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POST UTME AAUA 2018 Mathematics | Objective

Prepare for your exams with POST UTME AAUA questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

Solve the inequality ($\frac{x}{x-2}\(> 0$\) for x in \$(frac{x}{x-2}\(> 0$$-infty$, infty \ ).

Correct A. $-\infty, 2$ \cup $2, \infty$

B. $-\infty, 0$ \cup $2, \infty$

C. $-\infty, 0$ \cup (0, 2)

D. (0, 2)

Correct Answer: A

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Question 2 View Details

Find the equation of the line passing through the points ( A(2, 3) ) and ( B(4, 5) ).

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

B. $y = 2x - 1$

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

D. $y = x + 2$

Correct Answer: A

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Question 3 View Details

A histogram is shown below. What is the mean of the data set?

A. 20

B. 22

Correct C. 25

D. 30

Correct Answer: C

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Question 4 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. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 5 View Details

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = 0$

C. $x = -1$

D. $x = 1$

Correct Answer: A

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Question 6 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and $-1, 2$.

Correct A. $x^2$ + \$(y^2 - 6x - 2y + 12$$= 0$\)

B. $x^2$ + \$(y^2 - 4x + 2y - 10$$= 0$\)

C. $x^2$ + \$(y^2 + 2x - 4y + 15$$= 0$\)

D. $x^2$ + \$(y^2 + 4x + 2y - 20$$= 0$\)

Correct Answer: A

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Question 7 View Details

Evaluate the definite integral \int_$0^1$ $2x + 1$ dx.

Correct A. 3

B. 2

C. 1

D. 4

Correct Answer: A

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Question 8 View Details

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

Correct A. 55

B. 60

C. 65

D. 70

Correct Answer: A

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Question 9 View Details

Find the equation of the tangent to the curve $y = x\^2\\(tangent to the curve (y = x$ at the point (1, 1).

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 10 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$ about the x-axis.

Correct A. $\frac{32\pi}{3}$\)

B. $\frac{16\pi}{3}$\)

C. $\frac{64\pi}{3}$\)

D. $\frac{128\pi}{3}$\)

Correct Answer: A

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Question 11 View Details

Let ( f(x) = $\frac{1}{x^2 + 1}$\)) ). Find the value of $int_{0}^{\frac{\\() ). Find the value of (int_{0}^{\pi}{4}} f x \$ , dx ).

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 12 View Details

In a set of 10 students, 5 are boys and 5 are girls. If 2 students are selected at random, what is the probability that at least one of them is a girl?

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

B. $\frac{2}{5}$\)

Correct C. $\frac{3}{5}$\)

D. $\frac{4}{5}$\)

Correct Answer: C

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Question 13 View Details

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

Correct A. \left$-\infty, -\frac{3}{2} \right$ \cup \left$\frac{1}{2}, \infty \right$

B. \left$-\infty, -\frac{1}{2} \right$ \cup \left$\frac{3}{2}, \infty \right$

C. \left$-\infty, \frac{1}{2} \right$ \cup \left$\frac{3}{2}, \infty \right$

D. \left$-\infty, -\frac{3}{2} \right$ \cup \left$\frac{1}{2}, \infty \right$

Correct Answer: A

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Question 14 View Details

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

A. $\frac{1}{3}$\)

B. $\frac{2}{3}$\)

Correct C. $\frac{4}{3}$\)

D. $\frac{5}{3}$\)

Correct Answer: C

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Question 15 View Details

Let $A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}$. Find the product ( AB ).

Correct A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}

B. \begin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix}

C. \begin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}

D. \begin{bmatrix} 25 & 28 \ 49 & 56 \end{bmatrix}

Correct Answer: A

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Question 16 View Details

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

A. $\frac{2x + 3 x^2 - 4$ \ - $x^2 + 3x - 2$ (2x)}{ $x^2 - 4$ ^2}\)\) )

B. $\frac{2x + 3 x^2 - 4$ \ + $x^2 + 3x - 2$ (2x)}{ $x^2 - 4$ ^2}\)\) )

Correct C. $\frac{2x + 3 x^2 - 4$ \ - $x^2 + 3x - 2$ (2x)}{ $x^2 - 4$ ^2}\)\) )

D. $\frac{2x + 3 x^2 - 4$ \ + $x^2 + 3x - 2$ (2x)}{ $x^2 - 4$ ^2}\)\) )

Correct Answer: C

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Question 17 View Details

Solve the inequality $\frac{x - 2}{x + 1} > 0$ using interval notation.

Correct A. $-\infty, -1 \$ cup (2, infty) )

B. $-\infty, -1 \$ cup (1, 2) )

C. $-\infty, -1 \$ cup (2, infty) )

D. $-\infty, -1 \$ cup (1, 2) )

Correct Answer: A

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Question 18 View Details

Find the area under the curve $y = $1x$ from $x = 0$ to $x = \frac{\pi}{2}$ using integration.

A. $\frac{\pi}{2}$

Correct B. $\frac{\pi}{4}$

C. $\frac{\pi}{2}$

D. $\frac{\pi}{4}$

Correct Answer: B

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Question 19 View Details

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

Correct A. $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$

B. $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$

C. $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$

D. $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$

Correct Answer: A

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Question 20 View Details

Find the value of ( x ) in the equation $2^x = 16$.

A. $x = 2$

Correct B. $x = 4$

C. $x = 2$

D. $x = 4$

Correct Answer: B

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Question 21 View Details

A random sample of 16 students from a population of 50 students has a mean height of 170 cm with a standard deviation of 5 cm. Calculate the standard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 22 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student will score above 80?

A. 0.1587

B. 0.3413

Correct C. 0.4772

D. 0.6745

Correct Answer: C

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Question 23 View Details

Solve for x in the equation $x^2 + 5x + 6 = 0$.

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 24 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 25 View Details

A company has two factories, A and B, producing a total of 1000 units per day. Factory A produces 60% of the total units, while factory B produces the remaining 40%. If the profit per unit from factory A is ₦50 and from factory B is ₦30, what is the total profit per day?

A. ₦3500

Correct B. ₦4000

C. ₦4500

D. ₦5000

Correct Answer: B

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