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POST UTME MOUNTAIN TOP UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 \cdot $\frac{3^{10} - 1}{3 - 1}$\)

B. 2 \cdot $\frac{3^{11} - 1}{3 - 1}$\)

C. 2 \cdot $\frac{3^{12} - 1}{3 - 1}$\)

D. 2 \cdot $\frac{3^{13} - 1}{3 - 1}$\)

Correct Answer: A

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Question 2 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 5 \cdot 3 \cdot 2

B. 5 \cdot 3 + 2

C. 5 \cdot 2 + 3

D. 3 \cdot 2 + 5

Correct Answer: A

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Question 3 View Details

Solve for x in the equation $\frac{x}{2}$\) + $3 = 7$.

Correct A. $x = 8$

B. $x = 10$

C. $x = 12$

D. $x = 14$

Correct Answer: A

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Question 4 View Details

Find the determinant of the 3x3 matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5 View Details

A polynomial f(x) has roots $x = 1$, $x = 2$, and $x = 3$. Write the polynomial in factored form.

Correct A. $x - 1$, x - 2\)$x - 3$

B. $x - 1$, x - 2\)$x + 3$

C. $x - 1$, x + 2\)$x - 3$

D. $x + 1$, x - 2\)$x - 3$

Correct Answer: A

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Question 6 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}$. Find the unit vector in the direction of $\\(end{pmatrix}). Find the unit vector in the direction of \mathbf{a} + \mathbf{b}$.

Correct A. $egin{pmatrix} 0.6 \ 0.8 \end{pmatrix}$

B. $egin{pmatrix} 0.8 \ 0.6 \end{pmatrix}$

C. $egin{pmatrix} 0.4 \ 0.6 \end{pmatrix}$

D. $egin{pmatrix} 0.6 \ 0.4 \end{pmatrix}$

Correct Answer: A

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Question 7 View Details

A random variable ( X ) has a probability distribution given by $P X = x \$ = $frac{1}{2}$\) ) for \$frac{1}{2})\(x = 1, 2, 3$. Find the probability that ( X ) is greater than 2.

A. $\frac{1}{4}$

B. $\frac{1}{2}$

Correct C. $\frac{3}{4}$

D. $\frac{1}{3}$

Correct Answer: C

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Question 8 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$ using integration by substitution.

Correct A. $\frac{8}{3}$

B. $\frac{16}{3}$

C. $\frac{24}{3}$

D. $\frac{32}{3}$

Correct Answer: A

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Question 9 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using the chain rule.

Correct A. $2 \(1x$1x\)

B. $\cos^2 x$

C. $\sin^2 x$

D. $$1x$

Correct Answer: A

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Question 10 View Details

A set of data has a mean of 25 and a standard deviation of 5. Find the probability that a randomly selected value from the set is greater than 30.

A. $\frac{1}{4}$

B. $\frac{1}{2}$

Correct C. $\frac{3}{4}$

D. $\frac{1}{3}$

Correct Answer: C

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 12 View Details

Solve for ( x ) in the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}$.

Correct A. $x = 1$, $y = 2$

B. $x = 2$, $y = 1$

C. $x = 1$, $y = 1$

D. $x = 2$, $y = 2$

Correct Answer: A

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Question 13 View Details

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. $1/6$

Correct B. $1/12$

C. $1/36$

D. $1/24$

Correct Answer: B

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Question 14 View Details

The mean of a set of 5 numbers is 10. If one of the numbers is 15, what is the sum of the other 4 numbers?

Correct A. 40

B. 45

C. 50

D. 55

Correct Answer: A

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Question 15 View Details

The polynomial ( p(x) = $x^3 - 6x^2 + 11x - 6$ ) has a root at $x = 1$. What is the quotient when ( p(x) ) is divided by $x - 1$?

Correct A. $x^2 - 5x + 6$

B. $x^2 - 5x + 5$

C. $x^2 - 5x + 4$

D. $x^2 - 5x + 3$

Correct Answer: A

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Question 16 View Details

In a certain number base (b\), the number $101_5\\((b), the number$ is equivalent to $b^2 + 1$ in base $10$. Find the value of $b$.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 17 View Details

The line (y = 2x + 3\) intersects the circle $x^2 + y^2 = 16\\((y = 2x + 3) intersects the circle$ at two points. Find the coordinates of the point where the line is \tangent to the circle.

Correct A. $4, -1$

B. $-4, -1$

C. (4, 1)

D. $-4, 1$

Correct Answer: A

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Question 18 View Details

The quadratic equation $(x^2 + 4x + 4$ = 0\) has two equal roots. Find the value of $x\\((x^2 + 4x + 4 = 0) has two equal roots. Find the value of$.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 19 View Details

The mean of a set of numbers is (\bar{x}$= 10$\). If the sum of the numbers is \$(bar{x} = 10\(S = 50$, find the median of the set.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 20 View Details

The polynomial $P(x) = x^3 - 6x^2 + 11x - 6$ has a root at $x = 1$. Find the value of $P(2)$.

A. 0

B. 2

Correct C. 4

D. 6

Correct Answer: C

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Question 21 View Details

A set of 10 numbers has a mean of 20 and a standard deviation of 5. If the set is multiplied by 2, what is the new standard deviation?

A. 10

B. 20

Correct C. 40

D. 50

Correct Answer: C

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Question 22 View Details

Solve for x in the equation: $2^x + 3^x = 5^x$

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.68

B. 0.80

Correct C. 0.95

D. 0.99

Correct Answer: C

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Question 24 View Details

A sequence is defined by the formula: (a_$n = 2a$_{n-1} + 1\). If $a_1 = 3\\((a_n = 2a_{n-1} + 1). If$, find the value of $a_5$

A. 31

B. 33

Correct C. 35

D. 37

Correct Answer: C

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Question 25 View Details

A polynomial function is defined by:$(f(x) = \(x^3 - 6x^2 + 11x - 6$\)\). Find the value of $f -1\\((f(x) = x^3 - 6x^2 + 11x - 6). Find the value of$

A. -2

Correct B. 0

C. 2

D. 4

Correct Answer: B

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