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POST UTME REDEEMERS UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Solve for x in the quadratic equation \(x^2 + 5x + 6 = 0\).

Correct A. \(x = -2\)

B. \(x = -3\)

C. \(x = 2\)

D. \(x = 3\)

Correct Answer: A

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Question 2 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 3 View Details

Solve the system of linear equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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 4 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 5\)^\(2 = 16\) )

D. \(x - 5 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 5 View Details

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, with the first bar representing scores 0-10, the second bar representing scores 11-20, and so on. If the mean score is 25, what is the median score?

Correct A. 25

B. 26

C. 27

D. 28

Correct Answer: A

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Question 6 View Details

Find the value of \(\log_{10} \left \frac{1000}{\sqrt{100}} \right\)\).

Correct A. 3

B. 2

C. 1

D. 0

Correct Answer: A

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Question 7 View Details

A histogram of exam scores is shown below. If the mean score is 60, find the value of \(\sigma\).

A. 10

Correct B. 5

C. 15

D. 20

Correct Answer: B

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Question 8 View Details

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

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

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

C. \pi

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

Correct Answer: A

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Question 9 View Details

A circle with center \(C\) and radius \(r\) is shown below. If the point (P\) lies on the circle, find the value of \(CP\\((P) lies on the circle, find the value of\).

Correct A. r

B. 2r

C. 3r

D. 4r

Correct Answer: A

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Question 10 View Details

A quadratic equation is given by \((ax^2 + bx + c\) = 0\). If the roots are \(\\((ax^2 + bx + c = 0). If the roots are \alpha\) and \(\beta\), find the value of \(\alpha + \beta\).

Correct A. -\(\frac{b}{a}\)\)

B. \(\frac{c}{a}\)\)

C. \(\frac{b}{a}\)\)

D. -\(\frac{c}{a}\)\)

Correct Answer: A

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Question 11 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12 View Details

A circle has a radius of 5 cm. Find the area of the circle.

A. 25π

Correct B. 50π

C. 75π

D. 100π

Correct Answer: B

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Question 13 View Details

Find the derivative of the function \(y = \sin^2 x\) using the chain rule.

Correct A. \(2\(1x\)1x\)

B. \(\cos^2 x\)

C. \(\(1x\)1x\)

D. \(\sin^2 x\)

Correct Answer: A

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Question 14 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the median.

Correct A. 25

B. 30

C. 35

D. 40

Correct Answer: A

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Question 15 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. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: B

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Question 16 View Details

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 17 View Details

Solve the inequality \(\log_{10} x^2 \\)\(> 4 ).\)

Correct A. \(x > 10\)

B. \(x < 10\)

C. \(x > 100\)

D. \(x < 100\)

Correct Answer: A

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Question 18 View Details

Find the equation of the circle with center at ( (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 19 View Details

Find the area under the curve \(y = x^3\) from \(x = 0\) to \(x = 2\).

A. 8

B. 16

Correct C. 32

D. 64

Correct Answer: C

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Question 20 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 22 View Details

Solve the inequality |x - 2|\(> 3.\)

Correct A. x < -1 or \(x > 5\)

B. \(x < 1\) or \(x > 5\)

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

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

Correct Answer: A

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Question 23 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 + \(y - 3\)^\(2 = 32\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 64\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 128\)

Correct Answer: A

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Question 24 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 2\).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 25 View Details

Solve the system of equations \(x + y = 4\) and \(xy = 6\).

Correct A. \(x = 2\), \(y = 2\)

B. \(x = 2\), \(y = 3\)

C. \(x = 3\), \(y = 2\)

D. \(x = 3\), \(y = 3\)

Correct Answer: A

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