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POST UTME NOUN 2019 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. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 2 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 3 View Details

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

Correct A. 2\sin x \cos x

B. \\(\cos^2\) x

C. \sin x \cos x

D. \\(\sin^2\) x

Correct Answer: A

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Question 4 View Details

Solve the equation \(\frac{1}{2}x^2 + 3x - 2 = 0\) using the quadratic formula.

Correct A. \(x = -2\)\pm \(\sqrt{3}\)

B. \(x = 1\) \pm \(\sqrt{2}\)

C. \(x = -1\)\pm \(\sqrt{3}\)

D. \(x = 2\) \pm \(\sqrt{2}\)

Correct Answer: A

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 6 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 7 View Details

A circle with center (0,0) and radius 5 passes through which of the following points?

A. (3,4)

B. (4,3)

Correct C. (5,0)

D. (0,5)

Correct Answer: C

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Question 8 View Details

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

A. 16π/3

B. 32π/3

Correct C. 64π/3

D. 128π/3

Correct Answer: C

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Question 9 View Details

A vector [ mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} ] is rotated by 90° about the x-axis. What is the new vector?

Correct A. \begin{pmatrix} 1 \ -3 \ -2 \end{pmatrix}

B. \begin{pmatrix} 1 \ 3 \ 2 \end{pmatrix}

C. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

D. \begin{pmatrix} 1 \ -2 \ 3 \end{pmatrix}

Correct Answer: A

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Question 10 View Details

Find the equation of the line passing through the points (1,2) and (3,4).

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

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

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

D. \(y = 2x - 3\)

Correct Answer: A

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Question 11 View Details

Determine the value of (x\) in the equation \(2^x + 5^x = 7^x\\((x) in the equation\).

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 12 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x^2\) and \(y = 4 - x^2\) 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 13 View Details

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

Correct A. \(-\infty, -1\) \cup \(2, \infty\)\)

B. \(-\infty, -1\) \cup \(-1, 2\)\)

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

D. \(-\infty, -1\) \cup \(2, \infty\)\)

Correct Answer: A

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Question 14 View Details

Find the equation of the line passing through the points \(-2, 3\)\) and \((1, 4)\).

Correct A. \(y =\)\(\frac{7}{3}\)\) x + \(\frac{5}{3}\)\)

B. \(y =\)\(\frac{3}{7}\)\) x - \(\frac{5}{7}\)\)

C. \(y =\)\(\frac{7}{3}\)\) x - \(\frac{5}{3}\)\)

D. \(y =\)\(\frac{3}{7}\)\) x + \(\frac{5}{7}\)\)

Correct Answer: A

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Question 15 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

A. 25\pi

Correct B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: B

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Question 16 View Details

Find 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 17 View Details

A survey of 1000 people showed that 60% preferred coffee, 20% preferred tea, and 20% preferred both. What percentage of people preferred coffee or tea?

A. 70%

Correct B. 80%

C. 85%

D. 90%

Correct Answer: B

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Question 18 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19 View Details

A rectangle has a length of 5 cm and a width of 3 cm. Find the area of the rectangle.

A. 10 \(cm^2\)

Correct B. 15 \(cm^2\)

C. 20 \(cm^2\)

D. 25 \(cm^2\)

Correct Answer: B

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Question 20 View Details

Find the value of x in the equation \(2^x = 16\).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 21 View Details

Find the equation of the line passing through the points ( (1, 2) ) and ( (3, 4) ).

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 22 View Details

Solve the quadratic 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 23 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 24 View Details

Solve the system of equations \(x + y = 2\) and \(x - y = 0\).

Correct A. \(x = 1, y = 1\)

B. \(x = 1, y = 0\)

C. \(x = 0, y = 1\)

D. \(x = 0, y = 0\)

Correct Answer: A

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Question 25 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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