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POST UTME DELSU 2023 Mathematics | Objective

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Question 1 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 2 View Details

Solve for x in the equation \(\sin^2 x + \cos^2 x = 1\).

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

Correct B. \(x = \frac{\pi}{4}\)

C. \(x = \frac{3\pi}{4}\)

D. \(x = \frac{5\pi}{4}\)

Correct Answer: B

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Question 3 View Details

Find the volume of the cylinder with radius 6 and height 8.

Correct A. ( 384pi )

B. ( 384pi )

C. ( 384pi )

D. ( 384pi )

Correct Answer: A

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Question 4 View Details

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

Correct A. \(x < -\frac{3}{2}\) or \(x > \frac{1}{2}\)

B. \(x < -\frac{3}{2}\) or \(x < \frac{1}{2}\)

C. \(x > -\frac{3}{2}\) or \(x < \frac{1}{2}\)

D. \(x < -\frac{3}{2}\) or \(x > \frac{1}{2}\)

Correct Answer: A

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Question 5 View Details

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

Correct A. \(\frac{3}{5}\)

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

C. \(\frac{3}{12}\)

D. \(\frac{3}{25}\)

Correct Answer: A

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Question 6 View Details

Find the value of k such that the quadratic equation \(x^2 + kx + 16 = 0\) has equal roots.

A. 4

Correct B. -4

C. 8

D. -8

Correct Answer: B

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Question 7 View Details

A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75, what is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 8 View Details

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

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

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

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

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

Correct Answer: A

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Question 9 View Details

Find the derivative of the function ( f(x) = \(3x^2 - 2x + 1\) ) using the power rule.

Correct A. 6x - 2

B. \(3x^2 - 2\)

C. 2x - 1

D. \(x^2 - 1\)

Correct Answer: A

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Question 10 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 11 View Details

A histogram is a graphical representation of a frequency distribution of a continuous variable. What is the primary advantage of using a histogram over a bar chart?

Correct A. It allows for the visualization of the distribution of the data.

B. It is more suitable for categorical data.

C. It is easier to create than a bar chart.

D. It is more suitable for numerical data.

Correct Answer: A

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Question 12 View Details

A sequence is defined as \(a_n = 2n + 1\). Find the 10th term of the sequence.

A. 21

B. 22

Correct C. 23

D. 24

Correct Answer: C

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Question 13 View Details

A polynomial function is defined as (f(x) = \(x^3 - 6x^2 + 11x - 6)\). Find the value of (f(2)).

Correct A. 0

B. 2

C. 4

D. 6

Correct Answer: A

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Question 14 View Details

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

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 15 View Details

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

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 16 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.

A. 48\pi \(cm^3\)

B. 64\pi \(cm^3\)

Correct C. 96\pi \(cm^3\)

D. 128\pi \(cm^3\)

Correct Answer: C

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Question 17 View Details

Solve the inequality \(\frac{x^2 - 4x - 5}{x^2 - 6x + 8}\)\)\\() > 0.\)

Correct A. \left\(-\infty, -1\right\) \cup \left\(5, \infty\right\)

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

C. \left\(-\infty, 2\right\) \cup \left\(5, \infty\right\)

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

Correct Answer: A

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Question 18 View Details

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

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 19 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

A. 124

Correct B. 126

C. 128

D. 130

Correct Answer: B

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Question 20 View Details

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

A. \left\(-2, \infty\right\)

Correct B. \left\(-\infty, -2\right\)

C. \left\(-\infty, 2\right\)

D. \left\(2, \infty\right\)

Correct Answer: B

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].

Correct A. -2

B. 2

C. -1

D. 1

Correct Answer: A

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Question 22 View Details

A fair six-sided die is rolled. If the number 5 appears, a second die is rolled. What is the probability that the second die shows an even number?

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

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

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

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

Correct Answer: A

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Question 23 View Details

In the diagram below, the line (l\) has equation \(y = 2x - 3\\((l) has equation\). Find the coordinates of the point on the line \(l\) that is 5 units from the origin.

Correct A. (4, 7)

B. (3, 5)

C. (5, 13)

D. (2, 1)

Correct Answer: A

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Question 24 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. -\(\frac{1}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 25 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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