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POST UTME WELLSPRING UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 2 View Details

Solve for 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 3 View Details

Find the equation of the circle with center at (2, 3) and radius 4.

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

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 4\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)

Correct Answer: A

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Question 4 View Details

Find the derivative of the function [\(f(x) =\)\(\frac{1}{x^2 + 1}\)\)\) ].

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 5 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = 2x - 1\)

D. \(y = -2x + 1\)

Correct Answer: A

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Question 6 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \boxed{ 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 7 View Details

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

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

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

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

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

Correct Answer: B

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Question 8 View Details

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

A. 6x + 2

B. \(6x^2 + 2\)

Correct C. \(6x^2 + 2x\)

D. 6x + \(2x^2\)

Correct Answer: C

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Question 9 View Details

A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 2, 3, 4, 5, and 6. What is the mean score of the class?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 10 View Details

Simplify the expression \(\sqrt{16x^2y\)^4}\)

A. \(4xy^2\)

Correct B. \(4x^2y\)^2

C. \(4xy^4\)

D. \(4x^2y\)^4

Correct Answer: B

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Question 11 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 10.95%

Correct B. 12.55%

C. 14.15%

D. 16.75%

Correct Answer: B

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Question 12 View Details

Solve for x in the equation \(2x^2 + 5x - 3 = 0\).

Correct A. -1.5

B. 1.5

C. 3

D. -3

Correct Answer: A

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Question 13 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

A. 150

B. 200

Correct C. 250

D. 300

Correct Answer: C

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Question 14 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

A. 8

B. 10

C. 12

Correct D. 14

Correct Answer: D

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Question 15 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 45

B. 48

Correct C. 50

D. 52

Correct Answer: C

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Question 16 View Details

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

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 17 View Details

Find the sum of the first 10 terms of the geometric series \(2 + 6 + 18 + \cdots\).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 18 View Details

Let ( f(x) = \(x^2 + 2x + 1\) ). Find the derivative of ( f(x) ) using the chain rule.

A. 2x + 2

Correct B. 2x + 1

C. \(x^2 + 2\)

D. \(x^2 + 1\)

Correct Answer: B

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Question 19 View Details

Solve the system of linear equations \(\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\).

Correct A. \left\(\frac{5}{2}, \frac{1}{2} \right\)

B. \left\(\frac{1}{2}, \frac{5}{2} \right\)

C. \left\(-\frac{1}{2}, \frac{5}{2} \right\)

D. \left\(\frac{5}{2}, -\frac{1}{2} \right\)

Correct Answer: A

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Question 20 View Details

Find the derivative of ( 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 21 View Details

In a right-angled triangle, the length of the hypotenuse is 10cm and one of the other sides is 6cm. Find the length of the third side using the Pythagorean theorem.

A. 8cm

Correct B. 12cm

C. 6cm

D. 4cm

Correct Answer: B

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Question 22 View Details

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

Correct A. 16

B. 8

C. 4

D. 2

Correct Answer: A

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Question 23 View Details

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

Correct B. 17

C. 16

D. 15

Correct Answer: B

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Question 24 View Details

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

Correct A. 50.\(24cm^2\)

B. 25.\(12cm^2\)

C. 50.\(12cm^2\)

D. 25.\(24cm^2\)

Correct Answer: A

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Question 25 View Details

A rectangular garden measures 10m by 5m. Find the area of the garden.

A. \(50m^2\)

Correct B. \(75m^2\)

C. \(60m^2\)

D. \(40m^2\)

Correct Answer: B

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