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POST UTME CRAWFORD UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 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. 36π cm³

C. 48π cm³

D. 60π cm³

Correct Answer: B

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Question 7 View Details

A particle moves in a plane with its position given by the equation \(x = 2 \(1t\) and \(y = 3\)1t\). Find the equation of the tangent line at the point where \(t = \frac{\\(tangent line at the point where (t = \pi}{2}\).

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 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. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 9 View Details

Find the equation of the line passing 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 View Details

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 View Details

Find the equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

Two events A and B are independent. 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 View Details

Find the vector equation of the line passing 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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