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POST UTME AAUA 2024 Mathematics | Objective

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Question 1 View Details

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

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

Correct Answer: A

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Question 2 View Details

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 View Details

Solve the system of equations using 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 View Details

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 View Details

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 View Details

Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)\) ). Find the derivative of ( f(x) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the equation \\((2x^2 + 5x - 3\)\(= 0\)\) using 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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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 View Details

Find the derivative of ( f(x) = \(\frac{1}{2}\)\) \log_{10} \(x^2 + 1\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

Two events, A and B, are independent. 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 View Details

Let ( X ) and ( Y ) be independent 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 \(X + Y\\(text{otherwise} end{cases} ). Find the probability that\) 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 View Details

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

Correct Answer: B

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Question 23 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

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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