Exam Body

Year

Subject

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POST UTME AAUA 2017 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 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

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

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

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

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

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

B. \( \frac{5pi}{3} \)

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

D. \( \frac{2pi}{3} \)

Correct Answer: A

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Question 7

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

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

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

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

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

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

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

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

Find the equation of the line pas\sing 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

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

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

Two events, A and B, are indep\endent. 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

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

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

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

Solve the system of linear equations u\sing 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

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

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

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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