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PreAlgebra End-of-Year Study Guide
Name: ___________________________
Day 1
I. Tools for Algebra and Geometry
A. Order of Operations
1. 100 " 32 # 4
!
2. 6 + 2 " 7 # 5
3.
14 + 6 ÷ 3
5+ 3
B. Prime Numbers
1. What are the prime factors
! of 120? (Hint: make a factor tree.)
!
2. Are 12 and 25 relatively prime? Explain.
C. Factors & GCF
1. Find the GCF of 24 and 54.
2. Is 3 a factor of 315? How do you know?
D. Multiples & LCM
1. List the first 5 multiples of 6.
2. Find the LCM of 9 and 15.
E. Squares & Square Roots
1. 122 =
2.
!
3.
81
!
42 " 7
II. Fractions
A. Simplify Fractions
1. Change
2. Simplify
!
25
to a mixed number.
6
4
.
36
B. Compare & Order Fractions
1.!Write 43 , 13 , 12 , 37 in order from least to greatest.
C. Change Fractions to Decimals
!1. 2 38 =
!
!
!
!
D. Change Fractions to Percents
1. 58 =
2.
!
E. Add & Subtract Fractions & Mixed Numbers !
1. 43 + 38 =
F. Multiply & Divide Fractions
1. 43 ÷ 38 =
III. Decimals
2
3
=
2. 3 14 =
2. 5 14 " 3 13 =
!
2. 5 14 " 3 13 =
!
A. Compare & Order Decimals
1. Write 0.17, 0.07, 0.7, 0.017 in order from least to greatest.
!
B. Change Decimals to Percents
1. 0.98
2. 2.04
C. Multiply & Divide Decimals
1. 1.26 " 3.1 =
2. 0.72 10.8
)
!
Day 2
IV. Percents
A. Change Percents to Fractions
1. 14.3% =
2. 0.5% =
B. Change Percents to Decimals
1. 204% =
2. 5.6% =
C. Find Percent of a Quantity
1. What is 12% of 144?
2. 20% of 72 =
D. Find a Missing Percent
1. What percent of 16 is 4?
2. 25 out of 75 is what % ?
E. Find a Missing Whole Part
1. 17 is 15% of what number?
2. 40% of what is 100?
V. Patterns
A. Pascal’s Triangle
1. Find the next row of Pascal’s Triangle.
1
1
1
1
1
1
3
3
1
_________________________________________
B. Sequences
1. Find the next three terms of the pattern: 5, 7, 11, 17, 25, 35, …
2
VI. Graphs
A. Interpret Graphs
1. The graph at right shows the relationship between
the speed of Car A and Car B. Choose the
sentence that best describes the relationship.
a.
b.
c.
d.
The speed of Car A is greater than the speed of Car B.
The speed of Car B is greater than the speed of Car A.
The speed of Car A is equal to the speed of Car B.
There is not enough information to decide.
B. Create Graphs from an Input/Output Table
1. Complete the I/O table , then plot the points on
the coordinate plane at right.
y = 3x "1
!
x
1
y
2
2
4
5
VII. Statistics
A. Stem & Leaf Plots
1. Use this data to make a stem & leaf plot: 90, 98, 82, 80, 80
B. Mode & Median
1. Find the median & mode of the data in your stem & leaf plot.
C. Mean
1. Find the mean of 10, 12, 8, 9, 11.
D. Histograms
1. Define histogram.
VIII. Algebra
A. Translate Words into Expressions (Symbols)
1. Choose the correct rule for the following: For every 18 students in the 6th grade, there is one
teacher.
a. t = 18s
b. s = t + 18
c. s = 18t
d. t = s + 18
B. Model Situations with Input/Output Tables
1. Annie charges $6 per hour for babysitting.
# of hours
1
Annie’s
earnings
$6
2
4
C. Solve Equations
1. 4a = "32
!
2.
!
3. b + ("12) = "28
!
1
h=5
4
4. x " 5 = 13
!
5
Day 3
IX. Geometry
A. Angles
1. Classification
Classify the angle at right as acute, obtuse, right, or straight.
2. Measurement
Explain how to use a protractor to measure the angle above.
3. Angle Measures in Triangles
1. A triangle has angles with measures of 90° and 52°. Find the measure of the third angle.
B. Polygons
1. Classification
a. What is the name of a polygon that has five sides?
b. What is the name of a polygon that has nine sides?
2. Symmetry
How many lines of symmetry does the figure have?
3. Perimeter
a. Find the perimeter of a square with each side equal to 7.5 in.
b. Find the perimeter of a rectangle with length of 7 m and width of 3 m.
4. Area
a. Find the area of a square with each side equal to 10 yd.
b. Find the area of a rectangle with length of 11 cm and width of 6 cm.
c. Find the area of a triangle with base of 5 mm and height of 20 mm.
d. Find the area of a parallelogram with base of 21 in and height of 4 in.
C. Circles
1. Circumference
Find the circumference of a circle with diameter of 14 ft. Use " =
22
.
7
!
2. Area
Find the area of a circle with radius of 10 m. Use " = 3.14 .
!
D. Solids
1. Surface Area
a. Find the surface area of a rectangular prism with length = 5 in, width = 4 in, height = 6 in.
b. Find the surface area of a cylinder with radius = 2 yd and height = 15 yd. Use " = 3.14 .
!
2. Volume
a. Find the volume of a rectangular prism with length = 5 in, width = 4 in, height = 6 in.
b. Find the volume of a cylinder with radius = 2 yd and height = 15 yd. Use " = 3.14 .
!
X. Probability
A. Theoretical & Experimental Probability (p. 608)
1. What is the theoretical probability of getting a 2 when rolling a six-sided number cube?
2. Jamie rolled a die 10 times and got the following results:
6 1 1 2 4 2 3 5 4 5
What is the experimental probability of rolling a 2?
B. Dependent Probability
1. There are 3 cherry, 2 lemon, and 1 green apple Jolly Ranchers in a bag. If Tom & Jerry both
reach in and take out one piece of candy, what is probability they will both select lemon?
XI. Metric System
1. 40 kg = ______g
2. 40 mm = ________m
XII. Integers
1. Write the integers "5,1,"6,"3,5 in order from least to greatest.
!
2. Which integer
is the opposite of 7?
3. The temperature dropped 20° overnight. Which integer represents this situation?
4. "5 + 14 =
!
5. 25 " ("4) =
!
6. ("6)("9) =
!
7.
!
36
=
"12