{4} \)

Correct Answer: A

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Question 17

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

Correct A. \( x < -\frac{5}{2} \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{2} \)

C. \( x < -\frac{5}{2} \) or \( x < \frac{3}{2} \)

D. \( x > -\frac{5}{2} \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 18

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

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 19

Determine the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).

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 20

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

Correct A. \( x = 1, y = 1 \)

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

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

D. \( x = 3, y = 3 \)

Correct Answer: A

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Question 21

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

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

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

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

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

Correct Answer: A

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Question 22

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. \( x = 1 \)

Correct B. \( x = 2 \)

C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: B

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Question 23

Find the value of \( \log_{10} \( 1000 \ \) ).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24

Solve the inequality \( x^2 - 4x + 3 > 0 \).

Correct A. \( x < -1 \) or \( x > 3 \)

B. \( x < 1 \) or \( x > 3 \)

C. \( x < -1 \) or \( x < 3 \)

D. \( x > 1 \) or \( x > 3 \)

Correct Answer: A

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Question 25

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ldots ).

Correct A. ( 62 )

B. ( 64 )

C. ( 66 )

D. ( 68 )

Correct Answer: A

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