Free Printable 8th Grade Math EOG Review (Part 3) ALGEBRA/FUNCTIONS FOCUS

1.

Solve the equation for x:

$-10\left(x+2\right)-5x=-9x+16$

a)

$x=-6$

b)

$x=6$

c)

$x=\frac{1}{6}$

d)

$x=\frac{3}{2}$

2.

Simplify $\frac{4^{12}\times4^8}{4^{13}}$

a)

$4^{33}$

b)

$4^{-33}$

c)

$4^7$

d)

$4^{-7}$

3.

Evaluate $\sqrt[]{100}$

a)

10

b)

50

c)

25

d)

98

4.

Evaluate $\sqrt[3]{64}$

a)

10

b)

8

c)

21.3

d)

4

5.

Find the value of x: $x^2=16$

a)

$\pm4$

b)

$\pm8$

c)

$4$

d)

$8$

6.

Find the value of x: $x^3=-8$

a)

$\pm4$

b)

$\pm2$

c)

-2

d)

-4

7.

What is $6.79\ \times10^5$ written in standard form?

a)

67,900,000

b)

679,000

c)

0.00000679

d)

0.0000679

8.

The width of a human hair is approximately 0.0002 𝑖𝑛. What is this width written in scientific notation?

a)

$2\ \times\ 10^3\ in$

b)

$2\ \times\ 10^{-3}\ in$

c)

$2\ \times\ 10^{4\ }in$

d)

$2\ \times\ 10^{-4\ }in$

9.

Evaluate: $\left(6.7\ \times\ 10^4\right)\times\left(9.1\ \times10^6\right)$

a)

$6.097\ \times\ 10^{11}$

b)

$6.097\ \times10^{10}$

c)

$6.097\ \times\ 10^9$

d)

$60.97\ \times\ 10^{10}$

10.

How many times larger is $\left(5.4\ \times10^6\right)$ than $\left(9\ \times\ 10^3\right)$ ?

a)

$0.6\times10^3$

b)

$6\ \times\ 10^3$

c)

$6\ \times\ 10^2$

d)

$6\ \times\ 10^4$

11.

Which graph shows a linear relationship?

a)

b)

c)

d)

12.

Choose the best description of the graph:

a)

Linear because each section of the graph is a different straight line segment.

b)

Nonlinear because each segment has a different slope.

c)

Both linear and nonlinear because it is made up of straight line segments but is not a complete straight line.

d)

Neither linear nor nonlinear because it is made up of straight line segments but is not a complete straight line.

13.

Which table shows a nonlinear relationship?

a)

b)

c)

d)

14.

Which equation represents the table?

a)

$y=18x+3$

b)

$y=3x+18$

c)

$y=-3x+18$

d)

$y=\frac{1}{3}x+18$

15.

Which equation represents the graph?

a)

$y=4x-2$

b)

$y=\frac{1}{2}x+4$

c)

$y=-2x+4$

d)

$y=-\frac{1}{2}x+4$

16.

Which equation represents a line passing through the points (2, 5) and (4, 10)?

a)

$y=\frac{5}{2}x$

b)

$y=\frac{2}{5}x$

c)

$y=5x+2$

d)

$y=2x+5$

17.

David’s allowance is $5 every week, plus $2 for each extra chore he does. Which equation shows his total allowance (A) every week, depending on the number of extra chores (c) he completes?

a)

𝐴=5𝑐+2

b)

𝐴=2𝑐+5

c)

𝐴=7𝑐

d)

𝐴=2+5

18.

What is the slope of the equation below?

$2y=10x-8$

a)

2

b)

-8

c)

10

d)

5

19.

Compare the equation in Item 1 with the graph in Item 2.

a)

Items 1 and 2 have the same rate of change, and the same y-intercepts.

b)

Items 1 and 2 have the same rate of change, but different y-intercepts.

c)

Items 1 and 2 have different rates of change, but the same y-intercepts.

d)

Items 1 and 2 have the different rates of change, and different y-intercepts.

20.

Consider the table of values and the graph below. Choose the statement below that best compares the two.

a)

The table has an increasing rate of change while the graph has a decreasing rate of change; the graph and the table have the same y-intercepts.

b)

Both the table and graph have increasing rates of change; The y-intercept of the graph is greater than that of the table.

c)

Both the table and graph have decreasing rates of change; The y-intercept of the table is greater than that of the graph.

d)

The table has a decreasing rate of change while the graph has an increasing rate of change; The y-intercept of the graph is greater than that of the table.

21.

Consider the table of values and the equation below. Choose the statement that best compares the two.

a)

The table and equation have the same slope and the same y-intercepts.

b)

The table and the equation have the same slope, but different y-intercepts.

c)

The table and the equation have different slopes and different y-intercepts.

d)

The table and the equation have different slopes, but the same y-intercept.

22.

Compare the equation and the graph. Choose the statement below that best describes the functions:

a)

The difference between the y-intercepts is 2.

b)

The difference between the y-intercepts is 1.

c)

The y-intercepts are equal.

d)

The rates of change are equal.

23.

The graph below show’s Maggie’s distance from home. Which scenario could be a possible explanation for the path shown by the graph?

a)

Maggie starts at home and walks down a hill to her friend’s house.

b)

Maggie starts at her friend’s house and walks straight home.

c)

Maggie starts at home and walks south-east.

d)

Maggie starts at her friend’s house, passes her home and goes to the store.

24.

Isaac is attempting to inflate a large beach ball. The graph below shows the amount of air in the beach ball over a period of time. Between which points does it show that Isaac had to take a break from inflating the beach ball?

a)

$\overline{AB},\ \overline{CD},\ \&\ \overline{EF}$

b)

$\overline{BC},\ \overline{DE},\ \&\ \overline{FG}$

c)

$\overline{FG}\ only$

d)

$\overline{EG}\ only$

25.

Between which points was he inflating the beach ball the fastest?

a)

$\overline{AB}$

b)

$\overline{BC}$

c)

$\overline{CD}$

d)

$\overline{EF}$

26.

Jordan is training to run a marathon. He can already run seven miles without stopping. Each week he is hoping to increase the amount he can run by at least ½ a mile. An equation of the situation is shown below. Interpret the y-intercept.

$y=7\ +\ 0.5x$

a)

The y-intercept represents the total number of miles Jordan wants to be able to run.

b)

The y-intercept represents the number of miles Jordan wants to add to his run each week.

c)

The y-intercept represents the number of miles Jordan can run at the beginning of his training.

d)

The y-intercept represents the total weeks he will have to train to reach his goal.

27.

A study was done to investigate the relationship between a between eating sugary snacks and a test that measures a student’s memory and attention. The correlating linear model is shown below, where x represents the number of sugary snacks a student ate, and y represents the student’s test score.

Interpret the rate of change (slope).

$y=-5x$

a)

Eating zero sugary snacks is associated with a loss of five points on the test.

b)

Each additional sugary snack eaten is associated with a loss of five points on the test.

c)

An additional five sugary snacks is associated with a loss of five points on the test.

d)

Not enough information is provided to interpret the slope.

28.

The graph below shows the cost of a particular taxi cab service in Chicago. Interpret the initial value and the rate of change for the graph.

a)

The taxi charges $2 to enter the cab and an additional $2 for every mile traveled.

b)

The taxi charges $4 to enter the cab and an additional $1 for every mile traveled.

c)

The taxi charges $4 to enter the cab and an additional $2 for every mile traveled.

d)

The taxi charges $0 to enter the cab and an additional $2 for every mile traveled.

29.

Luis worked at the town pet store and was in charge of draining and cleaning the fish tanks. He decided to record the amount of water in the tank and the time it took to drain the tank. Luis’ data is shown in the table below. Interpret the initial value and the rate of change.

a)

The tank started with 60 gallons and drained at a rate of 5 gallons per minute.

b)

The tank started with 60 gallons and drained in 10 minutes.

c)

The tank started with 50 gallons and drained at a rate of 10 gallons per minute.

d)

The tank started with 60 gallons and drained at a rate of 10 gallons per minute.

30.

Julie planted sunflowers in her garden. She was curious about how fast they grow so she kept a weekly log of their height. Once the sunflowers were full grown, Julie analyzed her data and calculated the equation below to represent the (H) height, in centimeters, of her sunflowers, depending how many (W) weeks had passed after planting. Interpret the y-intercept.

a)

The y-intercept in this situation means that each sunflower was 5 cm tall when planted.

b)

The y-intercept in this situation means that each sunflower was 24 cm tall when they were fully grown.

c)

The y-intercept in this situation means that each sunflower grew 24 cm each week.

d)

The y-intercept in this situation means that each sunflower grew 29 cm each week.

31.

James is remodeling his home and wants to put in all hard-wood flooring. The graph below shows the price of hard-wood flooring per square foot. What is the unit rate per square foot of hard-wood flooring?

a)

$500 per square foot

b)

$6.25 per square foot

c)

$100 per square foot

d)

$5 per square foot

32.

Mike and Anna are having a weight loss competition. Mike wants to practice kickboxing to burn calories while Anna prefers to run. Mike records his calories burned in the table below and Anna graphs her calories burned in the graph. Who burns more calories per minute?

a)

Mike and Anna burn the same amount of calories per min.

b)

Mike burns more calories per minute than Anna.

c)

Anna burns more calories per minute than Mike.

d)

There is not enough information to determine who burns more calories per minute.

33.

Payton and Elizabeth are working on their keyboarding skills. Payton uses the equation below to show how many words (W) she can type per minute (m). The graph below represents how many words per minute Elizabeth can type. Which statement below is most accurate?

a)

Payton types at a faster rate.

b)

Elizabeth types at a faster rate.

c)

Payton and Elizabeth type at the same rate.

d)

There is not enough information to compare the typing rates of Payton and Elizabeth.

34.

Kinnady is applying to work at two different restaurants to earn money while she attends college. Both restaurants offer an hourly rate of pay as well as any tips she earns during her shift. The first restaurant gave their pay scale information in a table, while the second restaurant gave their information in a graph. Both are shown below. Which restaurant will pay Kinnady more money per hour?

a)

Restaurant 1 will pay more per hour.

b)

Restaurant 2 will pay more per hour.

c)

Both restaurants will pay the same amount per hour.

d)

There is not enough information provided to compare pay rates.

35.

Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line AX. The slope between point C and point A is $\frac{2}{3}$ . What is the slope between point X and point C?

a)

$-\frac{2}{3}$

b)

$-\frac{3}{2}$

c)

$\frac{2}{3}$

d)

$\frac{3}{2}$

36.

Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line 𝐴𝑋 . Which proportional statement below is TRUE?

a)

$\frac{AB}{BC}=\frac{YC}{XY}$

b)

$\frac{AB}{BC}=\frac{XY}{XC}$

c)

$\frac{AB}{AC}=\frac{XY}{XC}$

d)

$\frac{AB}{BC}=\frac{YC}{XC}$

37.

Consider the graph below. Which statement is true about Line 1 and Line 2?

a)

Line 1: 𝑦=𝑚𝑥+𝑏

Line 2: 𝑦=𝑚𝑥

b)

Line 1: 𝑦=𝑚𝑥

Line 2: 𝑦=𝑚𝑥+𝑏

c)

Line 1: 𝑦=𝑚𝑥+𝑏

Line 2: 𝑦=𝑚𝑥−𝑏

d)

Line 1: 𝑦=𝑚𝑥

Line 2: 𝑦=𝑚𝑥−𝑏

38.

Given the equation $y=\frac{2}{3}x+4$ , which statement below is FALSE?

a)

The line of the equation will have a positive slope, going up from left to right.

b)

The y-intercept of the line will be (0, 4).

c)

The line of the equation will have a negative slope, going down from left to right.

d)

The graph will be a line with a constant slope which rises 2 units for every 3 units across.

39.

Given the equation 𝒚=−𝟒𝒙, which statement below is TRUE?

a)

The line of the equation will go down and through the origin.

b)

The line of the equation will go up and through the origin.

c)

The line of the equation will go down and through the point (0, -4)

d)

The line of the equation will go up and through the point (0, -4)

40.

In a barn there are 17 animals. Some are cows and some are ducks. There are 54 legs in all. Which system of equations below could be used to find how many cows and how many ducks are in the barn?

a)

c + d = 17

4c + 2d = 54

b)

c + d = 54

4c + 2d = 17

c)

c + d = 17

2c + 4d = 54

d)

c + d = 17

4c + 2d = 6cd