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POST UTME UNILORIN 2018 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 \(x = 4\).

A. ( 4 )

B. ( 8 )

Correct C. ( 12 )

D. ( 16 )

Correct Answer: C

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Question 2 View Details

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

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

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

C. \(x < 1\) or \(x > 3\)

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

Correct Answer: A

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Question 3 View Details

A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

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

B. \(\frac{2}{5}\)

C. \(\frac{3}{5}\)

Correct D. \(\frac{4}{5}\)

Correct Answer: D

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Question 4 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ) using the power rule.

Correct A. ( f'\((x) = 6x + 2 )\)

B. ( f'\((x) =\)\(3x^2 + 2x - 5\) )

C. ( f'\((x) = 6x - 2 )\)

D. ( f'\((x) =\)\(3x^2 - 2x + 5\) )

Correct Answer: A

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Question 5 View Details

A circuit consists of a 12V battery, a 4Ω resistor, and a 6Ω resistor connected in series. What is the total resistance of the circuit?

A. ( 8Ω )

B. ( 10Ω )

Correct C. ( 12Ω )

D. ( 16Ω )

Correct Answer: C

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Question 6 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7 View Details

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

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 8 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is its volume?

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 9 View Details

A circle has a radius of 4 cm. What is its circumference?

Correct A. 8π

B. 10π

C. 12π

D. 16π

Correct Answer: A

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Question 10 View Details

A matrix A has the following elements: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\). What is the determinant of matrix A?

A. -2

Correct B. 0

C. 2

D. 4

Correct Answer: B

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Question 11 View Details

Let \(X\) and \(Y\) be independent random variables with probability density functions \(f_X(x) = egin{cases} 2x, & 0 < x < 1 \ 0, & \text{otherwise} \end{cases}\) and \(f_Y(y) = egin{cases} 3y^2, & 0 < y < 1 \ 0, & \text{otherwise} end{cases}\). Find the probability that \(X + Y < 1\\(end{cases}). Find the probability that\).

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 12 View Details

Solve for \(x\): \(\log_{10} x^2\)\(= 4\)\).

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 13 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 \\(), and (x = 2\(x\)-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 14 View Details

In the diagram below, (ABCD\) is a square with side length \(s\\((ABCD) is a square with side length\). If (E\) is the midpoint of \(AD\\((E) is the midpoint of\), find the length of \(BE\).

A. \(\frac{s}{2}\)\)

B. s

Correct C. \(\frac{\sqrt{2}s}{2}\)

D. ssqrt{2}

Correct Answer: C

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Question 15 View Details

Find the area of the region bounded by \(y = x^2\), \(y = 0\)\), and \(x = 2\).

A. 8

Correct B. 16

C. 32

D. 64

Correct Answer: B

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_\(X(x) =\)\begin{cases} 2x, & \(0 < x\)\(< 1\)\\ 0, & \text{otherwise} \end{cases} and f_\(Y(y) =\)\begin{cases} \(3y^2\), & \(0 < y\)\(< 1\)\\ 0, & \text{otherwise} \end{cases}. Find P\(X > Y\).

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

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

Correct Answer: B

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Question 18 View Details

Solve the inequality \log_2\(x^2 - 4 > 2\).

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

B. \(x < 2\) or \(x > 4\)

C. x < -4 or \(x > 4\)

D. x < -2 or \(x > 4\)

Correct Answer: A

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Question 19 View Details

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

Correct A. \(\frac{8}{3}\)\)

B. \(\frac{16}{3}\)\)

C. \(\frac{32}{3}\)\)

D. \(\frac{64}{3}\)\)

Correct Answer: A

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Question 20 View Details

A polynomial function f(x) has zeros at x = -2, \(x = 1\), and \(x = 3\). If f\(-1 = 16\), find f(2).

A. -16

B. 16

C. 32

Correct D. 64

Correct Answer: D

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Question 21 View Details

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

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 22 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 23 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?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 24 View Details

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

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

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

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

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

Correct Answer: A

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Question 25 View Details

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

Correct A. \(\frac{8}{3}\)\)

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

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

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

Correct Answer: A

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