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POST UTME AAUA 2017 Mathematics | Objective

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Question 1 View Details

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

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 2 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 72π cm³

D. 96π cm³

Correct Answer: B

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Question 3 View Details

A random variable X has a probability distribution given by $P X = x \$ = $\frac{1}{2}$\) \) for $x = 1$, 2, 3, 4, 5. Find the expected value of X.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 4 View Details

Solve the system of linear equations $\begin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y + 2z = 5 \end{cases}$.

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 5 View Details

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 6 View Details

Determine the value of x in the equation $\sin^2 x + \cos^2 x = 1$ if $$1x = \frac{3}{5}$.

Correct A. $\frac{4\pi}{3}$

B. $\frac{5\pi}{3}$

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

D. $\frac{2\pi}{3}$

Correct Answer: A

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Question 7 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

A. 200

B. 240

Correct C. 300

D. 320

Correct Answer: C

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Question 8 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even and the coin lands heads up, what is the probability that the number on the die is greater than 4?

A. $\frac{1}{6}$\)

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

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

Correct D. $\frac{2}{3}$\)

Correct Answer: D

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Question 9 View Details

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

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

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

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

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

Correct Answer: B

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Question 10 View Details

A sequence is defined by the formula $a_n = 2n + 1$. Find the sum of the first 10 terms of the sequence.

A. 220

B. 240

Correct C. 260

D. 280

Correct Answer: C

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Question 11 View Details

Find the value of x in the equation $\frac{1}{2}x^2 + 5x - 3 = 0$.

A. 1

Correct B. -2

C. 3

D. -1

Correct Answer: B

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Question 12 View Details

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

Correct A. x < -1 or $x > 3$

B. $x < 1$ or x > -3

C. x < -3 or $x > 1$

D. $x < 3$ or x > -1

Correct Answer: A

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Question 13 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

Correct A. 4

B. 2

C. 1

D. 3

Correct Answer: A

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Question 14 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. $x + 2$^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 15 View Details

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

Correct A. $y = 2x - 2$

B. $y = 2x + 2$

C. $y = x - 2$

D. $y = x + 2$

Correct Answer: A

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Question 16 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -4

Correct B. 0

C. 4

D. -1

Correct Answer: B

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Question 17 View Details

A histogram of exam scores is shown below. What is the mean score?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 18 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 19 View Details

Solve the equation [ \$\sin^2$ x + \$\cos^2$ $x = 1$ ].

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

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

C. $x =$$\frac{\pi}{3}$\)

D. $x =$$\frac{\pi}{6}$\)

Correct Answer: A

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Question 20 View Details

Find the area under the curve [ $y = x\^2 + 2x + 1$ ] from $x = 0$ to $x = 2$.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 21 View Details

Find the area under the curve $y = 2x\^2 + 3x - 1$ from $x = 0$ to $x = 2$.

Correct A. $\frac{8}{3}$\)

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

C. $\frac{32}{3}$\)

D. $\frac{64}{3}$\)

Correct Answer: A

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Question 22 View Details

Solve the system of linear equations using matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \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 23 View Details

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

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

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

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

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

Correct Answer: A

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Question 24 View Details

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

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 25 View Details

Find the surface area of the solid formed by revolving the region bounded by $y = x\^2$ and $y = 4 - x\^2$ about the x-axis.

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

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

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

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

Correct Answer: A

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