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POST UTME KSU 2017 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. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 2 View Details

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

Correct A. 78.5

B. 78.5

C. 78.5

D. 78.5

Correct Answer: A

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Question 3 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -1\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 4 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.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 5 View Details

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

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

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

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 6 View Details

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

Correct A. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4\)

B. \(\frac{1}{2} \times 4^2 + 3 \times 4 - 2\)

C. \(\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2\)

D. \(\frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4\)

Correct Answer: A

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Question 7 View Details

A polynomial function is defined as ( f(x) = \((ax^3 + bx^2 + cx + d\)\) ). If ( f(1) = 3 ), \(f -1 \\((ax^3 + bx^2 + cx + d) ). If ( f(1) = 3 ), \\)\(= -3 )\), and ( f(0) = 2 ), find the value of \(a + b + c + d\).

Correct A. \(3a + b + c + d\)

B. \(a + 3b + c + d\)

C. \(a + b + 3c + d\)

D. \(a + b + c + 3d\)

Correct Answer: A

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Question 8 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. \(5 \times 3 \times 2\)

B. \(5 \times 3 + 2\)

C. \(5 \times 3 + 2 \times 5\)

D. \(5 \times 3 \times 2 \times 5\)

Correct Answer: A

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Question 9 View Details

A curve is defined by the equation \(y = \frac{1}{x}\). Find the derivative of the curve.

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

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

C. \(-\frac{1}{x}\)

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

Correct Answer: A

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Question 10 View Details

A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

Correct A. \(2 1 + 2 + 3 + 4 + 5 \\) + 5 )

B. \(2 1 + 2 + 3 + 4 + 5 \\) - 5 )

C. \(2 1 + 2 + 3 + 4 + 5 \\) + 1 )

D. \(2 1 + 2 + 3 + 4 + 5 \\) - 1 )

Correct Answer: A

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Question 11 View Details

In a circle of radius 5 cm, a chord of length 8 cm subtends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii.

Correct A. \(\frac{1}{6} \pi 5 \\)^2 )

B. \(\frac{1}{6} \pi 8 \\)^2 )

C. \(\frac{1}{6} \pi 5 \\)^2 - \(\frac{1}{2}\)\) \((8)^2\) )

D. \(\frac{1}{6} \pi 5 \\)^2 + \(\frac{1}{2}\)\) \((8)^2\) )

Correct Answer: A

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Question 12 View Details

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } \(x = 1\) \\(text{if} (x = 1\ 0.3 & text{if} \(x = 2\) \\(text{if} (x = 2\ 0.5 & text{if} \(x = 3\) \\(text{if}\((x = 3\)\end{cases} ). Find the expected value of X.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13 View Details

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

A. \(y = \frac{2}{2} x + \frac{1}{2}\)

B. \(y = \frac{1}{2} x + \frac{3}{2}\)

Correct C. \(y = 2x + 1\)

D. \(y = x + 2\)

Correct Answer: C

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Question 14 View Details

Solve the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\).

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

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

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

D. \(x = 2, y = 2\)

Correct Answer: A

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Question 15 View Details

Find the mean deviation about the mean of the data set: 2, 4, 6, 8, 10.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) = 2x\), \(0 < x\) < 1 and f_\(Y(y) =\)\(3y^2\),\((0 < y\)\) < 1. Find the probability that \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

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

B. \(\frac{1}{3}\)\)

C. \(\frac{2}{3}\)\)

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

Correct Answer: A

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Question 17 View Details

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

Correct A. \(\frac{32\pi}{3}\)\)

B. \(\frac{64\pi}{3}\)\)

C. \(\frac{128\pi}{3}\)\)

D. \(\frac{256\pi}{3}\)\)

Correct Answer: A

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Question 18 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{256}{5}\)\)

B. \(\frac{512}{5}\)\)

C. \(\frac{1024}{5}\)\)

D. \(\frac{2048}{5}\)\)

Correct Answer: A

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Question 19 View Details

Find the vector projection of the vector mathbf{a}\(= 2\)\mathbf{i} + 3\mathbf{j} onto the vector \\(mathbf{a}\(= 2mathbf\){i} + 3\mathbf{b} = \mathbf{i} + \mathbf{j}.

Correct A. \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{i} + \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{j}

B. \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{i} - \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{j}

C. \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{i} + \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{j}

D. \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{i} - \(\frac{5}\){\(\sqrt{2}\)}\)\mathbf{j}

Correct Answer: A

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Question 20 View Details

Find the sum of the infinite geometric series \sum_{\(n = 1\)}^\infty \(\frac{2}{3^n}\)\)\).

Correct A. \(\frac{2}{3}\)\)

B. \(\frac{4}{3}\)\)

C. \(\frac{6}{3}\)\)

D. \(\frac{8}{3}\)\)

Correct Answer: A

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Question 21 View Details

Given that ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ), find the derivative of ( f(x) ) using the chain rule.

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

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

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

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

Correct Answer: B

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Question 22 View Details

A binary operation ( odot ) is defined as \(a odot b = a^2 + b^2\). Find the value of ( 2 odot 3 ).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 23 View Details

A vector ( mathbf{a} ) is given by \(\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}\). Find the magnitude of ( mathbf{a} ).

A. 3.60555

Correct B. 4.1231

C. 5.19615

D. 6.40312

Correct Answer: B

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Question 24 View Details

A probability experiment consists of rolling a fair six-sided die. What is the probability that the number rolled is greater than 4?

A. \(1/6\)

B. \(1/3\)

C. \(2/3\)

Correct D. \(5/6\)

Correct Answer: D

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Question 25 View Details

A polynomial function ( f(x) ) is defined as ( f(x) = \((x^3 - 2x^2 + 3x - 1\)\) ). Find the value of \(f -1 \\((x^3 - 2x^2 + 3x - 1) ). Find the value of \\) ).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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