Exam Body

Year

Subject

Paper Type

POST UTME AAUA 2024 Mathematics | Objective

Are you preparing for POST UTME AAUA 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

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

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

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

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

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

Correct Answer: A

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Question 2

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

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

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

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

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 3

Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 4

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 5

Solve the equation \( x^2 + 4x + 4 = 0 \).

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 0 \)

D. \( x = 1 \)

Correct Answer: A

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Question 6

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the chain rule and limits.

Correct A. ( f'(x) = 2x + 2 \)

B. ( f'(x) = 2x - 2 \)

C. ( f'(x) = x^2 + 2 \)

D. ( f'(x) = x^2 - 2 \)

Correct Answer: A

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Question 7

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

Correct A. \( x \in \( -\infty, -1 \ \) \cup [3, \infty) \)

B. \( x \in \( -\infty, -3 \ \) \cup [1, \infty) \)

C. \( x \in \( -\infty, 1 \ \) \cup [3, \infty) \)

D. \( x \in \( -\infty, -3 \ \) \cup [1, \infty) \)

Correct Answer: A

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Question 8

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).

Correct A. \( 3094 \ \)

B. \( 3095 \ \)

C. \( 3096 \ \)

D. \( 3097 \ \)

Correct Answer: A

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Question 9

Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).

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

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

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

D. \( x = -1, y = -1 \ \)

Correct Answer: A

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Question 10

Find the area of the triangle with vertices ( (0, 0), (3, 0), ) and ( (0, 2) ).

Correct A. \( 6 \ \)

B. \( 6.5 \ \)

C. \( 6.75 \ \)

D. \( 7 \ \)

Correct Answer: A

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Question 11

Find the area under the curve y = \sin(x) from x = 0 to x = π/2.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12

Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.

A. x = -1/2

Correct B. x = 1/2

C. x = -3/2

D. x = 3/2

Correct Answer: B

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Question 13

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

Correct Answer: A

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Question 14

Find the volume of the solid formed by rotating the region bounded by y = x^2 and y = 4 - x^2 about the x-axis.

A. \pi/12

Correct B. \pi/6

C. \pi/4

D. \pi/2

Correct Answer: B

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Question 15

Find the equation of the line pas\sing through the points (1, 2) and (3, 4).

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x - 2

Correct Answer: A

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Question 16

Find the derivative of ( f(x) = \frac{1}{2} \log_{10} \( x^2 + 1 \) ) u\sing the chain rule.

Correct A. \frac{1}{2} \cdot \frac{1}{x^2 + 1} \cdot 2x

B. \frac{1}{2} \cdot \frac{1}{x^2 + 1}

C. \frac{1}{2} \cdot \frac{2x}{x^2 + 1}

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

Correct Answer: A

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Question 17

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

Correct A. x = \frac{\pi}{4}

B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: A

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Question 18

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

Correct Answer: A

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Question 19

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

Correct A. \langle 4.33, 2.5 \rangle

B. \langle 2.5, 4.33 \rangle

C. \langle 5 \cos 30^\circ, 5 \sin 30^\circ \rangle

D. \langle 5 \sin 30^\circ, 5 \cos 30^\circ \rangle

Correct Answer: A

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Question 20

Two events, A and B, are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find \( P\( A \cap B \ \) ).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 21

Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y \) is less than 1.

Correct A. \( \frac{1}{4} \)

B. \( \frac{1}{2} \)

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

D. \( \frac{5}{8} \)

Correct Answer: A

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Question 22

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

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

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

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

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

Correct Answer: B

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Question 23

Solve the inequality \( |x^2 - 4x + 3| geq 2 \).

A. \( x leq -1 \) or ( x geq 3 )

Correct B. ( x leq 1 ) or ( x geq 3 )

C. \( x leq -1 \) or ( x geq 1 )

D. \( x leq -3 \) or ( x geq 1 )

Correct Answer: B

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Question 24

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If a student scored 80, what is the z-score of this score?

A. 1.5

Correct B. 2.0

C. 2.5

D. 3.0

Correct Answer: B

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Question 25

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

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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