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POST UTME GREENFIELD UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Solve the inequality ($\frac{x}{x-2}\(> 1$\) for \$(frac{x}{x-2} > 1\(x > 2$\).

A. $2 < x$$< 3$

Correct B. $x > 3$

C. $x < 2$

D. $x = 3$

Correct Answer: B

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Question 2 View Details

Find the value of ( x ) in the quadratic equation $x^2 + 5x + 6 = 0$.

Correct A. $x = -2$

B. $x = -3$

C. $x = 2$

D. $x = 3$

Correct Answer: A

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Question 3 View Details

A sequence is defined by the formula $a_n = 2n^2 - 3n + 1$. Find the 5th term of the sequence.

A. $a_5 = 21$

B. $a_5 = 25$

Correct C. $a_5 = 29$

D. $a_5 = 31$

Correct Answer: C

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Question 4 View Details

Solve the system of equations $egin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}$.

Correct A. $x = 1$, $y = 3$

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

C. $x = 3$, $y = 1$

D. $x = 4$, $y = 0$

Correct Answer: A

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Question 5 View Details

Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}$.

A. $det(A) = 0$

B. $det(A) = 1$

Correct C. $det(A) = 2$

D. $det(A) = 3$

Correct Answer: C

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Question 6 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. $5√3$ cm

C. $10√3$ cm

D. 20 cm

Correct Answer: B

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Question 7 View Details

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

Correct A. 50.24 cm²

B. 50.24 cm²

C. 50.24 cm²

D. 50.24 cm²

Correct Answer: A

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Question 8 View Details

Find the value of x in the equation $2^x$ + \$(2^x$$= 64.$\)

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 9 View Details

A sequence is defined by the formula $an = 2n + 1$. Find the sum of the first 5 terms of the sequence.

A. 15

Correct B. 21

C. 25

D. 30

Correct Answer: B

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Question 10 View Details

A histogram is shown below. Find the mean of the data.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 11 View Details

Find the value of $int_{0}^{1} \frac{1}{x^2 + 1} dx$ using the method of substitution.

Correct A. π/2

B. π/4

C. π/3

D. π/6

Correct Answer: A

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Question 12 View Details

Solve the equation $2^x + 2^{-x} = 4$ for ( x ).

A. 1

Correct B. 2

C. -1

D. -2

Correct Answer: B

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Question 13 View Details

A binary operation ( odot ) is defined as $a odot b = a^2 + b^2$. Find the value of ( 2 odot 3 ).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 14 View Details

A circle has an equation of the form $x - h \$^2 + $y - k$^$2 = r\^2$ ). If the center of the circle is at ( (3, 4) ) and the radius is 5, find the equation of the circle.

Correct A. $x - 3$^2 + $y - 4$^$2 = 25$

B. $x - 3$^2 + $y - 4$^$2 = 30$

C. $x - 3$^2 + $y - 4$^$2 = 35$

D. $x - 3$^2 + $y - 4$^$2 = 40$

Correct Answer: A

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Question 15 View Details

A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experiment is repeated. If the outcome is an odd number, the experiment is stopped. What is the probability that the experiment will be stopped after exactly two rolls?

A. $1/6$

Correct B. $1/3$

C. $1/2$

D. $2/3$

Correct Answer: B

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Question 16 View Details

Let ( f(x) = $\frac{1}{x^2 + 1}$\)) ). Find $f^{-1} x \\\() ). Find (f^{-1} x$ ) using the method of substitution.

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

B. $f^{-1}(x) = \frac{1}{x + 1}$

Correct C. $f^{-1}(x) = \frac{1}{\sqrt{x} + 1}$

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

Correct Answer: C

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Question 17 View Details

A random variable ( X ) has a probability distribution given by $P X = x \$ = $\frac{1}{2}$\) \) for $x = 1, 2, 3, 4$. Find the probability that ( X ) is greater than 2.

A. 0.5

B. 0.75

C. 0.875

Correct D. 0.9375

Correct Answer: D

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Question 18 View Details

Let $\mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 end{pmatrix}$. Find the cross product $\\(end{pmatrix}). Find the cross product \mathbf{a} \times \mathbf{b}$.

Correct A. $\mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ 3 \ -7 \end{pmatrix}$

B. $\mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ 7 \end{pmatrix}$

C. $\mathbf{a} \times \mathbf{b} = \begin{pmatrix} -5 \ 3 \ 7 \end{pmatrix}$

D. $\mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ -7 \end{pmatrix}$

Correct Answer: A

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Question 19 View Details

A histogram of the heights of students in a class is shown below. If the mean height is 175 cm, find the median height.

A. 170 cm

Correct B. 175 cm

C. 180 cm

D. 185 cm

Correct Answer: B

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Question 20 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$ for ( x ) in the interval $[0, 2\\\() for ( x ) in the interval ([0, 2\pi]$.

A. $x = \frac{\pi}{2}$

Correct B. $x = \frac{\pi}{4}$

C. $x = \frac{3\pi}{4}$

D. $x = \frac{5\pi}{4}$

Correct Answer: B

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Question 21 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 22 View Details

Solve the equation $x^2 + 4x + 4 = 0$ using the quadratic formula.

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 23 View Details

Find the value of $\log_{10} (1000)$.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24 View Details

Solve the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x < 4$

C. $x > 2$

D. $x < 2$

Correct Answer: A

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Question 25 View Details

Find the value of $$160^\circ$.

A. $\frac{1}{2}$\)

Correct B. $\frac{\sqrt{3}}{2}$

C. $\frac{1}${$\sqrt{2}$}\)

D. $\frac{\sqrt{2}}{2}$

Correct Answer: B

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