Algebra I Back to School Review Packet
Section A
Name________________________
SHOW YOUR WORK!
Answer the following.
1) Calculate the simple interest earned on a deposit of $500 with 4% interest for 2 years. I = Prt
2) Find the simple interest and the total on a deposit of $250 with 5.5% interest for ½ a year.
3) Find the average speed of an airplane that travels 1540 miles in 4 hours.
4) Write an expression for the perimeter of the triangle, then
find the perimeter if x = 8.
3x
D = rt
2x
4x
5) Write an expression for the area of a rectangle with length x and width x + 5, then find the area if x = 7.
6) Find the temperature in Celsius if the temperature is 50º F.
C=
5
(F – 32)
9
Write the expression in exponential form.
7) 3x • 3x • 3x • 3x
8) 4 • a • b • a • b • b • c
9) the quantity 5a cubed
Evaluate the expression for each value.
10) y² when y = 3.5
11) (x – y)
4
when x = 10 and y = 8
PEMDAS
14) 3y³ ÷ 4 when y = 2
15)
36
+ a if a = -9
a
12) -b³+ a² if a = 7 and b = 3
16) 2y³ -3y when y = -3
13) (7x – 8)² when x = 2
17) -(-6x)² if x = 2
1
Simplify each expression.
18) 5² - 14 ÷ 7
PEMDAS
22)
6+4
3³ - 4 ÷ 2
19) 4 – 20 ÷ 10 + 7
23)
3(4 + 2[5])
20) 2³ • 5
3² - 3 • 2
24) 2[(9-8)² + (12 – 5)²]
21) [(7 – 5) ÷ 8] – 4
5
Is the given number a solution of the equation or inequality?
25) x - 19 = 30 ; 7
2
26)
m
- 4 = 12 ; 24
3
27) x + 7
2
≥ 10 ; 2
Show your work as proof!
28) 5x+ 3x = 30 – 2x ; 5
29) 4w + 1 < 8 ; 2
30) 6(m + 1)
≤ 8m – 7 ; 2
Write the verbal phrase as an algebraic expression.
31) The difference between a number and 4
32) Nine more than twice a number
33) Seven less than four times a number
34) Five times the sum of a number and one
35) The product of 4 less than a number and 9
Write a verbal sentence as an equation or an inequality.
36) Eight more than a number y is greater than or equal to 12.
37) Fourteen is less than three times a number x.
38) The quotient of 11 and a number is 22.
39) Five less than the product of six and a number is at least nine.
40) The quotient of a number and six is at most 12.
2
Section B
Write the real numbers in increasing order.
1)
−1
−3
, -.5, -3,
3
5
2) -1.62, 1.8, 1.75, -1.7
3) -1,
4
, - 5 , 13 , -2.5,
3
9,
1
,2
2
For each number find its opposite, absolute value, and reciprocal.
4) 13
8) .2
5) -8
6)
9) 1
3
4
2
5
10) -.375
11)
Simplify.
12) -9 + 2
17) 5 + (-7) + (-12)
22) 0 ÷ 5
13) -| 14 |
18) |(-4) |
23) -15 ÷ 3
14) (-8)(-6)
19)
15) -| -2.3 |
20) -(-5)
16) 8 ÷ (
8
)
11
-2
5
6
7) 0
3
3 −1 −1
+
+
4 2
4
2
21) | 10 - 5²| ÷ 5
24) 5 + (-7) - (-2)
25) -48 ÷ (-4)
26) (-3) (-4)
3
2
3
Answer the following.
27) Find the mean, median, mode, range, and outlier of the numbers:
20, -6, -8, 4, 0, 3, 1
28) Nancy has the following test scores in Algebra I class: 88, 80, 93, 91, 85, 96, 92. What grade must she get on
the next test to maintain an average of 90? Show your work!
29) In Bermuda, the average temperature for the last week of July was 87°. If the temperatures for the first 6
days were 84, 83, 90, 92, 86, and 85, what was the temperature on the 7th day that week? Show your work!
30) Which measure of central tendency (mean, median, mode) best describes each group below and why?
a) favorite summer movie
b) grades on a quiz - 10, 9, 8, 10, 2
c) bowling scores – 153, 145, 148, 158
Classify each as rational or irrational and then find each square root.
(approximate to the nearest unit if necessary)
31) ±
36
34)
32) -
9
42
33)
196
37)
35) -
48
38)
36) ±
351
Find the length of the missing side using the Pythagorean Theorem.
(approximate answer to the nearest tenth if necessary)
39) a = 3, b = 4, find c
a
c
a²+b²= c²
b
40) a = 6, c = 12, find b
41) b = 3.1, c = 10.2, find a
4
Section C
Perform each matrix operation.
1)
 2 − 3 − 5 1 
 − 4 1  +  0 2

 

2)
1
 − 3 − 8 4  5 2
 6 − 7 9  - 0 − 2 − 1

 

Evaluate.
4) x – 2 when x = 8, y = -2
y
6) xy
x+y
5) 9y – 2x if x = -2, y = -3
7) -x(5 – y)
 2 − 3

− 1 4 
3) -3 
when x = 3, y = -3
if x = 4, y = -2
Use the data below to make a Stem and Leaf Plot and a Box and Whisker Plot for each problem.
8) the number of pretzels found in several samples of snack mix
22, 12, 9, 20, 8, 15, 30, 22, 17, 18, 14, 31, 11, 25, 27
9) the number of visitors to a park each day over a two week period in the summer
25, 25, 26, 19, 27, 57, 59, 46, 41, 29, 22, 23, 54, 60
In a bag of 20 marbles, there are 4 red, 6 blue, 5 green, 2 yellow, and 3 orange.
Find each probability or odds. (reduce if necessary)
10) probability of choosing a red marble
14) odds in favor of choosing red
11) P(green)
15) odds (in favor of) picking green
12) P(blue or yellow)
16) odds against choosing orange
13) probability of not picking orange
5
Find the rate, ratio, or proportion.
17) Shampoo costs $3.59 for a 28 oz bottle. Find the unit rate.
18) Find the ratio of women to men working at a factory if there are 1215 men and 945 women on the payroll.
19) A yellow jacket can fly 4.5 meters in 9 seconds, how far does it fly in one second?
20) The ratio of faculty members to students at a college is 1:15. There are 675 faculty members, how many
students are there?
21) The scale on a map is 1 in : 5 mi. If the distance on a map from Chicago to Evanston is 0.625 inches, what
is the actual distance?
22) The ratio of boys to girls in a classroom is 3:5. If the class has 32 students, how many are girls?
23) A cheetah can run at a rate of 57 mph in short bursts. What is this speed in feet per second?
24) A pool is filling with water at a rate of 50 ounces per sec. What is the rate in gallons per hour?
Answer the following.
25) Find 82% of 116.
26) 440 is what percent of 400?
27) 15% of what number is 48?
28) What is the tax on a $359 mountain bike if the tax rate is 7%?
29) The serving size of a popular orange drink is 12 oz. If the drink contains only 0.6 oz of orange juice, what
percent of the drink is actually orange juice?
30) An 18% tip on a family’s dinner check at PJ’s was $27. What was the cost of their dinner?
31) The entrance fee at an amusement park is $35. People over the age of 65 receive a 20% discount.
What is the amount of the discount? How much do people over 65 pay?
32) A computer salesperson earns a base salary of $32,000 per year plus a commission of 6% on total sales.
Total sales for one year were $350,000. Find the salesperson’s commission and total pay for the year.
6
Use the coordinate planes below to answer the following questions.
33) Graph each point. Name the quadrant in which each point lies or the line it falls on.
a)
b)
c)
d)
e)
f)
A (2,3)
B (-4,-2)
C ( 0,3)
D (5,-3)
E (-1,4)
F (-2,0)
34) List the coordinates for each point on the graph.
a)
b)
c)
d)
e)
f)
g)
G
H
I
J
K
L
M
35) Using a table, generate ordered pairs for y = 3x - 2 with x = 2, 1, 0, -1 and then graph the line.
x
36) Graph the line: y =
y
-½x + 1 using a chart with x = 4, 2, 0, -2, -4
x
y
7
Section D
Simplify each expression. Combine similar terms where possible.
1) 6x + 10x
14) 6(x + 3)
2) 35y – 15y
15) -4(2y – 2)
3) -3m + 9m
16) 8(-3 – m²)
4) -8r – r
17) 5(x – 1) + 6x
5) 5x²+ 2x²
18) 9(2w + 2) – 7
6) 17w³- w³
19) 5x² - 2(1 – 3x²)
7) 7d + 5d²
20) 6x – x – 3x²+ 2x
8) -15x ÷ 5
21) 12y + 8x – 5y – 15x
9) -81p²÷ -3
22) 4a – 2(a – 3a²)
10) 24 ÷ -4w
23) -2(3x + 2y + 4x – 5y)
11) 32x – 8
4
24)
2x + 4 +
-2
12) -30y + 45
15
25)
-3m - 6 - 3(4m – 6)
-3
5x - 15
5
13) 24m – 6
-3
8
Solve each equation.
26) x – 10 = 4
36) 4x + 10 = 18
27) y + 7 = -5
37) 5m – 2 = -32
28) 16 = m + 9
38) 10 = 6 – 2w
29) w +
⅜ =½
39)
30) 3r = -39
40) 14 – c = 6
31)
41) 2(3p – 1) = 16
= 1.5
32) -2w = -13
42)
33)
43) 6x + 3 – 8x = 13
34)
35)
¾v = 24
44) 10y – (4y + 8) = -20
45) 4(f – 2) + 2f = 40
9