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POST UTME AFE BABALOLA UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

Correct A. ( 14 )

B. ( 28 )

C. ( 42 )

D. ( 56 )

Correct Answer: A

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Question 2 View Details

Solve for ( x ) in the equation \(2^x = 8\).

A. ( 1 )

Correct B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: B

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Question 3 View Details

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

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

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

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 4 View Details

Find the area of the circle with radius ( 4 ) cm.

Correct A. ( 16pi ) \(cm^2\)

B. ( 32pi ) \(cm^2\)

C. ( 64pi ) \(cm^2\)

D. ( 128pi ) \(cm^2\)

Correct Answer: A

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Question 5 View Details

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

Correct A. \(-2\)

B. \(-1\)

C. ( 1 )

D. ( 2 )

Correct Answer: A

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Question 6 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( AB ) if it exists.

Correct A. \(egin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}\)

B. \(egin{bmatrix} 17 & 20 \ 39 & 46 \end{bmatrix}\)

C. \(egin{bmatrix} 21 & 24 \ 45 & 52 \end{bmatrix}\)

D. \(egin{bmatrix} 23 & 26 \ 49 & 56 \end{bmatrix}\)

Correct Answer: A

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Question 7 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random without replacement, what is the probability that both balls are blue?

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

B. \(\frac{3}{7}\)

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

D. \(\frac{1}{6}\)

Correct Answer: A

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Question 8 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{64}{3}\)

B. \(\frac{32}{3}\)

C. \(\frac{16}{3}\)

D. \(\frac{8}{3}\)

Correct Answer: A

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Question 9 View Details

Solve the inequality \(2x^2 + 3x - 1 > 0\).

Correct A. \(x < -\frac{1}{2}\) or \(x > \frac{1}{2}\)

B. \(x < -\frac{1}{2}\) or \(x < \frac{1}{2}\)

C. \(x > -\frac{1}{2}\) or \(x < \frac{1}{2}\)

D. \(x > -\frac{1}{2}\) or \(x > \frac{1}{2}\)

Correct Answer: A

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Question 10 View Details

Find the value of ( x ) in the equation \(x^2 + 2x - 3 = 0\).

Correct A. \(x = -3\) or \(x = 1\)

B. \(x = -1\) or \(x = 3\)

C. \(x = 1\) or \(x = -3\)

D. \(x = -1\) or \(x = -3\)

Correct Answer: A

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Question 11 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. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 12 View Details

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

Correct A. \(x < -\frac{1}{2}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > \frac{1}{2}\)

C. \(x < -\frac{1}{2}\) or \(x < \frac{3}{2}\)

D. \(x < -\frac{3}{2}\) or \(x < \frac{1}{2}\)

Correct Answer: A

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Question 13 View Details

Find the surface area of the sphere with radius 5 cm.

A. ( 50pi ) cm²

Correct B. ( 100pi ) cm²

C. ( 150pi ) cm²

D. ( 200pi ) cm²

Correct Answer: B

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Question 14 View Details

Solve the quadratic equation \(x^2 + 2x - 6 = 0\).

Correct A. \(x = -3\) or \(x = 2\)

B. \(x = -2\) or \(x = 3\)

C. \(x = -1\) or \(x = 6\)

D. \(x = 1\) or \(x = -6\)

Correct Answer: A

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Question 15 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

Correct A. ( 1 )

B. \(-1\)

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 16 View Details

Determine the value of the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].

Correct A. -10

B. 10

C. 20

D. 30

Correct Answer: A

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Question 17 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, the coin is flipped twice. If the number on the die is odd, the coin is flipped only once. What is the probability that at least one of the coin flips shows heads?

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

Correct B. \(\frac{2}{3}\)\)

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

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

Correct Answer: B

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Question 18 View Details

Solve for x in the equation [ \(2^x\) + \\((3^x\)\(= 5\)\\()^x\) ].

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 19 View Details

A right triangle has a hypotenuse of length 10 and one leg of length 6. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 20 View Details

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

A. \(y = 2x - 1\)

Correct B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: B

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Question 21 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 - 4y + 12\)\(= 0\)\)

B. \(x^2\) + \\((y^2 + 2x - 4y + 5\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 4x + 2y - 6\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 2x + 4y - 8\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

Evaluate the integral \int_\(0^1\) \(2x^3 - 5x^2 + 3x - 1\) dx.

Correct A. [1, 2, 3, 4]

B. [1, 2, 3, 4]

C. [1, 2, 3, 4]

D. [1, 2, 3, 4]

Correct Answer: A

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Question 23 View Details

If \(\vec{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \vec{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), find the cross product \(\vec{a}\) \times \(\vec{b}\).

Correct A. \begin{pmatrix} -1 \ 8 \ -5 \end{pmatrix}

B. \begin{pmatrix} 1 \ -8 \ 5 \end{pmatrix}

C. \begin{pmatrix} -1 \ -8 \ 5 \end{pmatrix}

D. \begin{pmatrix} 1 \ 8 \ -5 \end{pmatrix}

Correct Answer: A

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Question 24 View Details

Solve the system of equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

Correct A. \begin{pmatrix} 1 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ 2 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \end{pmatrix}

D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 25 View Details

Find the area under the curve \(y = x\^2\) from \(x = 0\) to \(x = 4\).

Correct A. 32

B. 64

C. 16

D. 128

Correct Answer: A

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