Name Date Hour

ALGEBRA – 1ST SEMESTER EXAM REVIEW 2016 Unit 0 - Radicals 1. Express the radical in simplest form 2. Perform the indicated operation. Express your Answer in simplest form.

a. 48 b. 545 a. 4035 b. 453272

3. Add or subtract the given expression 4. Perform the indicated operation. Express your answer in simplest form.

a. 654 b. 63283 a. )723(2 b. (2 + 3)2

Unit 1 - Linear Equations Solve for x, show all work!

1. -2(4x + 5) = 54 2. x + 1 = -2x – 8 3. 8 – (3x + 4) = -4x + 5

4. 3(2x + 4) = 24 - 2(6x - 3) 5. 361

432

xx 6. 64

37

x

7. Solve the following equation. Justify each step using the properties. Check your answer! Equation Reasons / Justify Check your solution here!

5 + 2(4x - 3) = 15 ___________________

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Unit 2 – Understanding Functions 1. You go to a candy shop and buy a candy jar for $6 and some 5 jawbreakers. The total cost was $21. Write an

equation to find the price of each jawbreaker. Let x = number of jawbreakers.

2. Use the diagram to determine the pattern.

a. Make a table to organize the

Design Number and the Number of Squares

b. Write an equation that represents the pattern. Let D = design number and N = number of squares.

c. Find the number of squares that will be in Design 8.

3. Write an equation to model the relationship represented in each table.

4. For the following situation, draw a graph that shows the relationship between the time (horizontal axis) and the

heart rate (vertical axis). Label the axes and make an appropriate scale.

a. You decide to do a running workout. You start your workout by jogging slowly. Then, you pick up the race and run hard. Finally, you do a cool down jog.

b. Does this situation represent a function? Explain your answer. In your explanation, do not use the vertical line test as your reason. Instead, use the terms heart rate and time in your explanation.

5. The graph below describes what happens when three athletes—

Jaime, Brad, and Chris—enter a 600-meter foot race. (a) Who is running the fastest during the first 50 seconds? (b) What is Chris doing from 50 seconds - 75 seconds? (c) Does Brad ever catch Chris? If so, at what time? Circle this point on the graph. (d) Who wins the race? And how long does it take that person to finish the race? (e) How fast did Brad run? (f) Describe each person’s race - use terms like sprinted, slowed down, constant speed, stopped, etc. Jaime’s race: Brad’s race: Chris’ race:

6. Do the following problems represent a function? Why or why not?

a. {(-1, 2), (3,3), (2, 3), (5, 3)}

b. c. d.

7. Given f(x) = 3x – 2, find f(-3)

8. Find the range of the function f(x) = x - 4 with the given domain { -3, 1, 0}

Unit 3 - Linear Functions 1. Find the slope of the line that passes through the

points (3,5) and (6,9)

2. Find the rate of change using the given table.

3. Find the slope of the line.

4. Graph the line y = 3.

x y

3 5

4 8

5 11

7 17

8 20

5. Identify the x-intercept and the y-intercept using the given graph.

6. Graph the equation y = 3x + 4

7. Write an equation that gives the total sales(y) from a basketball concession stand if they sell x bags of popcorn at

$3.50 per bag.

8. Do the following tables represent a linear function? a) b)

x y

4 4

5 6 6 10

7 18 9. Hannah's electricity company charges her $0.11 per kWh (kilowatt-hour) of electricity, plus a basic connection

charge of $15.00 per month. Write a linear function that models her monthly electricity bill as a function of electricity usage.

a) Write a linear function that models her monthly electricity bill as a function of electricity usage. b) What is the rate of change? c) What is the y-intercept? d) What will be her bill if she uses 350 kWh? e) Graph the situation.

x y

3 4 4 8

6 16 7 20

Unit 4 – Systems of Equations 1. 𝑦 = – 3𝑥 – 3 2. 𝑦 = –2 3. 5x – 3y = 6 𝑦 = 𝑥 + 5 𝑥 = 5 2x + 6y = 24 Use substitution to solve each system. Show your work. 4. 𝑦 = 3𝑥 5. 𝑦 = 4𝑥 – 3 6. 3x + 2y = 10 𝑦 = – 𝑥 + 4 -5x + y = -1 x – 2y = 6 Use elimination to solve each system. Show your work. 7. 𝑥 – 3𝑦 = 9 8. 4𝑥 – 5𝑦 = 11 9. 5x + 4y = 11 – 𝑥 + 2𝑦 = 1 6𝑥 + 7𝑦 = 31 10x + y = -6 10. The concession stand sells pizza by the slice and soda during the NCWHS basketball games. Trish bought 3 slices of

pizza and 4 sodas and paid $8.50. joey bought 2 slices of pizza and 2 sodas and paid $5. Use a system of equations to find the price of a slice of pizza and a soda.

.Unit 5 – Linear and Systems of Linear Inequalities

1. Which point is a solution of y –2x + 5? a. (5, 2) b. (–1, 8) c. (4, 0) d. (3, –3)

2. Write an inequality that represents the solutions given on the number lines below. a. b.

3. Use the inequality to graph the solution. a. x – 6 < 15 + 8x b. -5x + 6 > -7(5x – 6) – 6x c. 6 – 4(6x +7) > 122

4. Write an inequality for the graphs below.

Graph the solution for the linear and systems of inequalities

5. 𝑦 – 3𝑥 + 2 6. y < 5 7. y > -3x + 2 x + y > 4 2x – y > -2

a. b.

8. Sarah has a bracelet making business. She can make 5 bracelets in 1 hour. Sarah needs to make at least 100 bracelets for the craft fair this weekend. Write and solve an inequality to determine the minimum number of hours Sarah needs to work in order to prepare for the craft fair. Graph the solution on a number line. 9. You need A’s and B’s to get through your Algebra I class. They each come for a price. A’s cost $10 each, and B’s cost $7 each. How many A’s and B’s could you obtain if you only have $70? Identify the following and graph: Variables: x = y = Inequality: Constraints: Combinations: (Using your graph, list three possible solutions for this scenario.)

10. You and your family attend your brother’s championship basketball game. Between quarters you decide to go to the snack stand. You go to the snack stand with $18 and find that sodas are $3 and that popcorn is $2. You want to buy more than four items. a) Write a system of inequalities to represent the situation, include any related constraints. b) Graph the inequalities c) List three possible combinations that will satisfy both requirements. d) Would you be able to buy 4 sodas and 2 popcorns?