Q: A cylindrical water tank has a radius of 3 meters and a height of 5 meters. What is the volume of the tank? (Use $$\pi \approx 3.14)$$

$$V = \pi r^2$ h = 3.14 \times 3^2$ \times 5 = 3.14 \times 9 \times 5 = 141.3$$

Q: A store is having a 25% off sale. If an item originally costs $80, what is the sale price?

$$80 - (0.25 \times 80) = 80 - 20 = 60$$

Question 1

A car travels at a constant speed of 60 miles per hour. How far will it travel in 2.5 hours?

Accepted Answer

$$60 	imes 2.5 = 150$$

Question 2

Which of the following is the solution to the equation $$2x + 5 = 17$$?

Accepted Answer

$$x = 6$$

Question 3

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Accepted Answer

$$c = \sqrt{6^2$ + 8^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 4

If the area of a rectangle is 48 square units and its length is 8 units, what is its width?

Accepted Answer

$$w = \frac{48}{8} = 6$$

Question 5

Which of the following is the solution to the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 6

A cylindrical water tank has a radius of 3 meters and a height of 5 meters. What is the volume of the tank? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$V = \pi r^2$ h = 3.14 	imes 3^2$ 	imes 5 = 3.14 	imes 9 	imes 5 = 141.3$$

Question 7

If the probability of raining on any given day is $$0.2$$, what is the probability that it will NOT rain?

Accepted Answer

$$1 - 0.2 = 0.8$$

Question 8

A student scored 80, 85, 90, and 95 on four tests. What is the mean (average) score?

Accepted Answer

$$\frac{80 + 85 + 90 + 95}{4} = \frac{350}{4} = 87.5$$

Question 9

Which of the following is the solution to $$3(x - 2) = 12$$?

Accepted Answer

$$x = 6$$

Question 10

A company’s profit, $$P$$, is given by $$P = 5x - 200$$, where $$x is $$the number of items sold. What is the minimum number of items that must be sold for the company to make a profit?

Accepted Answer

$$x \u003e 40$$

Question 11

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(2)$$?

Accepted Answer

$$2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3$

Question 12

A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly selecting a blue ball?

Accepted Answer

$$\frac{3}{10}$$

Question 13

Which of the following is the solution to $$\frac{2x}{5} = 8$$?

Accepted Answer

$$x = 20$$

Question 14

A triangle has sides of length 7, 24, and 25. Is this a right triangle?

Accepted Answer

$$7^2$$ + $$24^2 = 49 + 576 = 625$$ = $$25^2$$; Yes

Question 15

If $$y = 3x + 2$$ and $$y = 8$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 16

A store is having a 25% off sale. If an item originally costs $80, what is the sale price?

Accepted Answer

$$80 - (0.25 	imes 80) = 80 - 20 = 60$$

Question 17

Which of the following is the solution to $$x^2 = 49$?

Accepted Answer

$$x = 7 or$$ $$x = -7$$

Question 18

A data set has the following values: 2, 4, 4, 6, 8. What is the median?

Accepted Answer

$$4$$

Question 19

If $$a = 3$$ and $$b = 4$$, what is the value of $$a^2$$ + $$b^2$$?

Accepted Answer

$$3^2$$ + $$4^2 = 9 + 16 = 25$

Question 20

A train travels 180 miles in 3 hours. What is its average speed?

Accepted Answer

$$\frac{180}{3} = 60$$ miles per hour

Mathematics Test Overview and Key Algebraic Formulas

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