Mid Term ReviewBybee & Holloway 7th Grade Math

Fall 2011

What Will It Look Like?O Covers Chapters 1-6O Multiple Choice (scan sheet)O 60 QuestionsO 90 MinutesO No CalculatorO Based on the textbook (like all other

tests)

How Do I Study?O Complete the Mid Term Review Test providedO Review old notesO Study old testsO Memorize rules/formulas O Make notecards with vocabularyO 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 PatternsO Powers and ExponentsO Numerical ExpressionsO Algebraic ExpressionsO PropertiesO SequencesO Square RootsO Cube Roots

Powers and ExponentsO BaseO ExponentO FactorO Exponential Form/ Standard FormO Be able to evaluate powers

p. 27 #18-24 even

Numerical ExpressionsO Order of Operations!!!!O PEMDAS

p. 31 #20-26 even

Algebraic ExpressionsO VariablesO CoefficientsO PLUG IT IN, PLUG IT IN!!!!O Write an expression when given a

situation

p. 36 #8, 14-20 even

PropertiesO CommutativeO AssociativeO IdentityO DISTRIBUTIVE!!!!!! (focus here)O “Justify each step”; know how to use

eachO FOLDABLE

p. 40 #14-22 even

SequencesO SequenceO TermO Arithmetic SequenceO Geometric SequenceO Be able to “Extend” any sequence by

seeing the pattern

p. 47 #10-16 even

Squares & Square Roots

O SquareO Square RootO Cube RootO Radical SignO FOLDABLEO 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 ValueO Coordinate PlaneO Adding IntegersO Subtracting IntegersO Multiplying and Dividing Integers

Absolute ValueO IntegerO Absolute ValueO Number LineO Be able to evaluate expressions with

absolute value

p. 79 #14-18 even#28-32 even

Coordinate PlaneO OriginO x-axis, y-axis/ x-coordinate, y-coordinateO Four QuadrantsO Ordered PairsO Know how to plot points & identify the

quadrant

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Add & Subtract Integers

ADDITION: Same signs, add and keepDifferent signs subtractTake the sign of the larger numberThen, 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- POSITIVEO Different Signs- NEGATIVEO Pay attention to when you have

exponents

p. 107 #20-28 evenp. 112 #24-30 even

Chapter 3:Rational Numbers

O Terminating and Repeating DecimalsO Comparing & Ordering Rational NumbersO Add & Subtract Like FractionsO Add & Subtract Unlike FractionsO Add & Subtract Mixed NumbersO Multiply FractionsO Divide FractionsO Multiply & Divide MonomialsO Negative ExponentsO 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

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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. Must have a COMMON DENOMINATOR2. Add the numerator3. Keep the denominator4. Simplify

O BE CAREFUL WITH THE NEGATIVES!!!!! O All Integer Rules apply here

p. 142 #14-20 evenp. 149 #20-28 even

Add & Subtract Mixed Numbers

1. Add or subtract the fraction2. You might need to rename using the LCD3. Add or subtract the whole numbers4. Simplify

OR5. Change to improper fractions6. Get a common denominator7. Add or Subtract8. Simplify p. 155 #14-24

even

Multiply Fractions1. Change any Mixed # to Improper Fraction2. Multiply the numerators3. Multiply the denominators4. SimplifyO YOU DO NOT NEED COMMON

DENOMINATORS!O Pay attention to those negatives

p. 163 #14-20 even

Divide FractionsO You will have to change any Mixed #

to an Improper FractionO LEAVE, CHANGE, FLIP or…O Multiply by the reciprocalO 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

p. 183 #22-40 even

• Look at the textbook here to review.

• Rewrite using positive and negative exponents

Scientific NotationO Writing really big numbers or really

small numbers in a manageable wayO 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 InequalitiesO Solve One-Step Addition and Subtraction

EquationsO Solve One-Step Multiplication and Division

EquationsO Solve Equations with Rational CoefficientsO Solve Two-Step EquationsO Solve Equations with Variables on Both SidesO Solve Inequalities by Addition or SubtractionO 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 operationO Remember: be careful when given

negatives

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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 operationsO Remember the Integer Rules from

Chapter 2

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Solve Equations with Rational Coefficients

O Multiplicative Inverse/ ReciprocalIf 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.

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Solve Two-Step Equations

O Undo the operations in the REVERSE order of the Order of Operations

1. Undo any addition and subtraction2. Undo any multiplication and divisionO You are working to isolate the variableO 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

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Chapter 5: Proportions and SimilarityO Rates/ Unit RatesO Proportional and Nonproportional

RelationshipsO Solve ProportionsO Scale DrawingsO Similar FiguresO Perimeter and Area of Similar Figures

Rates/ Unit RatesO 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!

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Proportional & Nonproportional Relationships

O Proportional: have a constant ratioO Nonproportional: do not have a

constant ratioO Simplifying of ratiosO Tables

p. 274 #5-8 all

Solve ProportionsO Two equivalent ratiosO A variable in one of the four

“positions”O Use cross multiplication to solveO Be able to WRITE a proportion AND

solve it

p. 279 #10-20 even

Scale DrawingsO Scale DrawingsO Scale ModelO ScaleO Scale FactorO Be able to use a scale within a

proportion to find the missing measurement of something

p. 287 #2-7 even

Similar FiguresO Figures that have the same shape

but NOT the same sizeO 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 Areaof Similar Figures

O Perimeter- if two figures are similar, you can multiply the original perimeter by the scale factor to get the new perimeterO 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 areaO New A = Old A (scale factor)2

p. 301 #5-10 allLook at the Pencast on

these questions.

Chapter 6: Percent

O Percent of a NumberO Percent and EstimationO Percent ProportionO Percent EquationO Percent of ChangeO Sales Tax, Tip, DiscountO Simple Interest

Percent of a NumberO Find the percent of the number two

possible ways:1. Write the percent as a fraction then

multiply2. Write the percent as a decimal then

multiplyO 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 EstimationO 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

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The Percent ProportionO Using a proportion to find a

PERCENT, a PART, or a WHOLEO Look at your FOLDABLEO Part – ISO Whole- OF

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The Percent EquationO Using an equation to find the

PERCENT, PART, or WHOLEO part = percent (whole)O Part – ISO Whole – OF

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Percent of ChangeO Finding a percent of increase or a

percent of decreaseO Write a ratio/fractionO Numerator is the difference in the

numbersO Denominator is the original amountO 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 allp. 357 #6-12 even

Simple InterestO PrincipalO RateO InterestO I = prtO 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