Algebra 2 – TERM 1 Review NAME ________________________________________________ Ch. 1, 2, & 3 Limestone Community High School

1

Section 1-1 Evaluating Expressions & Formulas

1. Evaluate the expression if

𝐚 = 𝟐, 𝐛 = −𝟏. 𝟐, 𝐚𝐧𝐝 𝐜 = −𝟖

𝒃𝒄 𝒂 − 𝒃 ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅

A. −18

B. −2

C. 3

D. 7

E. 9.6

2. Solve using the given formula.

𝑭 =𝟗

𝟓𝑪 + 𝟑𝟐

The temperature within our classroom is about 𝟔𝟖 ℉. What would be the temperature in degrees Celcius?

A. 20°

B. 25°

C. 30°

D. 35°

E. 40°

Section 1-3 Re-writing Equations & Formulas

3. Re-write the equation by solving for x.

𝒚 = 𝟒𝒙 − 𝟑

A. 𝑥 = 4𝑦 − 3

B. 𝑥 =𝑦 + 3

4 ̅̅ ̅̅ ̅̅ ̅̅

C. 𝑥 =𝑦

4 ̅̅ ̅ + 3

D. 𝑥 = −3𝑦 + 4

4. Re-write the equation by solving for r.

𝒅 = 𝒓𝒕

A. 𝑟 = 𝑑𝑡

B. 𝑟 =𝑡�̅�

C. 𝑟 =𝑑𝑡̅

D. 𝑟 = (2𝑑)𝑡

2

Section 1-3 Solving Equations

5. If

𝟒𝒙 + 𝟑 = −𝟕 What is

𝟖𝒙 + 𝟏𝟏 = ?

A. −14

B. −9

C. 2

D. 5

E. 19

6. Your local cable company charges $50 per month for basic cable service. Premium channels are available for a surcharge of $9 per channel. This relationship can be modeled by the following equation:

𝑩 = 𝟗𝒄 + 𝟓𝟎 Where B is the bill to you per month and c is the number of premium channels you subscribe to. What is the meaning of the value 50 in this equation?

A. 𝑇ℎ𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑝𝑒𝑟 𝑐ℎ𝑎𝑛𝑛𝑒𝑙

B. 𝑇ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑖𝑙𝑙

C. 𝑇ℎ𝑒 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ

D. 𝑇ℎ𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

Section 1-3 Re-writing Equations & Formulas

7. Solve the equation.

𝟒𝒙

𝟑 + 𝟏𝟖 = 𝟒𝟐

A. 𝑥 = 18

B. 𝑥 = 24

C. 𝑥 = 32

D. 𝑥 = 5

E. 𝑥 = 1

8. Your school band needs to buy new percussion equipment. The equipment will cost $2000. You have collected $800 in previous fundraisers. If you sell sandwiches at $4 each, how many sandwiches will you need to sell to raise the remaining funds?

A. 800

B. 560

C. 410

D. 300

E. 150

3

Section 2-1 Relations & Functions

9. State the Domain of the relation.

(−𝟐, −𝟑), (−𝟏, −𝟏), (𝟎, 𝟏), (𝟏, 𝟓)

A. 𝐷 = {−2, −1, 0, 1}

B. 𝐷 = {−3, −1, 1, 5}

C. 𝑅 = {−2, −1, 0, 1}

D. 𝑅 = {−3, −1, 1, 5}

10. State the Range of the relation.

A. 𝐷 = {0, 1, 2, 3, 4}

B. 𝐷 = {0, 1, 3, 5}

C. 𝑅 = {0, 1, 2, 3, 4}

D. 𝑅 = {0, 1, 3, 5}

Section 2-1 Relations & Functions

11. Tell if the relation is a function or not. Pick the best explanation. A. 𝑌𝑒𝑠, 𝑒𝑣𝑒𝑟𝑦 𝑖𝑛𝑝𝑢𝑡 ℎ𝑎𝑠 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 𝑜𝑛𝑒 𝑜𝑢𝑡𝑝𝑢𝑡.

B. 𝑌𝑒𝑠, 𝑖𝑡𝑠 𝑎 𝑡𝑎𝑏𝑙𝑒 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠.

C. 𝑁𝑜, 𝑡ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝐷𝑜𝑚𝑎𝑖𝑛.

D. 𝑁𝑜, 𝑡ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑅𝑎𝑛𝑔𝑒.

12. Tell if the relation is a function or not. Pick the best explanation.

A. 𝑌𝑒𝑠, 𝑒𝑣𝑒𝑟𝑦 𝑖𝑛𝑝𝑢𝑡 ℎ𝑎𝑠 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 𝑜𝑛𝑒 𝑜𝑢𝑡𝑝𝑢𝑡.

B. 𝑌𝑒𝑠, 𝑖𝑡𝑠 𝑎 𝑚𝑎𝑝𝑝𝑖𝑛𝑔 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠.

C. 𝑁𝑜, 𝑡ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝐷𝑜𝑚𝑎𝑖𝑛.

D. 𝑁𝑜, 𝑡ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝑟𝑒𝑝𝑒𝑎𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑅𝑎𝑛𝑔𝑒.

4

Section 2-2 Function Evaluation

13. Evaluate the function value at 𝒇(−𝟑)

𝒇(𝒙) = 𝟐𝒙𝟐 − 𝟑𝒙 + 𝟒

A. 𝑓(−3) = −23

B. 𝑓(−3) = −5

C. 𝑓(−3) = 5

D. 𝑓(−3) = 31

14. Evaluate the function value at 𝒈(𝟏. 𝟓)

𝒈(𝒙) = −𝟒𝒙 + 𝟑

A. 𝑔(1.5) = −6.5

B. 𝑔(1,5) = −5

C. 𝑔(1.5) = −3

D. 𝑔(1.5) = −1.5

Section 2-2 Linear Functions

15. Re-write in Slope-Intercept Form.

(𝒚 = 𝒎𝒙 + 𝒃)

−𝟑𝒙 + 𝟐𝒚 = 𝟏𝟎

A. 𝑦 = −2

3𝑥 − 5

B. 𝑥 = 2𝑦 − 4

C. 𝑦 = −3𝑥 + 10

D. 𝑦 =3

2𝑥 + 5

16. Re-write in Standard Form.

(𝑨𝒙 + 𝑩𝒚 = 𝑪)

𝒚 + 𝟓 = 𝟐𝒙 − 𝟑

A. 2𝑥 − 𝑦 = 8

B. −2𝑥 + 2𝑦 = 2

C. 𝑥 + 2𝑦 = 10

D. −3𝑥 + 2𝑦 = −8

5

Section 2-3 Slopes and Rates of Change

17. Find the slope of the line that passes through the pair of points. Express your answer as a fraction in simplest form.

(𝟒, 𝟕) 𝒂𝒏𝒅 (𝟔, 𝟑)

A. 𝑚 = −2

B. 𝑚 = −1

C. 𝑚 = 1

D. 𝑚 =12̅

18. Find the rate of change for the table.

A. 𝑚 = 1.0

B. 𝑚 = 1.5

C. 𝑚 = 2.0

D. 𝑚 = 3.2

𝒎 =𝒚𝟐 − 𝒚𝟏

𝒙𝟐 − 𝒙𝟏

19. Determine the rate of change of the graph.

A. 𝑚 = 1

B. 𝑚 = 2

C. 𝑚 = −2

D. 𝑚 =12̅

20. Last weekend you left for a camping trip with 110 miles on the odometer and 14.5 gallons of gas in the tank of your car. When you returned the odometer read 299 miles and you still had 7.5 gallons of gas left. What was the fuel efficiency of your car on this trip?

A. 14 𝑚𝑝𝑔

B. 27 𝑚𝑝𝑔

C. 35 𝑚𝑝𝑔

D. 42 𝑚𝑝𝑔

6

Section 2-4

Writing Equations of Lines 𝒚 = 𝒎𝒙 + 𝒃 21. Write the equation of the line that has a slope of 𝟐 and y-intercept at −𝟏 .

A. 𝑦 = −1𝑥 + 2

B. 𝑦 = −2𝑥 + 1

C. 𝑦 = 2𝑥 + 1

D. 𝑦 = 2𝑥 − 1

22. The membership to your local video store includes onetime cost of $25 and the DVD rental rate is $2 per DVD. Write an equation that models the total amount of money you will spend on DVD rentals this year.

A. 𝑦 = 5𝑥 + 20

B. 𝑦 = 25𝑥 + 2

C. 𝑦 = 3𝑥

D. 𝑦 = 2𝑥 + 25

Section 2-4

Writing Equations of Lines 𝑨𝒙 + 𝑩𝒚 = 𝑪 23. Find the x and y-intercepts from the equation.

𝟐𝒙 − 𝟑𝒚 = 𝟏𝟐

A. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (2, 0)𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (0, 3)

B. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (2, 0)

𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (0, 12)

C. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (6, 0)

𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (0, −4)

D. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (−4, 0)𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = (0, 6)

24. You sold tickets to the school play. Advanced tickets were $4. Tickets bought at the door were $5. Total ticket sales were $400. Let x represent the number of advanced tickets sold and y represent the number of tickets sold at the door.

A. 𝑥 + 𝑦 = 4

B. 𝑥 + 𝑦 = 5

C. 4𝑥 + 5𝑦 = 400

D. 𝑥 + 𝑦 = 400

7

Section 2-4 Writing Linear Equations

25. Write the equation of the line that has a

slope of 𝟏�̅�

and passes through the point (𝟒, 𝟓) .

A. 𝑦 =12̅

𝑥 + 5

B. 𝑦 =12̅

𝑥 + 3

C. 𝑦 = 2𝑥 + 5

D. 𝑦 = −2𝑥 + 13

26. Write an equation of the line that passes through the points.

(𝟑, 𝟕), (−𝟏, 𝟑)

A. 𝑦 = 𝑥 + 3

B. 𝑦 = 𝑥 + 4

C. 𝑦 = −1𝑥 + 4

D. 𝑦 = 7𝑥 − 11

27. Tell whether the lines are parallel, perpendicular, or neither. Compare the slopes.

Line 1: 𝒚 =𝟏�̅�

𝒙 − 𝟓

Line 2: 𝒚 = −𝟐𝒙 + 𝟑

A. 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙

B. 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟

C. 𝑛𝑒𝑖𝑡ℎ𝑒𝑟

28. Write the equation of the line that is parallel to the line 𝒚 = 𝟑𝒙 − 𝟕 and passes through the point (−𝟓, −𝟖).

A. 𝑦 = −13̅

𝑥 − 8

B. 𝑦 = −13̅

𝑥 − 5

C. 𝑦 = 3𝑥 − 8

D. 𝑦 = 3𝑥 + 7

8

Section 3-2 Solving Systems of Equations

29. Solve the system using Substitution.

𝒚 = 𝒙 + 𝟏𝒙 + 𝒚 = 𝟕

A. (3, 4)

B. (3, 1)

C. (−1, 3)

D. (−2, 1)

E. 𝑁𝑜 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛

30. Solve the system using Substitution.

𝒚 = 𝟐𝒙 − 𝟖𝒚 = 𝒙 − 𝟏𝟎

A. (3, −2)

B. (−2, 3)

C. (−2, −12)

D. (3, −7)

E. 𝑀𝑎𝑛𝑦 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

Section 3-2 Solving Systems of Equations

31. Solve the system using Elimination.

𝟐𝒙 + 𝟒𝒚 = 𝟐−𝟐𝒙 + 𝟓𝒚 = −𝟏𝟏

A. (1, 0)

B. (3, −1)

C. (−1, −1)

D. (4, 0)

E. 𝑀𝑎𝑛𝑦 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

32. Solve the system using Elimination.

−𝟓𝒙 + 𝟑𝒚 = 𝟏𝟖𝟑𝒙 − 𝟐𝒚 = −𝟏𝟏

A. (−3, 0)

B. (−3, 1)

C. (−3, 2)

D. (−3, 3)

E. 𝑁𝑜 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛

9

Section 1-5 Solving Inequalities

33. Write the inequality.

A. 𝑥 ≤ 25

B. 𝑥 ≤ 20

C. 𝑥 ≥ 25

D. 𝑥 ≥ 0

34. Graph the inequality.

𝒙 ≥ −𝟐

A.

B.

C.

D.

Section 1-5 Solving Inequalities

35. Solve the inequality.

−𝟑𝒙 ≤ 𝟓𝟒

A. 𝑥 ≤ 18

B. 𝑥 ≤ −18

C. 𝑥 ≥ 18

D. 𝑥 ≥ −18

36. Solve the inequality.

𝟑(𝟑𝒛 − 𝟕) < 𝟓𝒛 + 𝟏𝟏

A. 𝑧 < 8

B. 𝑧 < 7

C. 𝑧 > 6

D. 𝑧 > 5

10

Graphing

37. Graph Equation.

𝒚 = − 𝟏�̅�

𝒙 + 𝟐

38. Graph the Inequality.

𝒚 ≥ 𝟐𝒙 − 𝟓

NAME _________________________________

39. Graph the System of Equations.

𝒙 = −𝟓𝒚 = 𝟐𝒙 + 𝟔

40. Graph the System of Inequalities.

𝒙 < 𝟒

𝒚 < −𝟏

𝟐𝒙 + 𝟏