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POST UTME RHEMA UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $\frac{1}{2}x^2 + 5x - 3 = 0$ using the quadratic formula.

Correct A. $\frac{-5 + \sqrt{109}$}{2}\)

B. $\frac{-5 - \sqrt{109}$}{2}\)

C. $\frac{5 + \sqrt{109}$}{2}\)

D. $\frac{5 - \sqrt{109}$}{2}\)

Correct Answer: A

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Question 2 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ by factoring.

Correct A. $-\infty, -1$ \cup $3, \infty$

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

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

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

Correct Answer: A

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Question 3 View Details

Find the sum of the first 5 terms of the geometric series $2, 6, 18, \ldots$.

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 4 View Details

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

Correct A. \begin{pmatrix} 2 \ 1 \end{pmatrix}

B. \begin{pmatrix} 1 \ 2 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \end{pmatrix}

D. \begin{pmatrix} 4 \ 3 \end{pmatrix}

Correct Answer: A

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Question 5 View Details

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

Correct A. -5

B. -6

C. -7

D. -8

Correct Answer: A

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Question 6 View Details

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

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 7 View Details

Solve the inequality $\frac{x-1}{x+1} > 0$.

Correct A. x < -1 or $x > 1$

B. x < -1 or $x = 1$

C. x > -1 or $x < 1$

D. $x > 1$ or x < -1

Correct Answer: A

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Question 8 View Details

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

A. 16\pi

Correct B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: B

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Question 9 View Details

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

Correct A. 20

B. 30

C. 40

D. 50

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices $A(0,0)$, $B(3,0)$, and $C(1,2)$.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 11 View Details

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

Correct A. $\frac{4\pi}{3}$

B. $\frac{5\pi}{3}$

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

D. $\frac{2\pi}{3}$

Correct Answer: A

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Question 12 View Details

A cylindrical \tank with a radius of 4m and a height of 10m is filled with water. If the water level is at 6m, what is the volume of the water in the \tank?

A. ( 800pi ) m³

Correct B. ( 1600pi ) m³

C. ( 2400pi ) m³

D. ( 3200pi ) m³

Correct Answer: B

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Question 13 View Details

A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the die is rolled again. If the outcome is an odd number, the die is rolled three more times. What is the probability that the final outcome is a 6?

A. $\frac{1}{6}$

B. $\frac{1}{12}$

C. $\frac{1}{36}$

Correct D. $\frac{1}{24}$

Correct Answer: D

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Question 14 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using the quadratic formula.

Correct A. $x < -\frac{3}{2}$ or $x > \frac{1}{2}$

B. $x < -\frac{1}{2}$ or $x > \frac{3}{2}$

C. $x < -\frac{3}{2}$ or $x < \frac{1}{2}$

D. $x > -\frac{3}{2}$ or $x < \frac{1}{2}$

Correct Answer: A

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Question 15 View Details

A right-angled triangle has a hypotenuse of length 10cm and one leg of length 6cm. Find the length of the other leg.

Correct A. ( 8 ) cm

B. ( 6 ) cm

C. ( 4 ) cm

D. ( 2 ) cm

Correct Answer: A

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Question 16 View Details

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

Correct A. ( f'$(x) =$$\frac{-x}${ $x^2 + 1$ \)^{$3/2$}}\) )

B. ( f'$(x) =$$\frac{x}${ $x^2 + 1$ \)^{$3/2$}}\) )

C. ( f'$(x) =$$\frac{1}${ $x^2 + 1$ \)^{$3/2$}}\) )

D. ( f'$(x) =$$\frac{-1}${ $x^2 + 1$ \)^{$3/2$}}\) )

Correct Answer: A

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Question 17 View Details

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 18 View Details

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

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x > \frac{3}{2}$

D. $x > -1$ or $x < \frac{3}{2}$

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + ldots$.

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

B. $2 1 + 2^{10} \$ )

C. $2 1 - 2^{10} \$ )

D. $2 1 + 2^{10} \$ )

Correct Answer: A

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Question 20 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

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

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

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

D. $\frac{64}{3}$

Correct Answer: A

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Question 21 View Details

Find the equation of the tangent to the curve $y = \frac{1}{2}x^2 + 3x - 2\\(tangent to the curve (y =$ at the point where $x = 1$.

A. $y = x + 5$

Correct B. $y = 2x - 1$

C. $y = 3x - 2$

D. $y = x - 1$

Correct Answer: B

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Question 22 View Details

A circle has equation $(x^2 + y^2$ = 4\). Find the equation of the \tangent to the circle at the point where \$(x^2 + y^2 = 4). Find the equation of the \(x = 2$.

Correct A. $y = -x + 2$

B. $y = x + 2$

C. $y = -x - 2$

D. $y = x - 2$

Correct Answer: A

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Question 23 View Details

The mean of five numbers is 10. If one of the numbers is 5, find the sum of the other four numbers.

Correct A. 25

B. 30

C. 35

D. 40

Correct Answer: A

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Question 24 View Details

A rectangular prism has dimensions 5 cm, 6 cm, and 7 cm. Find its volume.

A. 210 $cm^3$

B. 240 $cm^3$

Correct C. 270 $cm^3$

D. 300 $cm^3$

Correct Answer: C

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Question 25 View Details

A histogram has a mean of 20 and a standard deviation of 5. Find the value of the highest bar.

A. 25

B. 30

C. 35

Correct D. 40

Correct Answer: D

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