Download Algebra I summer skill sharpener

Algebra I Summer Skill Sharpener
The problems below represent mathematics taught prior to Algebra I. These skills will be used
throughout the year. If you have any questions, please feel free to email Mrs. Sullaway at
[email protected].
Simplify each expression. Show all work.
1.
6 + (–3)
2.
−4 – 6
3.
–4.51 + 11.65
4.
3 3
–
10 4
5.
–85 ÷ (–5)
6.
 6
7 
 14 
7.
14k − (−2k)
8.
4xy + 9xy
9.
6t + 2 – 4t
10.
3
11.
2
12.
2
13.
5
14.
– ÷ 18
15.
3 – 11
16.
–0.6 – 0.67
17.
–7 + 7
18.
13 – (–5)
19.
2(–5)( –4)
20.
(–3)( –2)( –5)
21. −6 ÷ 18 • 27
4
7
+
•
5
8
7
10
3
–
5
6
2
5
3
( 15)
Solve each equation. Check your solution.
22.
x − 4 = −2
23.
n − 7 = 22.5
24.
b
= 12
4
25.
 y=9
3
4
26.
4.2m = 21
27.
m
= 2.7
12
28.

12
z = 48
7
29.
5y
= −15
4
30.
−16 = 8 + x
31.
15.9 = 5.3x
32.
m + 2.35 = 4.2
33.
5
t = −15
8
34.
2x + 3x + 3 = –12
35.
x8
2
36.
5x = 2 – (x – 7)
37.
40.
4𝑥 + 27 + 6𝑥 = 2𝑥 − 13
3p + 1 = – p + 5
7=
38.
v+5=v–5
41.
1
2
(6c – 4) = 4 + c
39. 6(2𝑥 − 3) = 96
Evaluate each expression for the given value(s) of the variable(s).
42. –w + 3w ; w = –3
45.
3x – 2y ; x = –1, y = 2
43.
3k
;k=3
k
44.
y = 7x – 5; (0, 5)
46.
–2x +4y ; x = –3, y = 7
47.
–4x +5y ; x = 2, y = 8
50.
5a + 2b(c – 1)
Evaluate each expression for a = –1, b – 3, and c = –2.
48.
2a – b2 + c
49.
b2 – 4ac
2a
Create a table and an equation to represent each relationship.
51.
Bob is 9 years older than his
dog.
52.
Sue swims 1.5 laps per
minute.
53.
The 8 students shared the
pencils.
54.
Seven less than a number x.
55.
Two-fifths of a number x.
56.
Three less than twice a
number.
Graph and label the ordered pairs in the same coordinate plane.
57.
(3, – 3)
(0, – 5)
(– 2, 2)
(6, 8)
(−7, −4)
(9, 0)
Make a table for each function rule. Then graph each equation using
the points you created.
58.
𝑓(𝑥) = 2𝑥 − 5
59.
𝑓(𝑥) = −3𝑥 + 6
60.
2
𝑓(𝑥) = 𝑥 + 4
3
Answer the following questions. Be sure to show all work.
61. Mr. Brown drives 174 miles
62. Mrs. Edwards spends $4 for 48
in 3 hours. At the same rate,
how far would you expect Mr.
Brown to drive in 8 hours?
64.
The length of the rectangle is
twice the width. If the
width is 13cm, what is
the area of the rectangle?
63.
One pizza feeds 6 people. If
there are 135 people, how
many pizzas do you need
to purchase?
pencils. At this rate, how
many pencils can she
purchase with $10?
65.
A birch tree grew 2.5 in. in 5
months. How much did
the tree grow in 1 month?
Write each ratio as a fraction in simplest form.
66. 10 to 2
67.
35 to 25
68.
42 to 95
69. 7:–56
70.
81:108
71.
–16:12
List all the factors of each number.
72. 12
73.
18
74.
121
75. 81
76.
56
77.
300
78. 250
79.
207
80.
126
81. f(x) = 2x + 8
82.
f(x) = 7x – 4
83.
f(x) = –5x + 3
84. f(x) = –3x – 9
85.
f(x) = 0.2x + 0.7
86.
For each function, find f(2) and f(3).
f(x) = 4x –
2
3