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POST UTME CRAWFORD UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Determine the value of \(\int_{0}^{\pi} \sin^2(x) dx\).

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

C. \(\frac{\pi}{6}\)\)

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

Correct Answer: A

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Question 2 View Details

A circle with center \(C\) and radius \(r\) is tangent to the \(x\)-axis at point \\(tangent to the (x\(P). If the area of the circle is \(\frac{\\(). If the area of the circle is (\pi}{2}r^2\), what is the \(y\\(pi}{2}r^2), what is the\)-coordinate of point \(P\)?

Correct A. -\(\frac{r}{2}\)\)

B. \(\frac{r}{2}\)\)

C. r

D. -r

Correct Answer: A

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Question 3 View Details

A polynomial \(p(x)\) has degree \(n\) and has roots (r_1, r_2, \ldots, r_n\). If \\((r_1, r_2, ldots, r_n\(p(x) = x - r_1\), x - r_2\) \cdots \(x - r_n)\), what is the value of \(p(1)\\()), what is the value of\)?

Correct A. \(1 - r_1\)\(1 - r_2\) \cdots \(1 - r_n\)

B. r_1r_2 \cdots r_n

C. 1 - r_1 - r_2 - \cdots - r_n

D. 1 + r_1 + r_2 + \cdots + r_n

Correct Answer: A

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Question 4 View Details

A histogram of the heights of students in a class is shown below.

A. The average height of the students is 175 cm.

Correct B. The median height of the students is 175 cm.

C. The mode height of the students is 175 cm.

D. The range of heights of the students is 175 cm.

Correct Answer: B

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Question 5 View Details

A function (f(x)\) is defined as \(f(x) = \\((f(x)) is defined as \sin(x) + cos(x)\). What is the value of \(f \\(cos(x)). What is the value of \frac{\pi}{4}\)\)?

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

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

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

D. \(\frac{1}{8}\)\)

Correct Answer: A

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Question 6 View Details

Find the determinant of the matrix \\(\n\begin{array}{ccc}\n2 & 3 & 4 \n5 & 6 & 7 \n8 & 9 & 10\n\end{array}\n\)

Correct A. -2

B. 2

C. -1

D. 1

Correct Answer: A

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Question 7 View Details

Solve the equation \\(\n x+2\), x+3\)\(x+4\)=0\n\)

A. -2

Correct B. -3

C. -4

D. -1

Correct Answer: B

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Question 8 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 9 View Details

Find the volume of the cylinder with radius 6 and height 8.

Correct A. 288\pi

B. 288\pi

C. 288\pi

D. 288\pi

Correct Answer: A

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Question 10 View Details

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

Correct A. 64

B. 64

C. 64

D. 64

Correct Answer: A

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Question 11 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \(3/4\).

Correct A. 2047

B. 2048

C. 2049

D. 2050

Correct Answer: A

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Question 12 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\() > 0.\)

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

B. x < -1 or \(x < 2\)

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

D. x > -1 or \(x > 2\)

Correct Answer: A

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Question 13 View Details

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

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

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

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

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

Correct Answer: A

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Question 14 View Details

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 1 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}

Correct Answer: A

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Question 15 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 16 View Details

Let f(x) = \((3x^2 + 2x - 5\)\). Find the value of f\(-2\\((3x^2 + 2x - 5). Find the value of f\) using the remainder theorem.

A. 1

B. -1

Correct C. 3

D. 5

Correct Answer: C

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Question 17 View Details

A histogram of exam scores is shown below. If the mean score is 60, find the value of the median.

A. 55

Correct B. 60

C. 65

D. 70

Correct Answer: B

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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, find P(\(A \cap B\)).

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 19 View Details

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 + \(y - 3\)^\(2 = 4\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

Correct Answer: A

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Question 20 View Details

Solve the equation sin(x) = 0.5 for \(0 \le x\\(sin(x) = 0.5 for (0\)\(\le 2\)π.

Correct A. π/6

B. π/2

C. 5π/6

D. 3π/2

Correct Answer: A

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Question 21 View Details

Find the area under the curve of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) from \(x = 0\) to \(x = 1\).

Correct A. \(\frac{\pi}{2}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{\pi}{6}\)

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

Correct Answer: A

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Question 22 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.68

B. 0.85

C. 0.95

D. 0.98

Correct Answer: A

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Question 23 View Details

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

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

Correct B. \(\frac{8}{3} \pi\)

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

D. \(\frac{32}{3} \pi\)

Correct Answer: B

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Question 24 View Details

A right circular cone has a radius of 4 cm and a height of 6 cm. Find the surface area of the cone.

A. ( 4 pi )

B. ( 8 pi )

Correct C. ( 12 pi )

D. ( 16 pi )

Correct Answer: C

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Question 25 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for ( x ) in the interval ( [0, 2 pi] ).

Correct A. \(x = 0, \pi, 2 \pi\)

B. \(x = \frac{\pi}{2}, \frac{3 \pi}{2}\)

C. \(x = \frac{\pi}{4}, \frac{3 \pi}{4}\)

D. \(x = \frac{\pi}{6}, \frac{5 \pi}{6}\)

Correct Answer: A

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