Semester 2 cumulative Final Study Guide
From the California State Board of Education Mathematics Content Standards for Grade 7, these are
the standards you should focus on for preparing for the final:
Number Sense
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating
decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimations,
computations, and applications.
1.6 Calculate the percentage of increases and decreases of a quantity.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect
square integer; for an integer that is not square, determine without a calculator the two integers
between which its square root lies and explain why.
Algebra and Functions
1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse,
distributive, associative, commutative) and justify the process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression,
constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a
graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots.
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number
powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate
expressions that include exponents.
4.0 Students solve simple linear equations and inequalities over the rational numbers.
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers,
interpret the solution or solutions in the context from which they arose, and verify the
reasonableness of the results.
Measurement and Geometry
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between
measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and
the surface area and volume of basic three-dimensional figures, including rectangles,
parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of
the missing side of a right triangle and the lengths of other line segments and, in some situations,
empirically verify the Pythagorean theorem by direct measurement.
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify
relationships among variables within a data set.
Mathematical Reasoning
2.2 Apply strategies and results from simpler problems to more complex problems.
Pre-Algebra 1/2 Study Guide- For the School Year 2007/2008
You may use this as a guide to prepare for 2008/2009
(Note we are using a different book-Chapters address different subjectmatter.)
Pre-Algebra 1-2
Vocabulary List & Study Guide - Chapter 11
Know the meaning and proper spelling. Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
11.1 Functions
function
input
output
Be able to find the output or input for a given function
11.2 Linear Equations and Linear Functions
linear equation in two variables
Be able to tell if an ordered pair is a solution of a given equation.
Be able to recognize if an equation is linear or nonlinear.
Be able to write an equation that represents a sentence (example: Three times
a number x and two times a number y is four 3x + 2y = 4).
11.3 Graphs of Linear Functions
Be able to complete an x-y table and graph a linear function (equation of a
line) using a ruler.
11.4 Intercepts of a Graph
x-intercept
y-intercept
Be able to identify the x-intercept and y-intercept from a graph of a line.
Be able to identify the x-intercept and y-intercept from the equation of a line.
11.5 The Slope of a Line
slope
Be able to identify the slope of a line from a graph.
Be able to identify the slope of a line from two given points.
11.6 The Slope-Intercept Form
slope-intercept form
Be able to identify the slope and y-intercept of a line from an equation.
Be able to identify the slope-intercept form of an equation for a given graph.
Be able to rewrite an equation in slope-intercept form (y = mx + b).
11.7 skip
11.8 skip
11.9 Systems of Equations (and Inequalities)
system of equations
solution of a system of equations
Be able to find the solution to a system of equations by graphing the lines
and verifying the point of intersection as the solution.
Vocabulary List & Study Guide
Know the meaning and proper spelling.
Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
Chapter 9 test will be on Monday March 24
9.1 Square Roots
square root
perfect square
Be able to find the square root of a perfect square.
Be able to find the best integer estimate of a square rot that is not a
perfect square.
9.2 The Real Number System
irrational numbers
real numbers
Be able to tell if a number is whole, integer, rational, irrational or real.
Be able to order rational and irrational numbers from least to greatest.
Be able to graph rational and irrational numbers on a number line.
Be able to compare two rational or irrational numbers using < or >.
9.3 The Pythagorean Theorem
leg
hypotenuse
Be able to find the missing length of a side of a right triangle.
9.4 The Converse of the Pythagorean Theorem
Be able to tell if a triangle is right, obtuse or acute if given the lengths
of the sides.
9.5 skip
9.6 Solving Inequalities Using Addition or Subtraction
Be able to find the solution of an inequality.
Be able to graph the solution of the inequality.
Be able to write an inequality from a graph.
9.7 Solving Inequalities Using Multiplication or Division
Be able to find the solution of an inequality.
Be able to graph the solution of the inequality.
Remember that when you multiply or divide by a negative number you must
reverse the direction of the symbol.
9.8 Solving Two-Step Inequalities
Be able to find the solution of an inequality.
Be able to graph the solution of the inequality.
9.9 Box-and-Whisker Plots
lower quartile
upper quartile
box-and-whisker plot
range
interquartile range
Be able to find the median, upper and lower quartiles, maximum, minimum, range
and interquartile range from a Box-and-Whisker plot.
Be able to draw a Box-and-Whisker plot from a set of data.
Know that each of the four parts contains 25% of the data.
BONUS HINTS:
Review how to write Roman Numerals
Solving more complex inequalities (negatives, fractions)
Square root of a larger number
Pythagorean theorem problem with larger numbers.
Chapter 9 test will be on Monday March 24
For extra practice, you can do the problems in the Study Guide and Assessment
in the book (answers
for odd numbered problems are in the back of the book). You can also check
your readiness using
this website:
http://glencoe.mcgraw-
hill.com/sites/0078738180/student_view0/chapter9/chapter_readiness_quiz.html.
If this doesn't work you can go to the Glencoe Website for Mathematics, choose
Parent Teacher and
Choose Chapter Tests & Section Quizzes page for Chapter 9-the site is really fun.
BONUS HINT:
Roman Numerals, of course!
Vocabulary List – Mid-Chapter 8.1 – 8.6
Know the meaning and proper spelling. Be able to identify an example.
Highlight each vocabulary word and definition in your math notebook.
8.1 Points, Lines and Planes
point
line
line segment
ray
plane
Be able to name a point, line, line segment, ray, or plane.
8.2 Angles
angle
vertex
sides
acute angle
obtuse angle
right angle
straight angle
complementary angles
supplementary angles
congruent angles
Know the parts of an angle.
Be able to classify an angle by its measure (acute, obtuse, right, or straight).
Be able to read an angle measurement using a protractor.
Be able to draw an angle given its measure.
Be able to find an angle measure if information is given (supplementary,
complimentary).
8.3 Parallel and Perpendicular angles
vertical angles
adjacent angles
transversal
corresponding angles
Know the properties of vertical angles and corresponding angles.
Know how to find an angle measurement with adjacent angles.
Know how to tell if two lines are parallel.
Know what properties (angle measurements) are present when two lines are
perpendicular.
8.4 Triangles and Quadrilaterals
triangle
scalene triangle
isosceles triangle
equilateral triangle
acute triangle
equiangular triangle
obtuse triangle
right triangle
quadrilateral
parallelogram
rectangle
square
rhombus
trapezoid
isosceles trapezoid
kite
Be able to classify a triangle by its sides or by its angles.
Be able to classify a quadrilateral.
Know that the sum of angles of a triangle is 180˚.
8.5 Polygons and Congruence
polygon
congruent figures
corresponding parts
regular polygon
diagonal
Be able to write congruence statements from a picture of two polygons and name
the corresponding parts.
Be able to determine the number of diagonals in a polygon.
Know what a regular polygon is.
Know what information is implied when two polygons are congruent.
8.6 Areas of Polygons
Be able to find the area of a trapezoid, parallelogram, or other polygon that
can be broken down into simpler shapes.
_____________________________________________________________________________
Vocabulary List & Study Guide
Chapter Test-February 7th
Know the meaning and proper spelling.
Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
Chapter 7 test will be on Thursday February 7
7.1 Ratios and Rates
ratio
rate
unit rate
Be able to write a ratio or rate in one or all of 3 ways, and reduce it to
lowest terms.
Know that ratios do not show units because they compare the same units.
Know that rates show units because they compare different units.
Know that a unit rate is a rate with a denominator or one.
Be able to use unit rates to compare the costs of items.
7.2 Writing and Solving Proportions
proportion
cross products
Be able to write and solve proportions.
7.3 Scale Drawings and Models
scale drawing
scale
scale factor
Be able to find the actual dimensions of an object if given the scale factor
and scale measurement.
Be able to find the scale dimensions of an object if given the scale factor
and actual measurement.
7.4 Probability
outcomes
probability
Be able to find the probability that an event will occur
Know what a probability of zero means.
Know what a probability of one means.
7.5 Solving Percent Problems
Be able to write and solve proportions using “a is p percent of b” template.
7.6 Markup and Discount
markup
discount
Be able to find the mark up or discount of an item in actual dollars or percent.
Be able to find the sale price of an item given the regular price and the
discount.
Be able to find the regular price of an item given the sale price and the
discount.
7.7 Percent of Increase or Decrease
percent of change
Be able to find the percent of change.
Be able to recognize whether the percent of change is a percent increase or
percent decrease.
7.8 Simple Interest
interest
principal
interest rate
simple interest
Be able to find the interest earned.
Be able to find the balance owed or in an account.
Be able to find the missing quantity using the formula I=Prt
7.9 skip
BONUS HINTS:
Review how to write Roman Numerals
Vocabulary List & Study Guide
Know the meaning and proper spelling.
Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
Chapter 5 test will be on Thursday December 13th
5.1 Factoring Numbers and Expressions
prime number
composite number
prime factorization
Be able to tell if a number is prime or composite.
Be able to find the prime factorization of a number, both positive and negative.
Be able to factor a variable expression completely.
5.2 Greatest Common Factor
greatest common factor
relatively prime
Be able to find the GCF of 2 numbers or 2 variable expressions.
5.3 Least Common Multiple
multiple
common multiple
least common multiple
Be able to find the LCM of 2 numbers or 2 variable expressions.
5.4 Simplifying and Comparing Fractions
simplest form
equivalent fractions
Be able to reduce a numerical or algebraic fraction to its simplest form.
Be able to compare fractions and put several fractions in order from least to greatest.
Be able to compare fractions with greater than, less than or equal to signs
5.5 Rational Numbers and Decimals
rational number
integer
whole number
natural number
terminating decimal
repeating decimal
Be able to identify all sets to which a number belongs.
Be able to change a fraction to a decimal.
5.6 Writing Percents
percent
Be able to change a fraction to an equivalent percent.
5.7 Percents, Decimals and Fractions
Be able to convert a percent to a decimal or fraction.
Be able to convert a decimal to a percent or fraction.
Be able to convert a fraction to a decimal or percent.
5.8 Stem-and-Leaf Plots
stem-and-leaf plot
Be able to create a stem-and-leaf plot.
Be able to read data from a stem-and-leaf plot.
BONUS HINTS:
Know how to write a fraction with a denominator of 1000 as a percent (fraction --> decimal -->
percent)
Be able to find the mean of a set of data shown on a stem-and-leaf plot.
Review how to write Roman Numerals
Pre-Algebra 1-2-Study Guide is due Nov. 20th
Vocabulary List – Chapter 4
Know the meaning and proper spelling. Create 3 examples for sections 4.1-4.5 and an thorough
example for both 4.8 and 3.9.
Highlight each vocabulary words and define for your study guide also (separate pieces of paper.)
4.1 Solving Two-Step Equations
Be able to solve equations involving more than one operation.
4.2 Solving Multi-Step Equations
Be able to find the solution to the equations by substitution.
4.3 Solving Equations Involving Negative Coefficients
Be able to find the solution to the equations by substitution.
4.4 Solving Equations Using the Distributive Property
Be able to find the solution to the equations by substitution.
4.5 Solving Equations With Variables on Both Sides
Be able to find the solution to the equations by substitution.
4.6 skip
4.7 skip
4.8 Measures of Central Tendency
measure of central tendency
mean
median
mode
outlier
Know how to find the mean of a data set.
Know how to find the median of a data set.
Know how to find the mode of a data set.
Know how to tell is a number in a data set is an outlier.
3.9 Scatter Plots
scatter plot
positive correlation
negative correlation
no obvious correlation
Be able to tell if a scatter plot shows a positive, negative, or no obvious
correlation.
Be able to create a scatter plot from data, and interpret the results.
Pre-Algebra 1/2 Study Guide
Chapter 3
Vocabulary List & Study Guide
Know the meaning and proper spelling.
Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
3.1 Integers and Absolute Value
integer
absolute value
opposite
(Be able to write a set of integers in order from least to greatest, or
greatest to least)
(Be able to find the opposite of an integer)
(Be able to find the absolute value of an integer)
3.2 Using a Number Line to Add Integers
3.3 Rules for Adding Integers
sum
(Know the rules for adding integers)
3.4 Subtracting Integers
difference
(Know the rules for subtracting integers)
3.5 Multiplying Integers
product
(Know the rules for multiplying integers)
3.6 Dividing Integers
undefined division
average
quotient
(Know the rules for dividing integers)
(Know how to find the average of a set of numbers)
3.7 Solving Equations Involving Integers
(Know how to solve equations involving positive and negative integers)
3.8 The Coordinate Plane
coordinate system
origin
quadrant
ordered pair
(Know how to plot points if you’re given an ordered pair)
(Know how to write an ordered pair for a point on a graph)
(Know how to name the quadrant of a point)
(Know how to find the length of a line segment plotted on a graph)
(Know how to find the area and perimeter for a quadrilateral plotted on a graph)
(Be able to determine if an ordered pair is a solution to an equation)
BONUS HINT:
Review how to tell if a long list of negative factors will give a positive or
negative product.
Example... (-1)(-1)(-1)(-1)(-3)(-1)(-2)(-1)(-1)(-1)=?
Review how to write Roman Numerals
Chapter 2 w/sections 1.7,1.8
Pre-Algebra 1-2
Vocabulary List – Chapter 2 (Includes Sections 1.7 & 1.8)
Know the meaning and proper spelling. Be able to identify an example.
Highlight each vocabulary word and definition in your math notebook.
1.7 Commutative, Associative & Identity Properties
Commutative Property of Addition / Commutative Property of Multiplication
Associative Property of Addition / Associative Property of Multiplication
Identity Property of Addition / Identity Property of Multiplication
(Be able to identify an example of the properties)
1.8 Distributive Property
Distributive Property
(Be able to identify an example of the Distributive Property)
(Be able to rewrite an expression using the Distributive Property)
2.1 Translating Phrases into Expressions
(Know the key words and what operation they indicate)
(Be able to translate a phrase into an expression)
2.2 Combining Like Terms
terms
like terms
coefficient
constant
variable
variable term
(Be able to identify the parts of an expression)
(Be able to combine like terms)
(Know how to distribute properly, and then combine like terms)
(Know that like terms are terms with the exact same variable with the exact same exponent)
2.3 Solving Equations – Mental Math
equation
conditional equation
identity equation
solution (of an equation)
2.4 Translating Sentences into Equations
expression
equation
(Be able to translate a sentence into an equation)
2.5 Solving Equations Using Addition and Subtraction
2.6 Solving Equations Using Multiplication and Division
inverse operation
equivalent equation
Addition/Subtraction/Multiplication/Division Properties of Equality
(Be able to solve equations using the properties of equality, and check your answer)
2.8 Solving Inequalities
inequality
equivalent inequality
solution (of an inequality)
(Be able to solve an inequality, and express the solution in proper form)
Vocabulary List & Study Guide - Chapter 1
Know the meaning and proper spelling.
Be able to identify an example.
Highlight each vocabulary word and definition in your notebook.
Chapter 1 test will be on Tuesday September 25th
Review Section – Place Value
(Know the place values from the thousandths to the millions)
Review Section – Rounding
(Know how to round a number to a specified place value)
Review Section – Adding and Subtracting Decimals
(Know how to add or subtract by lining up decimal points)
Review Section – Multiplying and Dividing Decimals
(Know how to multiply or divide decimal numbers)
1.1 Tables and Graphs
table
bar graph
double bar graph
line graph
(Know how to read information from a table, bar graph or line graph)
1.2 Expressions and Variables
expression
numerical expression
variable expression
variable
evaluate
addend, sum (+)
term, difference (–)
factor, product ( · , x)
dividend, divisor, quotient (÷)
(Be able to evaluate a variable expression for a given value of the variable
or variables)
(Be able to translate a verbal phrase into an expression)
1.3 Powers and Exponents
power
base
exponent
(Be able to write a repeated multiplication as a power, and a power as a
repeated multiplication)
(Be able to write a power as a verbal expression -- ex.: 53 à five to the
third power)
(Know that “squared” means to the second power and “cubed” means to the third
power)
(Be able to evaluate a power)
1.4 Order of Operations
order of operations
parentheses
brackets [aka square brackets]
(Be able to evaluate an expression using the correct order of operations)
1.5 Formulas (Perimeter and Area)
perimeter
area
square
rectangle
triangle
(Be able to find the area and perimeter of the three basic shapes and more
complex shapes)
BONUS HINT:
You might also want to know how to write numbers in Roman Numerals (example
125 = CXXV). Check the link to a good instructional Roman Numeral site.
