Algebra 2

Summer Review Packet

Welcome to Algebra 2! Attached you will find the learning targets your teacher thinks you should

know BEFORE you come to class in the fall and problems to help you practice these targets. The

answers and worked out solutions to these questions are included to help you review the material.

This material must be mastered and you will be assessed in the first week of school.

Use the following sites and QR codes in this review to help with any of the learning targets you

struggle with.

http://www.wolframalpha.com/

http://www.khanacademy.com/

We are looking forward to seeing you in the fall!

Algebra 2 Teachers

Niles West and Niles North High School

Summer Review Learning Targets

Target 1. Evaluate and re-write expressions

A. Evaluate using order of operations B. Simplify algebraic expression (re-write)

C. Re-write by factoring D. Re-write by distributing

Target 2. Solve equations and inequalities

A. Solve linear equations B. Solve and graph linear inequalities

C. Solve simple quadratic equations

Target 3. Write equations

A. Write equations for lines B. Find slope

Target 4. Graph equations and inequalities

A. Graph linear equations B. Graph linear inequalities

C. Graph absolute value equations

Target 5. Solve systems of linear equations

Target 1 - Evaluate and re-write expressions

A. Evaluate and re-write expressions using the order of operations.

(#1) Evaluate each expression.

a. ( ) b.

B. Simplify algebraic expression (re-write)

(#2) a. b. c.

d. e. f.

5 15 6 3 20 100

4 8 2x x 3(2 6)x 2( 4)x

5 2( 6)x x 6 3(4 1)x 2(3 4) 5( 7)x x

C. Re-write expressions by factoring.

(#3) Factor the following problems completely. Write “not factorable” if it is not possible to factor.

a. b. c.

d. e. f.

D. Re-write expressions by distributing.

(#4) Find the product.

a. (x + 3)(x - 2) b. (x + 3)(x - 3) c. (x + 3)(x + 3)

d. e. f.

2 6 9x x 2 25x 2 16x

2 12x x 22 18x 2 10 25x x

2( 3)x 2(2 3)x 2

2 3x

(#5) MULTIPLE CHOICE: Which equation is equivalent to

a. b. c. d.

Target 2 - Solve equations and inequalities

A. Solve linear equations.

(#6) Solve each equation.

a. 3x – 5 = 2 (4 – x) – 1 b.

c. d. 7x – 3x – 8 = 24

e. 18 – 3 (x – 2) = 21 f. 7x + 19 = –2x + 55

(#7) MULTIPLE CHOICE: If you multiply both sides of the equation by 3, the result would be:

a. b. c. d. none of these

2( 5) 3(2 4)y x x

4 22y x 4 2y x 4 1y x 4 6y x

49 2

5x

36 8

x

27 2 4

3x x

21 6 12x x 2 21 6 12x x

221 2 12

3x x

(#8) MULTIPLE CHOICE: The number of adult tickets sold at a school talent show, a, is 5 less than 3

times the number c of children’s tickets sold. Which equation represents the number of adult tickets

sold?

a. a = 3c + 5 b. a = 5 – 3c c. a = 5c + 3 d. a = 3c – 5

(#9) MULTIPLE CHOICE: Which function is equivalent to ?

a. b. c. d.

(#10) Solve for the indicated variable.

a. 3x + y = 4; Solve for x b. M = KV + KR; Solve for K

B. Solve and graph linear inequalities.

(#11) Solve and graph the linear inequality.

a. b.

A BC D

A BC D BC D A

DC

A B

D AB

C

8 5 v 3(5 4) 12 11w w

(#12) MULTIPLE CHOICE: Solve the inequality

a. b. c. d.

(#13) Write an inequality for each graph.

a. ______________________

b. _______________________

C. Solve SIMPLE quadratic equations.

(#14) Solve the following equations. Answers should be integers or in simplified radical form (no

decimals).

a. b. c. d. (x + 3)(x – 8)= 0

2 5 35x

15x 15x 20x 20x

2 36x 2 18x 2

3 16x

Target 3 - Write equations

A. Write linear equations and Target 3B - Find slope

(#15) Find a slope:

a.

m = _________

b.

m = ______________

c.

m = ______________

(#16)

(#17) MULTIPLE CHOICE:

(#18) MULTIPLE CHOICE:

3 4y x 3 2( 2)y x

(#19) Write the equation of the line if slope is 1/3 and y-intercept is -4.

(#20) Write the equation of the line if the line passes through points (2,-1) and (-1,-2)

(#21) MULTIPLE CHOICE:

(#22) MULTIPLE CHOICE: If a line contains the point (4,-15) and a slope of -3/4 which of the

following point(s) would also fall on the line?

a) (0,0) b) (-4,-9) c) (20,-30) d (-24,3) e) none of these

Target 4 - Graph equations and inequalities

A. Graph linear equations

(#23) Make a complete graph of each of the equations.

a. y = 2x – 2

b.

c. 2x – 5y = 10

d. y – 5 = -3(x + 1)

e.

B. Graph linear inequalities

(#24) Graph the following INEQUALITIES: .

A.

B. C. 3x - 2y < 4

C. Graph absolute value equations

(#25)

A. Sketch the graph of y = + 4 (If you need, you can use the table of values)

x

B. Graph the following absolute value functions:

Target 5 - Solve systems of linear equations

(#26) Solve each system using the indicated method.

a. Graphing

b. Elimination

c. Substitution

(#27) A company offers two plans for high-speed Internet service. With plan A, you pay $200 for the

modem and $25 per month for service. With plan B, you pay $100 for the modem and $35 per

month for service. After how many months are the total costs of the plans the same?