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POST UTME LASU 2021 Mathematics | Objective

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Question 1 View Details

Find the value of ( mathbf{a} cdot mathbf{b} ) if \(\mathbf{a} = egin{pmatrix} 2 \ 3 \ -1 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 \ 4 \end{pmatrix}\).

A. 10

Correct B. -10

C. 5

D. -5

Correct Answer: B

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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 will be 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

Solve the system of linear equations: \(egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y + 2z = 5 \end{cases}\).

Correct A. \(x = 1\), \(y = 2\), \(z = 3\)

B. \(x = 2\), \(y = 3\), \(z = 4\)

C. \(x = 3\), \(y = 4\), \(z = 5\)

D. \(x = 4\), \(y = 5\), \(z = 6\)

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: B

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Question 5 View Details

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

Correct A. \(x = -2\),\(x = -3\)

B. \(x = -1\),\(x = -6\)

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

D. \(x = 1\), \(x = 6\)

Correct Answer: A

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Question 6 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

Correct A. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

Correct Answer: A

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Question 7 View Details

Evaluate the definite integral \(int_0^1 2x^3 - 3x^2 + x - 1 \\) dx ).

Correct A. \(\left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1\)

B. \(\left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1\)

C. \(\left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1\)

D. \(\left[ \frac{2x^4}{4} - \frac{3x^3}{3} + \frac{x^2}{2} - x \right]_0^1\)

Correct Answer: A

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Question 8 View Details

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

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

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

C. \(x = \frac{\pi}{2}\)

D. \(x = \frac{\pi}{2}\)

Correct Answer: A

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Question 9 View Details

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

Correct A. \(\left[ \frac{x^3}{3} - x^2 + x \right]_0^2\)

B. \(\left[ \frac{x^3}{3} - x^2 + x \right]_0^2\)

C. \(\left[ \frac{x^3}{3} - x^2 + x \right]_0^2\)

D. \(\left[ \frac{x^3}{3} - x^2 + x \right]_0^2\)

Correct Answer: A

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Question 10 View Details

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

Correct A. \(x < -\frac{5}{2}\) or \(x > \frac{1}{2}\)

B. \(x < -\frac{5}{2}\) or \(x > \frac{1}{2}\)

C. \(x < -\frac{5}{2}\) or \(x > \frac{1}{2}\)

D. \(x < -\frac{5}{2}\) or \(x > \frac{1}{2}\)

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 \(x = 4\).

Correct A. \(32 \\)

B. \(64 \\)

C. \(96 \\)

D. \(128 \\)

Correct Answer: A

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Question 12 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 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. \(-\frac{2}{x^2 + 1 \ ^2}\)

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

Correct Answer: A

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Question 14 View Details

A vector \(\vec{a}\) has components \(a_x = 3\) and \(a_y = 4\). Find the magnitude of the vector.

Correct A. \(5 \\)

B. \(10 \\)

C. \(15 \\)

D. \(20 \\)

Correct Answer: A

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Question 15 View Details

Solve the equation \(x^2 + 2x - 6 = 0\) using the quadratic formula.

Correct A. \(x = -3 \\) or \(x = 2 \\)

B. \(x = -2 \\) or \(x = 3 \\)

C. \(x = -1 \\) or \(x = 6 \\)

D. \(x = 1 \\) or \(x = -6 \\)

Correct Answer: A

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Question 16 View Details

In a triangle with sides of length 5, 12, and 13, find the area using Heron's formula.

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 17 View Details

Solve for x in the equation \(\log_{2} x^2\)\(= 4\)\).

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 18 View Details

Find the volume of a sphere with radius 6 cm.

Correct A. 904.778

B. 904.778

C. 904.778

D. 904.778

Correct Answer: A

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Question 19 View Details

Solve the inequality \(x^2 - 4x + 4 \geq 0\).

Correct A. \(x \leq 2\)

B. \(x \geq 2\)

C. \(x < 2\)

D. \(x > 2\)

Correct Answer: A

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Question 20 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 21 View Details

Given that \(\(1\theta = \frac{1}{3}\), find the value of 1\theta \(1\theta\) using the identity 1\\(theta =\)\(\frac{\(1\theta}{\)1\theta}\)\).

Correct A. \(1/6\)

B. \(1/2\)

C. \(2/3\)

D. \(3/4\)

Correct Answer: A

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Question 22 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or x > \(-3/2\)

C. \(x <\)\(-3/2\) or \(x > 1\)

D. \(x < 3/2\)\) or x > -1

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

C. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

Correct Answer: A

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Question 24 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\), with initial term \(a_1 = 3\). Find the value of \(a_{10}\).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 25 View Details

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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