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POST UTME UNIPORT 2021 Mathematics | Objective

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Question 1 View Details

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

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 2 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(x < -1\) or \(x > 5\)

B. \(x < 1\) or \(x > 5\)

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

D. \(x < 1\) or \(x > 2\)

Correct Answer: A

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Question 3 View Details

A sequence is defined by \(a_n = \frac{1}{n} + \frac{1}{n + 1}\). Find the sum of the first 5 terms of the sequence.

Correct A. \(\frac{25}{12}\)

B. \(\frac{23}{12}\)

C. \(\frac{21}{12}\)

D. \(\frac{19}{12}\)

Correct Answer: A

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Question 4 View Details

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle.

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

B. \(x^2 + y^2 = 32\)

C. \(x^2 + y^2 = 64\)

D. \(x^2 + y^2 = 256\)

Correct Answer: A

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Question 5 View Details

A set of 5 numbers has a mean of 10 and a median of 8. Find the sum of the numbers.

Correct A. 50

B. 60

C. 70

D. 80

Correct Answer: A

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Question 6 View Details

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find the volume of the prism using the formula \(V = lwh\).

A. 100 \(cm^3\)

Correct B. 120 \(cm^3\)

C. 150 \(cm^3\)

D. 200 \(cm^3\)

Correct Answer: B

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Question 7 View Details

The mean of a set of numbers is 25. If the sum of the numbers is 150, how many numbers are in the set?

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 8 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}.

A. -1

Correct B. -2

C. 2

D. 4

Correct Answer: B

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Question 9 View Details

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

A. -1

Correct B. -2

C. 0

D. 2

Correct Answer: B

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Question 10 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. Find the mean of the scores.

A. 4.2

B. 4.4

Correct C. 4.6

D. 4.8

Correct Answer: C

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Question 11 View Details

Determine the value of \(\frac{d}{dx} \left \frac{1}{x^2} \right\)\) using the quotient rule.

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

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

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

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

Correct Answer: A

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Question 12 View Details

Solve the inequality \(|2x - 3| \geq 7\).

Correct A. x \leq -2 \text{ or } x \geq 5

B. x \geq -2 \text{ or } x \leq 5

C. x \leq 2 \text{ or } x \geq -5

D. x \geq 2 \text{ or } x \leq -5

Correct Answer: A

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Question 13 View Details

Find the sum of the first 10 terms of the geometric series \(\sum_{n = 1}^{10} \frac{2}{3^n}\).

Correct A. \(\frac{63}{32}\)\)

B. \(\frac{63}{64}\)\)

C. \(\frac{63}{128}\)\)

D. \(\frac{63}{256}\)\)

Correct Answer: A

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Question 14 View Details

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 15 View Details

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

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

B. \(x = 2\) \text{ or } \(x = 3\)

C. \(x = -3\)\text{ or } \(x = 2\)

D. \(x = 3\) \text{ or }\(x = -2\)

Correct Answer: A

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Question 16 View Details

Let \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) and \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\). Find ( AB ) if it exists.

Correct A. \(AB = \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix}\)

B. \(AB = \begin{bmatrix} 11 & 14 \\ 25 & 30 \end{bmatrix}\)

C. \(AB = \begin{bmatrix} 3 & 4 \\ 9 & 12 \end{bmatrix}\)

D. \(AB = \begin{bmatrix} 5 & 6 \\ 15 & 18 \end{bmatrix}\)

Correct Answer: A

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Question 17 View Details

A set ( S ) contains the elements ( 1, 2, 3, 4, 5, 6 ). Find the number of subsets of ( S ) that contain exactly two elements.

A. 6

Correct B. 12

C. 20

D. 30

Correct Answer: B

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Question 18 View Details

Let ( f(x) = \(x^2 - 4x + 3\) ) and ( g(x) = 2x - 1 ). Find ( (f circ g)(x) ).

Correct A. \(2x^2 - 5x + 2\)

B. \(2x^2 - 5x + 1\)

C. \(2x^2 - 5x - 2\)

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

Correct Answer: A

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Question 19 View Details

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

A. 30

B. 35

C. 40

Correct D. 45

Correct Answer: D

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Question 20 View Details

A random experiment has two possible outcomes: heads or tails. If the probability of getting heads is \(\frac{1}{3}\), find the probability of getting tails.

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

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

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

D. \(\frac{1}{4}\)\)

Correct Answer: B

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Question 21 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 24\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 72\pi \(cm^3\)

D. 96\pi \(cm^3\)

Correct Answer: B

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Question 22 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\()>0.\)

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

B. x<-1 or \(x < 2\)

C. \(x > 1\) or \(x > 2\)

D. x<-1 or \(x < 2\)

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

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

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 25 View Details

Solve the system of equations \begin{align*} x+y+z&=3\ x+2y+3z&=6\ 2x+3y+4z&=9\ \end{align*}.

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

B. \(x = 2\), \(y = 1\), \(z = 0\)

C. \(x = 3\), \(y = 0\), \(z = 0\)

D. \(x = 0\), \(y = 0\), \(z = 0\)

Correct Answer: A

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