Question 1

Which of the following numbers is both rational and an integer?

Accepted Answer

$$-5$$

Question 2

Evaluate the following expression using the order of operations: $$8 + 2 	imes (5^2$ - 3^2$)$$

Accepted Answer

Question 3

Convert $$4.56 	imes 10^3$ to decimal notation.

Accepted Answer

$$4560$$

Question 4

Which of the following is the correct scientific notation for $$0.00082$$?

Accepted Answer

$$8.2 	imes 10$$^{-4}$$

Question 5

A medication’s price increased from $$\40$ to $$\$$50. $$What is the percent increase?

Accepted Answer

$$20\%$$

Question 6

A scientist records the following temperatures (in $$^\circC$$): $$12, 15, 18, 21, 24. $$What is the mean temperature?

Accepted Answer

$$18$$

Question 7

Find the domain of the relation $$R = \{(2, 5), (3, 7), (4, 9), (5, 11)\}.$$

Accepted Answer

$$\{2, 3, 4, 5\}$$

Question 8

What is the distance between the points $$A(1, 2)$$ and $$B(4, 6)$$?

Accepted Answer

$$5$$

Question 9

Find the midpoint of the segment joining $$(2, 3)$$ and $$(8, 11).$$

Accepted Answer

$$(5, 7)$$

Question 10

A circular garden has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What are the center and radius of the garden?

Accepted Answer

Center: $$(3, -4)$$, Radius: $$5$$

Question 11

Which of the following is the standard equation of a circle with center $$(2, -1)$$ and radius $$4$$?

Accepted Answer

$$(x - 2)^2$ + (y + 1)^2$ = 16$$

Question 12

A soda can has a volume of $$355 mL. If $$the can is a cylinder with a height of $$12 cm$$, what is the approximate radius in cm? (Use $$V = \pi r^2$ h$$ and $$\pi \approx 3.14)$$

Accepted Answer

$$3.07$$

Question 13

If $$a = 2.5 	imes 10^3$ and b = 4$$ 	imes $$10^2$$, what is $$a 	imes b in $$scientific notation?

Accepted Answer

$$1.0 	imes 10^5$

Question 14

A population decreased from $$12,000 to$$ $$9,000$$ over a year. What is the percent decrease?

Accepted Answer

$$25\%$$

Question 15

Which of the following sets contains only irrational numbers?

Accepted Answer

$$\{\sqrt{2}, \pi, e\}$$

Question 16

Given the relation $$S = \{(x, y) | y = 2x + 1, x \in \mathbb{R}\}$$, what is the range of $$S$$?

Accepted Answer

$$\mathbb{R}$$

Question 17

A biologist measures the heights (in cm) of 5 plants: $$10, 12, 15, 18, 25. $$What is the median height?

Accepted Answer

$$15$$

Question 18

If $$f(x) = x^2$ - 4x + 7$$, what is the value of $$f(3)$$?

Accepted Answer

$$4$$

Question 19

A circle has the equation $$(x + 1)^2$ + (y - 2)^2$ = 25. $$Which point lies on the circle?

Accepted Answer

$$(4, 2)$$

Question 20

A car travels from point $$A(2, 3) to $$point $$B(10, 15). $$What is the distance covered?

Accepted Answer

$$14$$

College Algebra Study Guide: Numbers, Data, and Graphing

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