Mid Term Review
Bybee & Holloway 7th Grade Math
Fall 2012
What Will It Look Like?
O Covers Chapters 1-6
O Multiple Choice (scan sheet)
O 50-60 Questions
O 90 Minutes
O No Calculator
O Based on the textbook (like all other tests)
O Broken down into categories
How Do I Study?
O Complete the Mid Term Review Test provided
O Review old notes
O Study old tests
O Memorize rules/formulas
O Make notecards with vocabulary
O DO PRACTICE PROBLEMS!!!!
O Find the areas where you struggled the most
and focus there first.
O Take practice tests with the online textbook.
Chapter 1:
Expressions and Patterns
O Powers and Exponents
O Numerical Expressions
O Algebraic Expressions
O Properties
O Sequences
O Square Roots
O Cube Roots
Powers and Exponents
O Base
O Exponent
O Factor
O Exponential Form/ Standard Form
O Be able to evaluate powers
p. 27 #18-24 even
Numerical Expressions
O Order of Operations!!!!
O PEMDAS
p. 31 #20-26 even
Algebraic Expressions
O Variables
O Coefficients
O PLUG IT IN, PLUG IT IN!!!!
O Write an expression when given a situation
p. 36 #8, 14-20 even
Properties
O Commutative
O Associative
O Identity
O DISTRIBUTIVE!!!!!! (focus here)
O “Justify each step”; know how to use each
O FOLDABLE
p. 40 #14-22 even
Sequences
O Sequence
O Term
O Arithmetic Sequence
O Geometric Sequence
O Be able to “Extend” any sequence by seeing
the pattern
p. 47 #10-16 even
Squares & Square Roots
O
O
O
O
O
O
Square
Square Root
Cube Root
Radical Sign
FOLDABLE
Be able to find a SQUARE of a number and also
a SQUARE ROOT or CUBE ROOT of a number
p. 55 #14-24 even
Chapter 2:
Integers
O Absolute Value
O Coordinate Plane
O Adding Integers
O Subtracting Integers
O Multiplying and Dividing Integers
Absolute Value
O Integer
O Absolute Value
O Number Line
O Be able to evaluate expressions with absolute
value
p. 79 #14-18 even
#28-32 even
Coordinate Plane
O Origin
O x-axis, y-axis/ x-coordinate, y-coordinate
O Four Quadrants
O Ordered Pairs
O Know how to plot points & identify the
quadrant
p. 84 #10-18 even
Add & Subtract Integers
ADDITION:
Same signs, add and keep
Different signs subtract
Take the sign of the larger number
Then, you’ll be exact!
SUBTRACTION:
LEAVE, CHANGE, CHANGE/ADD THE OPPOSITE
p. 91 #20-28 even
p. 97 #22-28 even
Multiply & Divide Integers
O Same Signs- POSITIVE
O Different Signs- NEGATIVE
O Pay attention to when you have exponents
p. 107 #20-28 even
p. 112 #24-30 even
Chapter 3:
Rational Numbers
O
O
O
O
O
O
O
O
O
O
Terminating and Repeating Decimals
Comparing & Ordering Rational Numbers
Add & Subtract Like Fractions
Add & Subtract Unlike Fractions
Add & Subtract Mixed Numbers
Multiply Fractions
Divide Fractions
Multiply & Divide Monomials
Negative Exponents
Scientific Notation
Terminating & Repeating
Decimals
O Changing Fraction into a Decimal using
division
O Sometimes the answers terminate and other
times they repeat
O Bar Notation is used to show repeating
p. 131 #22-28 even
Compare & Order
Rational Numbers
O Rational Numbers (be aware of what they are)
O Comparing Fractions & Decimals using <, >, =
O Might need Common Denominators before
you can compare
O Might need to change the Fraction to Decimal
before you can compare
p. 136 #14-20 even
Add & Subtract Fractions
1.
2.
3.
4.
Must have a COMMON DENOMINATOR
Add the numerator
Keep the denominator
Simplify
O BE CAREFUL WITH THE NEGATIVES!!!!!
O All Integer Rules apply here
p. 142 #14-20 even
p. 149 #20-28 even
Add & Subtract
Mixed Numbers
1.
2.
3.
4.
1.
2.
3.
4.
Add or subtract the fraction
You might need to rename using the LCD
Add or subtract the whole numbers
Simplify
OR
Change to improper fractions
Get a common denominator
Add or Subtract
Simplify
p. 155 #14-24 even
Multiply Fractions
1. Change any Mixed # to Improper Fraction
2. Multiply the numerators
3. Multiply the denominators
4. Simplify
O YOU DO NOT NEED COMMON
DENOMINATORS!
O Pay attention to those negatives
p. 163 #14-20 even
Divide Fractions
O You will have to change any Mixed # to an
Improper Fraction
O LEAVE, CHANGE, FLIP or…
O Multiply by the reciprocal
O Apply the same rules as Multiplying
Fractions
p. 171 #22-28 even
Multiply & Divide Monomials
O To multiply powers with the same base, add
the exponents (Product of Powers)
O To divide powers with the same base,
subtract the exponents (Quotient of Powers)
O You can always write it out in expanded form
to help yourself!
p. 179 #20-34 even
Negative Exponents
• Look at the
textbook here
to review.
• Rewrite using
positive and
negative
exponents
p. 183 #22-40 even
Scientific Notation
O Writing really big numbers or really small
numbers in a manageable way
O Standard Form (1,457,000)
O Scientific Notation (1.457 x 106)
O Know which way to move the decimal when
using positive or negative exponents
p. 187 #18-28 even
Chapter 4:
Equations and Inequalities
O Solve One-Step Addition and Subtraction
O
O
O
O
O
O
Equations
Solve One-Step Multiplication and Division
Equations
Solve Equations with Rational Coefficients
Solve Two-Step Equations
Solve Equations with Variables on Both
Sides
Solve Inequalities by Addition or Subtraction
Solve Inequalities by Multiplication or
Division
Solve One-Step Addition and
Subtraction Equations
1. What’s your variable?
2. What happened to your variable?
3. How do you un-do that?
O Do the opposite operation
O Remember: be careful when given negatives
p. 211 #12-20 even
Solve One-Step Multiplication
and Division Equations
1. What’s your variable?
2. What happened to your variable?
3. How do you un-do that?
O Do the opposite operations
O Remember the Integer Rules from Chapter 2
p. 218 #16-22 even
Solve Equations with
Rational Coefficients
O Multiplicative Inverse/ Reciprocal
If there’s a fraction before a variable,
You gotta multiply it by the reciprocal!
O If there is a decimal before a variable, divide
both sides by that decimal.
p. 224 #22-32 even
Solve Two-Step Equations
O Undo the operations in the REVERSE order
of the Order of Operations
1. Undo any addition and subtraction
2. Undo any multiplication and division
O You are working to isolate the variable
O Just remember the rules for the one-steps
and remember the integer rules
p. 233 #12-20 even
Solve Equations with Variables
on Both Sides
1. Combine all variables to one side of the
equation using addition or subtraction
2. Combine all numbers to the other side of
the equation using addition or subtraction
3. Use multiplication or division to isolate the
variable
O This is called “COMBINING LIKE TERMS”
p. 238 #20-28 even
Solve Inequalities by
Addition or Subtraction
O Solve the same way as one-step equations
O The symbol will be >, <, ≤, ≥
O Solutions can be graphed on a number line
where <, and > have an open circle and , ≤,
≥ use closed circles
p. 247 #18-26 even
Solve Inequalities by
Multiplication or Division
Song!:
Only if you MULTIPLY by a negative number
(negative number)
Only if you DIVIDE by a negative number
(negative number)
You switch the inequality, You switch the
inequality, You switch the inequality
p. 252 #18-28 even
Chapter 5:
Proportions and Similarity
O Rates/ Unit Rates
O Proportional and Nonproportional
O
O
O
O
Relationships
Solve Proportions
Scale Drawings
Similar Figures
Perimeter and Area of Similar Figures
Rates/ Unit Rates
O Ratio (comparing 2 numbers)
O Rate (comparing with units)
O Unit Rate (comparing a number to 1)
O Be able to find the best deal!
p. 269 #12-16 even
Proportional & Nonproportional
Relationships
O Proportional: have a constant ratio
O Nonproportional: do not have a constant
ratio
O Simplifying of ratios
O Tables
p. 274 #5-8 all
Solve Proportions
O Two equivalent ratios
O A variable in one of the four “positions”
O Use cross multiplication to solve
O Be able to WRITE a proportion AND solve it
p. 279 #10-20 even
Scale Drawings
O Scale Drawings
O Scale Model
O Scale
O Scale Factor
O Be able to use a scale within a proportion to
find the missing measurement of something
p. 287 #2-7 even
Similar Figures
O Figures that have the same shape but NOT
the same size
O Be able to find the missing measurement of
a figure by finding the scale
O Use a proportion to solve
p. 297 #5-10 all
Perimeter and Area
of Similar Figures
O Perimeter- if two figures are similar, you can multiply
the original perimeter by the scale factor to get the
new perimeter
O New P = Old P (scale factor)
O Area- if two figures are similar, you can multiply the
original area by the scale factor SQUARED to get the
new area
O New A = Old A (scale factor)2
p. 301 #5-10 all
Look at the Pencast on these
questions.
Chapter 6:
Percent
O Percent of a Number
O Percent and Estimation
O Percent Proportion
O Percent Equation
O Percent of Change
O Sales Tax, Tip, Discount
O Simple Interest
Percent of a Number
O Find the percent of the number two possible
ways:
Write the percent as a fraction then multiply
2. Write the percent as a decimal then multiply
1.
O Be careful when you have decimals or
fractions WITHIN the percentage:
6.25% = 0.0625 AND 0.25% = 0.0025
p. 322 #24-30 even
Percent and Estimation
O Round numbers BEFORE you do the
multiplication.
O Find “compatible numbers”…numbers that
are easy to multiply in your head.
O Change numbers like 23% to 25% or 789 to
800
p. 328 #23-28 all
The Percent Proportion
O Using a proportion to find a PERCENT, a
PART, or a WHOLE
O Look at your FOLDABLE
O Part – IS
O Whole- OF
p. 335 #8-16 even
The Percent Equation
O Using an equation to find the PERCENT,
PART, or WHOLE
O part = percent (whole)
O Part – IS
O Whole – OF
p. 340 #14-22 even
Percent of Change
O Finding a percent of increase or a percent of
O
O
O
O
decrease
Write a ratio/fraction
Numerator is the difference in the numbers
Denominator is the original amount
Once you have your ratio, divide and get a
decimal. Change that decimal to a
percentage
p. 297 #5-10 all
Sales Tax, Tip, Discount
O Find the percentage of the price by solving a
multiplication problem
O Basically multiply the price by the percent (in
decimal form)
O Add or subtract to the original price to find
the final price
p. 353 #10-14 all
p. 357 #6-12 even
Simple Interest
O Principal
O Rate
O Interest
O I = prt
O Plug it in, Plug it in (and multiply)
O Make sure you change all the percentages
and months to decimals
p. 361 #8-16 even