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POST UTME CRAWFORD UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME CRAWFORD UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 2

A set A contains 3 elements. If a subset B of A is chosen such that it contains exactly half of the elements of A, what is the probability that B contains the element 5?

Correct A. 1/2

B. 1/3

C. 2/3

D. 1/4

Correct Answer: A

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Question 3

Find the sum of the first 10 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).

A. 2x + 3x^2 + 4x^3 + ldots + 20x^9

B. 2x + 3x^2 + 4x^3 + ldots + 21x^9

Correct C. 2x + 3x^2 + 4x^3 + ldots + 22x^9

D. 2x + 3x^2 + 4x^3 + ldots + 23x^9

Correct Answer: C

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Question 4

A polynomial function f(x) has a root at x = 2 and a root at x = 4. If f(0) = 6, what is the value of f(1)?

A. -2

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 5

A histogram shows the distribution of exam scores for a class of 100 students. The histogram has 5 bars, each representing a different score range. If the tallest bar represents 30 students, what is the probability that a randomly selected student scored between 70 and 80?

A. 0.3

B. 0.4

Correct C. 0.5

D. 0.6

Correct Answer: C

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Question 6

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. 36π cm³

C. 48π cm³

D. 60π cm³

Correct Answer: B

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Question 7

A particle moves in a plane with its position given by the equation \( x = 2 \cos t \) and \( y = 3 \sin t \). Find the equation of the \tangent line at the point where \( t = \frac{\pi}{2} \).

Correct A. y = -3x + 6

B. y = 3x - 6

C. y = 3x + 6

D. y = -3x - 6

Correct Answer: A

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Question 8

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 9

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

A. y = x - 1

Correct B. y = x + 1

C. y = 2x - 3

D. y = 2x + 3

Correct Answer: B

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Question 10

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

Correct A. x \leq -1 \text{ or } x \geq \frac{3}{2}

B. x \leq -1 \text{ or } x \leq \frac{3}{2}

C. x \geq -1 \text{ or } x \geq \frac{3}{2}

D. x \geq -1 \text{ or } x \leq \frac{3}{2}

Correct Answer: A

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Question 11

Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the form y = mx + c.

A. y = 2x - 1

Correct B. y = 2x + 1

C. y = -2x + 1

D. y = -2x - 1

Correct Answer: B

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Question 12

A circle has a radius of 4 cm and passes through the points (0, 0) and (3, 4). Find the equation of the circle in the form \( x - h \)^2 + \( y - k \)^2 = r^2.

Correct A. \( x - 1 \)^2 + \( y - 2 \)^2 = 16

B. \( x + 1 \)^2 + \( y - 2 \)^2 = 16

C. \( x - 1 \)^2 + \( y + 2 \)^2 = 16

D. \( x + 1 \)^2 + \( y + 2 \)^2 = 16

Correct Answer: A

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Question 13

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

Correct A. \frac{13}{3}

B. \frac{23}{3}

C. \frac{33}{3}

D. \frac{43}{3}

Correct Answer: A

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Question 14

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

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

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

C. x > -1 or x > \frac{3}{2}

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

Correct Answer: A

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Question 15

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).

A. 0.24

Correct B. 0.36

C. 0.48

D. 0.64

Correct Answer: B

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Question 16

Find the vector equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. \\vec{r} = \\vec{a} + t\\vec{b}

B. \\vec{r} = \\vec{a} - t\\vec{b}

C. \\vec{r} = \\vec{a} + t\\vec{c}

D. \\vec{r} = \\vec{a} - t\\vec{c}

Correct Answer: A

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Question 17

Solve the 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 18

Find the equation of the circle with center (1, 2) and radius 3.

A. \( x - 1 \)^2 + \( y - 2 \)^2 = 9

B. \( x + 1 \)^2 + \( y - 2 \)^2 = 9

C. \( x - 1 \)^2 + \( y + 2 \)^2 = 9

D. \( x + 1 \)^2 + \( y + 2 \)^2 = 9

Correct Answer: VIEW ANSWER

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Question 19

Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 20

Solve for x in the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix} \).

A. x = 1, y = 1

Correct B. x = 2, y = 1

C. x = 1, y = 2

D. x = 2, y = 2

Correct Answer: B

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Question 21

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

A. \frac{\pi}{6}

B. \frac{\pi}{3}

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

D. \frac{\pi}{4}

Correct Answer: C

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Question 22

A set of 5 numbers has a mean of 20 and a median of 15. If the largest number is 30, find the sum of the remaining 3 numbers.

A. 45

B. 50

Correct C. 55

D. 60

Correct Answer: C

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Question 23

Find the area of the triangle formed by the points ( A(2,3) ), ( B(4,5) ), and ( C(6,7) ).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 24

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

Correct A. \( -\\infty, -1 \) \\cup \( 3, \\infty \)

B. \( -\\infty, -3 \) \\cup \( 1, \\infty \)

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

D. \( -\\infty, -4 \) \\cup \( 4, \\infty \)

Correct Answer: A

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Question 25

Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \).

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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