Name:
Period:
Date:
Unit 1 Test Review
Be able to justify each step in a two-step equation. (HS.A-REI.A.1)
_____ 1.
𝑥
Solve the equation − 3 = 4. Write a reason for each numbered
2
step.
𝑥
2
−3 = 4
+3 + 3
𝑥
2∙ = 2∙ 7
2
Given
[1]
[2]
𝑥 = 14
a. [1] Addition Property of Equality
[2] Division Property of Equality
b. [1] Subtraction Property of Equality
[2] Division Property of Equality
c. [1] Addition Property of Equality
[2] Multiplication Property of Equality
d. [1] Subtraction Property of Equality
[2] Multiplication Property of Equality
_____ 2.
Solve the equation 3𝑥 + 2 = 11. Write a reason for each
numbered step.
3𝑥 + 2 = 11
−2 − 2
3𝑥
9
=3
3
Given
[1]
[2]
a. [1] Addition Property of Equality
[2] Division Property of Equality
b. [1] Subtraction Property of Equality
[2] Division Property of Equality
c. [1] Addition Property of Equality
[2] Multiplication Property of Equality
d. [1] Subtraction Property of Equality
[2] Multiplication Property of Equality
3. A classmate has just solved an equation without checking the
answer. Unfortunately, the solution has several mistakes.
Without redoing the entire problem, go through each step and
explain how the step was obtained. If the step is incorrect,
explain the error and the procedure that should have been
followed.
1
4 + (6𝑥 + 18) = −3𝑥 + 12
3
4 + 2𝑥 + 6 = −3𝑥 + 12
6𝑥 + 6 = −3𝑥 + 12
3𝑥 + 6 = 12
3𝑥 = 6
𝑥=
1
2
Interpret algebraic expressions in terms of a situation. (HS.A-SSE.A.1)
_____10.
_____11.
_____12.
How many terms are in the algebraic expression
3𝑥 − 2𝑦 + 4𝑥𝑧 − 8?
a) 4
b) 7
c) 8
d) 9
What are the factors of the term 4𝑥 2 𝑦𝑧 3 ?
a) 4, x, x, y, z
b) 4, x, y, z
c) 4, x, x, y, y, y, z, z, z
d) 4, x, x, y, z, z, z
What is the coefficient of y in the expression 3𝑥 − 2𝑦 + 4𝑥𝑧 − 8?
a) -8
b) -2
c) 3
d) 4
2
_____13.
_____14.
_____15.
_____16.
Write an algebraic expression that represents five less than four
times a number.
a) 4(𝑥 − 5)
b) 5 − 4𝑥
c) 4𝑥 − 5
d) 5𝑥 − 4
Write an algebraic expression that represents the three times
the sum of a number and 2.
a) 3(𝑥 + 2)
b) 3𝑥 + 2
c) 2(𝑥 + 3)
d) 2𝑥 + 3
Laurie rents 14 movies a month from her local video store for
m months in a row. Write an expression to show how many
movies Laurie watched in all, then find the number of movies
Laurie watched for 12 months.
a) 14 − 𝑚; 2 movies
b) 14 + 𝑚; 26 movies
c) 14𝑚; 168 movies
d)
14
𝑚
; 168 movies
At a movie theatre tickets for a matinee show are $7.25 each.
At the concession stand, drinks are $3.50 each, popcorn costs
$5.50 each and candy costs $2.25 per box. If Sammie and Tim
go to a matinee and purchases d drinks, p popcorns, and c
boxes of candy, the amount of money m they spend can be
represented by 𝑚 = 3.5𝑑 + 5.5𝑝 + 2.25𝑐 + 14.5. Which of the
following are correct interpretations for parts of this equation?
(there may be more than one answer)
a)
b)
c)
d)
e)
f)
g)
h)
3.5d
3.5d
3.5d
3.5d
5.5d
5.5d
5.5d
5.5d
represents the cost
represents the cost
represents the cost
represents the cost
represents the cost
represents the cost
represents the cost
represents the cost
of
of
of
of
of
of
of
of
the movie tickets
the popcorn
the drinks
the candy
the movie tickets
the popcorn
the drinks
the candy
3
At a supermarket, the apples cost $1.29 per pound, oranges cost $0.79 per
pound and grapes cost $2.99 per pound. Let a be the pounds of apples
purchased, r represent the pounds of oranges purchased and g be the
pounds of grapes purchased. Match the algebraic expressions with their
appropriate interpretations in this context.
a) The cost of four people
purchasing a pounds of
apples.
b) The cost of purchases g
pounds of grapes and r
pounds of oranges with a
25% off coupon.
c) The cost per person if four
people split a pounds of
apples, g pounds of grapes
and r pounds of oranges.
_____17.
2.99g + 0.79r
_____18.
0.75(2.99g + 0.79r)
_____19.
1.29a
d) The cost of purchasing a
pounds of apples, g pounds
of grapes and r pounds of
oranges.
e) The cost of purchasing g
pounds of grapes and r
pounds of oranges.
f) The cost of purchasing a
pounds of apples.
g) The cost of purchasing a
pounds of apples and r
pounds of oranges.
1.29a + 2.99g + 0.79r
4
Create and solve equations and inequalities in one variable. (HS.A-REI.B.3)
_____20.
(A) Write an equation or inequality to represent each situation. (B) Solve it.
21. Keith spent half of his allowance
going to the movies. He washed the
family car and earned 6 dollars. What
is his weekly allowance if he ended with
16 dollars?
22. Oceanside Bike Rental Shop
charges 16 dollars plus 8 dollars an
hour for renting a bike. Time paid 88
dollars to rent a bike. How many hours
did he pay to have the bike checked
out?
4
23. Mike bought 8 new baseball trading
cards to add to his collection. The next
day his dog ate half of his collection.
There are now only 29 cards left. How
many cards did Mike start with?
24. You want to rent a limousine for a
trip to the city. The limo costs $700 for
the night and $0.15 per mile. You have
$750 to spend. Write an inequality that
represen ts this scenario. How many
miles can the limo travel on your
budget?
25. Tom bought 8 candy bars and a soft
drink. The soft drink cost 3 dollars. He
spent a total of 19 dollars. How much
did each candy bar cost?
26. Tim sold half of his comic books
and then bought 7 more. He now has
16. How many did he begin with?
27. Sara goes to Fredonia University.
She has $900 in her savings account.
She needs to buy a small laptop
computer before the next semester.
The laptop costs $600. Every 2 weeks
she withdraws $60 from her savings
account for food. How many times can
Sara withdraw money for food? Write
an ineqaulity to represent this situation.
28. Skateland charges $50 flat fee for
birthday party rental and $5.50 for
each person. Joann has no more than
$100 to spend on her birthday party.
Write an inequality to represent this
and determine how many people she
can include.
5
Solve each equation.
29.
𝑛+4
5
= −2
𝑟
30. −2 = −3 + 9
31. 7 − 7𝑎 = 11 + 1 − 8𝑎 − 3
32. −8(4𝑝 − 1) − 4(1 − 2𝑝) = 28
33. −4 + 5(𝑥 + 8) = −6(𝑥 − 2) + 7𝑥
34. 7 + −2 = 10
𝑛
6
Solve and graph each inequality.
35. 1 < 𝑟 − 2
37. 1 ≥
7+𝑣
22
36. −4 ≤ 𝑛 + 2 ≤ 1
38. −2 < 7 − 3𝑚 ≤ 25
39. −4(−6𝑥 − 7) < 196
40. −5𝑛 ≥ 20 or 𝑛 − 5 ≥ −2
41. −20 − 4𝑥 ≥ −2(11 + 3𝑥 )
42. −6𝑥 + 5 ≥ 41 or 8𝑥 + 3 > 35
43. 4(𝑚 − 4) < 3(−7 + 5𝑚) − 6𝑚
44. 7𝑘 + 1 < −62 or −5𝑘 − 3 < −33
7
Solve a literal equation for a specified variable. (HS.A-REI.B.3)
Solve for the indicated variable.
45. 𝐼 = 𝑝𝑟𝑡, for r
46. 𝐴 = 2(𝐿 + 𝑊 ), for W
47. 2𝑥 − 3𝑦 = 8, for y
48. 𝑎𝑥 + 𝑏𝑦 = 𝑐 , for y
49. 𝑉 = 𝐿𝑊𝐻, for L
50.
51. 12𝑥 − 4𝑦 = 20, for y
52. 𝐴 = ℎ(𝑏 + 𝑐 ), for c
53. 𝐶 = 2𝜋𝑟, for r
54. 𝐴 =
𝑥+𝑦
3
= 5, for y
1
2
𝑟
2𝐿
, for L
8