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POST UTME RSU 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The slant height of the frustum is 8 cm.

Correct A. 48\pi $cm^3$

B. 64\pi $cm^3$

C. 80\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: A

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Question 2 View Details

Solve for x in the equation $2^x + 2^{x+1} = 3 \cdot 2^x$.

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 3 View Details

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

Correct B. 19

C. 20

D. 21

Correct Answer: B

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Question 4 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the line \$(y = x^2\(y = 4$, and the x-axis.

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 5 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

A. ₦1,250

Correct B. ₦1,500

C. ₦1,750

D. ₦2,000

Correct Answer: B

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Question 6 View Details

In the diagram below, the graph of $y = \frac{1}{2} $12x \$ ) is shown. What is the amplitude of the function?

A. 1

Correct B. 0.5

C. 2

D. 4

Correct Answer: B

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Question 7 View Details

Solve for ( x ) in the equation $\begin{vmatrix} 2 & 3 \ 1 & 4 \ \end{vmatrix} = 0$

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

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

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 9 View Details

In the diagram below, the circle with center ( C ) passes through the points ( A ) and ( B ). What is the equation of the circle?

Correct A. $x^2 + y^2 - 4x - 6y + 9 = 0$

B. $x^2 + y^2 - 4x - 6y + 11 = 0$

C. $x^2 + y^2 - 4x - 6y + 13 = 0$

D. $x^2 + y^2 - 4x - 6y + 15 = 0$

Correct Answer: A

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Question 10 View Details

Solve for ( x ) in the equation $\log_{10} x^2 \$$= 4$\)

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 11 View Details

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

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 12 View Details

A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.

A. $x - 4$² + $y - 5$$² = 9$

B. $x - 4$² + $y - 5$$² = 16$

Correct C. $x - 4$² + $y - 5$$² = 25$

D. $x - 4$² + $y - 5$$² = 36$

Correct Answer: C

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Question 13 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 14 View Details

The mean of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 45

B. 50

C. 55

D. 60

Correct Answer: A

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Question 15 View Details

Solve the quadratic equation x² + $5x + 6 = 0$.

Correct A. -2, -3

B. -3, -2

C. 2, 3

D. 3, 2

Correct Answer: A

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Question 16 View Details

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

Correct A. $\frac{x}${ 1 - $x^2$ \)^{$3/2$}}\)

B. $\frac{-x}${ 1 - $x^2$ \)^{$3/2$}}\)

C. $\frac{1}${ 1 - $x^2$ \)^{$3/2$}}\)

D. $\frac{2x}${ 1 - $x^2$ \)^{$3/2$}}\)

Correct Answer: A

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Question 17 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = \frac{3}{4}$ for ( x ) in the interval $[0, 2\\() for ( x ) in the interval \pi]$.

A. $\frac{\pi}{6}$\)

B. $\frac{\pi}{4}$\)

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

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

Correct Answer: C

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Question 18 View Details

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

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

B. $\frac{2}{5}$\)

Correct C. $\frac{3}{5}$\)

D. $\frac{4}{5}$\)

Correct Answer: C

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Question 19 View Details

Solve the polynomial equation $x^3 - 6x^2 + 11x - 6 = 0$ using the rational root theorem.

A. $x = 1$

Correct B. $x = 2$

C. $x = 3$

D. $x = 6$

Correct Answer: B

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Question 20 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 21 View Details

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

Correct A. $\frac{-x}{1 - x^2 \$^{$3/2$}} )

B. $\frac{x}{1 - x^2 \$^{$3/2$}} )

C. $\frac{1}{1 - x^2 \$^{$3/2$}} )

D. $\frac{-1}{1 - x^2 \$^{$3/2$}} )

Correct Answer: A

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Question 22 View Details

Solve the inequality $\frac{2x - 1}{x + 1} > 0$ using the sign table method.

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

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

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

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

Correct Answer: A

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Question 23 View Details

Find the equation of the \tangent line to the curve $y = x^2 - 2x + 1$ at the point ( (1, 0) ).

Correct A. $y = x - 1$

B. $y = x + 1$

C. $y = 2x - 1$

D. $y = 2x + 1$

Correct Answer: A

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Question 24 View Details

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

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

B. $x = 1, y = 3$

C. $x = 3, y = 1$

D. $x = 3, y = 3$

Correct Answer: A

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Question 25 View Details

Find the value of $\(12\theta \$ ) if 1\theta \\) = $\frac{3}{5}$\) ) and $$1\theta \$ = $\frac{4}{5}$\) ).

Correct A. $\frac{24}{25}$

B. $\frac{24}{25}$

C. $\frac{24}{25}$

D. $\frac{24}{25}$

Correct Answer: A

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