Algebra 2 Ch. 1 Review (Post-test)
Name:
Date:
Block:
Vocabulary:
Read each vocabulary word and make flashcards! (Use index cards or write
them down on a sheet of paper folded in half long-ways and write the word on
one side, definition AND an example on the other side.)
1. “Evaluate” means to plug in some numbers and find an answer at the end
2. “Simplify” means to do distributive property and combine like terms until
you get the most simplified answer (still has the variables in it) – you are
NOT solving
3. “Solve” implies you are finding a final answer like x = ____.
4. “Equation” has an equal sign and you have to SOLVE it. You do NOT need
to graph.
5. “Expression” does NOT have an equal sign and you only have to SIMPLIFY.
6. “Inequality” has a < > ≤ ≥ sign. You have to graph it on a number line and
write in interval and set builder notation when you finish.
7. “Compound inequality” has TWO inequality symbols and you have to
solve both separately.
8. “Absolute value” is the distance away from zero on a number line and
you always split up into 2 equations to solve.
Practice:
Try each practice problem broken down in sections. Read the “review notes”
before each topic to make sure you understand the problem. Show ALL work.
Order of Operations
 Parentheses  Exponents  Multiplication and Division left to right 
Addition and Subtraction left to right
 Work inner most parentheses first and work your way out
1.
20  15   5  2  
3.
32  2  4  3 5  3
2
2.
4.
14   2  5   3
 2 
3
7
6   3 
Algebra 2 Ch. 1 Review (Post-test)
Solving LITERAL equations
 Get the variable by itself.
 Get rid of “unattached” parts first. Always do the OPPOSITE operation.
 If you need to do “backwards distributive property” (also called
factoring), do it!
Solve for the indicated variable in the parenthesis.
5)
4x + xy = 18
7)
y = 5x - 6
9)
x+y=5
3
(x)
6)
A = 2(L + W)
(x)
8)
2x - 3y = 8
(x)
10)
V = pr2h
(W)
(y)
(h)
Solving REGULAR EQUATIONS
 Distribute and combine if needed
 Add or subtract first, then multiply or divide
 Get variables to one side, numbers on the other side
 Get rid of DENOMINATORS by multiplying
 Get rid of fractions by multiplying by the COMMON DENOMINATOR
 If you have the same thing on both sides – all real solutions.
 If you solve and get each side to be totally different like 5 = -2, then no
real solutions.
11.
3
5
125
x   5x 
4
6
3
12.
x 5
7 8
 x 
2 6
9 9
13.
2 – (x + 12) = 3x + 9
14.
3 – (4 – 4x) = 4 (x – 1)
Algebra 2 Ch. 1 Review (Post-test)
Solving ABSOLUTE VALUE equations
 Get the absolute value by itself first
 Split into TWO equations!!!! (one positive and one negative)
 IF it looks something like |3x + 1| = 5x where you have that 5x in there,
plug your solutions back into the 5x to see if it is extraneous.
 IF your problem looks something like |2x – 1| = -6 where the absolute
value portion equals a negative number, there is NO SOLUTION!
15.
|2x – 7|– 5 = 4
16.
|-2x – 5| = 21
17.
|3x – 2| = -10
18.
2|3x – 2 | = 20
Solving REGULAR INEQUALITIES and COMPOUND INEQUALITIES
 If you multiply or divide by a negative number, SWITCH the inequality.
 For regular inequalities with one symbol, solve like normal.
 For compound inequalities, split into 2 and solve separately.
 Graph on a number line!
 If you solve and cancel out all the x’s and get something like 1 < 5 which is
always true, ALL REAL NUMBERS!
 If you solve and cancel out all the x’s and get something like 6 < -1 which
is always false, NO SOLUTION!
 “AND” problems – shade in the middle
 “OR” problems – (hint: you will see the word “or”) shade away from
 Interval notation
o “AND”  what is the left most number? What is the right most
number?
 Ex. (-1, 5]
( ) for < >
[ ] for ≤ ≥
o “OR”  go from - to a number and then from a number to 
 Ex. (-, 3)  [5, )
 Set builder notation {x | _____________}
19.
4 + x – 3x – 2 < 9
21.
-9 < 4 + x or 2 + 3x < 32
Solving ABSOLUTE VALUE inequalities
20.
4<6–x<9
22.
-8 < 3x + 4 ≤ 10
Algebra 2 Ch. 1 Review (Post-test)




Split into TWO inequalities!
Keep one the same.
For the second one, SWITCH the inequality and make NEGATIVE.
Solve both inequalities separately.
23.
|7 – 8x| < 3
24.
|3x + 2| – 1 ≥ 10
25.
|3x + 4| ≤ 10
26.
|8x + 5| + 3 > 4
Word Problems
 Break it down one sentence at a time. What do you know?
 What is your variable and what does it stand for?
27. In order to show your team spirit at John Champe, you decide to purchase
a new football jersey with your name across the back. The jersey costs $20 plus
$0.50 per letter. Write an EQUATION to represent the cost of a jersey. Then, find
out how much it would cost to have your name. (Hint: How many letters in your
name?)
28. John loves to play video games. There are two game rental stores close to
his house. At Store A, he can go in and rent any video game for $3. At Store B,
to rent videos you have to pay $15 for a yearly membership fee, and then each
rental is $0.50. Write an EQUATION to represent the cost of renting video games
at each store (so you need two!).
29. At the school store, pencils cost $0.50 each and notebooks cost $1.50 each.
Write an EXPRESSION (hint: no equal sign) to represent how much you would
spend if you bought p pencils and n notebooks.
30. A soccer ball’s circumference must be within 0.5 inches of 27.5 inches. Write
an absolute value inequality to represent all possible circumferences of the
soccer ball.