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POST UTME GREENFIELD UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 - 4}}\)\) ) using the chain rule.

Correct A. \(\frac{-2}{x^2 - 4 \\)^{\(3/2\)}} )

B. \(\frac{2}{x^2 - 4 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 - 4 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 - 4 \\)^{\(3/2\)}} )

Correct Answer: A

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Question 2 View Details

A circle has a radius of 5 cm and a center at (0, 0). Find the equation of the circle in standard form.

Correct A. \(x^2 + y^2 = 25\)

B. \(x^2 + y^2 = 50\)

C. \(x^2 - y^2 = 25\)

D. \(x^2 + y^2 = 75\)

Correct Answer: A

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Question 3 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 4 View Details

Simplify the expression \(\frac{1}{2} \times \frac{3}{4} times \frac{5}{6}\) using the rules of \\(times frac{5}{6}\fractions.

Correct A. \(\frac{5}{24}\)

B. \(\frac{1}{24}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{12}\)

Correct Answer: A

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Question 5 View Details

A set of data has a mean of 25 and a standard deviation of 3. Find the z-score of the value 32.

A. 1.33

B. 1.67

Correct C. 2.00

D. 2.33

Correct Answer: C

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Question 6 View Details

Determine the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\) using the quadratic formula.

A. 1

B. -2

Correct C. 3

D. -4

Correct Answer: C

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Question 7 View Details

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

Correct A. 15

B. 20

C. 25

D. 30

Correct Answer: A

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Question 8 View Details

A polynomial function is defined as ( f(x) = \(x^3 - 2x^2 - 7x + 12\) ). Find the value of x that makes f(x) = 0.

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 9 View Details

A set of data is given as {1, 2, 3, 4, 5}. Find the mean and median of the data.

Correct A. 3, 3

B. 2, 3

C. 4, 4

D. 5, 5

Correct Answer: A

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Question 10 View Details

A matrix is given as \(egin{bmatrix} 1 & 2 \ 3 & 4 \ \end{bmatrix}\). Find the determinant of the matrix.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11 View Details

Determine 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 12 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).

Correct A. 124

B. 126

C. 128

D. 130

Correct Answer: A

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Question 13 View Details

Solve for x in the equation \(2^x + 2^x = 128\).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 14 View Details

Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 15 View Details

Solve the system of equations \(x + y = 5\) and \(x - y = 3\).

Correct A. (2, 3)

B. (3, 2)

C. (4, 1)

D. (1, 4)

Correct Answer: A

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Question 16 View Details

Solve for x in the equation \(\frac{1}{x+2} + \frac{1}{x-3} = \frac{1}{2}\).

Correct A. \(x = -\frac{5}{2}\)

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

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

D. \(x = \frac{1}{2}\)

Correct Answer: A

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Question 17 View Details

A particle moves in a straight line with its position given by the equation ( s(t) = \((2t^3 - 5t^2 + 3t + 1\)\) ). Find the velocity of the particle at time \(t = 2\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity of the particle at time\) seconds.

Correct A. \(( v(2) = 14 )\)\(m/s\)

B. \(( v(2) = -14 )\)\(m/s\)

C. \(( v(2) = 0 )\)\(m/s\)

D. \(( v(2) = 21 )\)\(m/s\)

Correct Answer: A

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Question 18 View Details

A fair six-sided die is rolled. What is the probability that the number showing is greater than 4?

A. \(\frac{1}{6}\)

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

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

Correct D. \(\frac{5}{6}\)

Correct Answer: D

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Question 19 View Details

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

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

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

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 20 View Details

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

Correct A. ( 16pi ) \(cm^2\)

B. ( 32pi ) \(cm^2\)

C. ( 64pi ) \(cm^2\)

D. ( 128pi ) \(cm^2\)

Correct Answer: A

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Question 21 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. 24\pi

B. 48\pi

C. 96\pi

D. 192\pi

Correct Answer: A

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Question 22 View Details

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

Correct A. x \in \(-\infty, -1\) \cup [3, \infty)

B. x \in \(-\infty, -3\) \cup [1, \infty)

C. x \in \(-\infty, -3\) \cup [1, 3]

D. x \in \(-\infty, -1\) \cup [3, 1]

Correct Answer: A

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Question 23 View Details

A box contains 5 red balls, 4 blue balls, and 3 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?

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

B. \(\frac{4}{6}\)\)

Correct C. \(\frac{5}{6}\)\)

D. \(\frac{2}{6}\)\)

Correct Answer: C

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Question 24 View Details

Solve for x in the equation \(2^x + 2^{x+1} = 3 \cdot 2^x\).

Correct A. \(x = 1\)

B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: A

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Question 25 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100\pi

B. 200\pi

Correct C. 300\pi

D. 400\pi

Correct Answer: C

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