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POST UTME WELLSPRING UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{5}$\) ).

Correct A. $\frac{4\sqrt{11}}{11}$

B. $\frac{3\sqrt{11}}{11}$

C. $\frac{4\sqrt{11}}{11}$

D. $\frac{3\sqrt{11}}{11}$

Correct Answer: A

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

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

Correct Answer: B

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Question 3 View Details

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 4 View Details

Solve the equation $2^x + 2^{-x} = 5$.

Correct A. \log_2(3)

B. \log_2(2)

C. \log_2(3)

D. \log_2(2)

Correct Answer: A

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Question 5 View Details

Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 6 View Details

Determine the value of x in the equation $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}$.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 7 View Details

Solve for y in the equation $\frac{dy}{dx} = \frac{2x}{y}$ where y(1) = 2.

Correct A. $y = 2x\^2$

B. $y = x\^2$

C. $y = 2x$

D. $y = x$

Correct Answer: A

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Question 8 View Details

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } $X = 1$ \$text{if} (X = 1\ 0.3 & text{if} \(X = 2$ \$text{if} (X = 2\ 0.5 & text{if} \(X = 3$ \$text{if}\((X = 3$\end{cases} ). Find the expected value of X.

A. 1.5

B. 2

Correct C. 2.5

D. 3

Correct Answer: C

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Question 9 View Details

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

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

Correct 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: B

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Question 10 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 85.

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 11 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 12 View Details

If f(x) = $3x^2 + 2x - 5$, find f'(x) using the chain rule.

Correct A. \boxed{6x + 2}

B. $3x^2 + 2$

C. 6x - 2

D. $3x^2 + 2x$

Correct Answer: A

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Question 13 View Details

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

Correct A. \boxed{ -\infty, -3 \cup 1, \infty }

B. $-\infty, -3$ \cup $-1, \infty$

C. $-\infty, 1$ \cup $3, \infty$

D. $-\infty, -1$ \cup $3, \infty$

Correct Answer: A

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Question 14 View Details

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

Correct A. \boxed{$\frac{13}{3}$\)}

B. $\frac{11}{3}$\)

C. $\frac{15}{3}$\)

D. $\frac{17}{3}$\)

Correct Answer: A

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Question 15 View Details

Find the vector projection of vector \mathbf{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto vector \mathbf{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.

Correct A. \boxed{\begin{pmatrix} $\frac{11}{14}$\) \ $\frac{13}{14}$\) \ $\frac{15}{14}$\) \end{pmatrix}}

B. \begin{pmatrix} $\frac{11}{14}$\) \ $\frac{13}{14}$\) \ $\frac{15}{14}$\) \end{pmatrix}

C. \begin{pmatrix} $\frac{13}{14}$\) \ $\frac{15}{14}$\) \ $\frac{17}{14}$\) \end{pmatrix}

D. \begin{pmatrix} $\frac{15}{14}$\) \ $\frac{17}{14}$\) \ $\frac{19}{14}$\) \end{pmatrix}

Correct Answer: A

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Question 16 View Details

Determine the value of k in the equation $2x^2 + 5x + k = 0$ if the sum of the roots is -2.

A. -1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17 View Details

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.65

B. 0.7

C. 0.75

D. 0.8

Correct Answer: A

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Question 18 View Details

Find the volume of the solid formed by rotating the region bounded by $y = x^2$ and $y = 4$ about the x-axis.

A. 64π

B. 128π

Correct C. 256π

D. 512π

Correct Answer: C

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Question 19 View Details

A random variable X has a probability distribution given by $P X = 1 \$ = $\frac{1}{2}$\) ) and $P X = 2 \$ = $\frac{1}{2}$\) ). Find the expected value of X.

A. 1

Correct B. 1.5

C. 2

D. 2.5

Correct Answer: B

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Question 20 View Details

Solve the inequality $\log_{10} x^2 \$$> 4 ).$

A. $x > 10$

B. $x < -10$

Correct C. $x > 100$

D. $x < -100$

Correct Answer: C

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Question 21 View Details

Let ( f(x) = $\frac{x^2 - 4}{x^2 - 9}$\)) ). Find the value of lim_{x \to 3} f\( x \\() ). Find the value of lim_{x to 3} f\ ).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22 View Details

In a triangle ABC, if angle $A = 30$^\$angle (A = 30\circ and angle \(B = 60$^\$angle (B = 60\circ, find the value of \($1C$.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 23 View Details

Let $A = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$. Find the value of ( AB ).

Correct A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}

B. \begin{pmatrix} 3 & 4 \ 6 & 8 \end{pmatrix}

C. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}

D. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}

Correct Answer: A

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Question 24 View Details

Let ( f(x) = $(2x^3 - 5x^2 + x - 1$\) ). Find the value of $f -1 \\((2x^3 - 5x^2 + x - 1) ). Find the value of \$ ).

Correct A. -9

B. -7

C. -5

D. -3

Correct Answer: A

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Question 25 View Details

Let $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 1 \ 3 & 4 end{pmatrix}$. Find the value of $A^2\\(end{pmatrix}). Find the value of$.

Correct A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}

B. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}

C. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}

D. \begin{pmatrix} 7 & 8 \ 11 & 16 \end{pmatrix}

Correct Answer: A

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