Integrated Algebra Review Packet

Quarters 1,2,3

Unit 13: Systems of Equations, Part 2

Unit 12: Quadratic Functions

Unit 11: Algebraic Fractions

Unit 10: Factoring Polynomials

Unit 9: Shapes

Unit 8: Polynomials

Unit 7: Exponents

Unit 6: Systems of Equations Part 1

Unit 5: Rates

Unit 4: Inequalities

Unit 3: Graphing Linear Functions

Unit 2: Solving Equations

Unit 1: Beat the Basics

Unit 13: Systems of Equations Part 2

o Topic 1: Graphical Solutions

o Learning Target 1: Solving a system (linear –quad or quad) graphically.

o Topic 2: Algebraic Solutions

o Learning Target 1: Solving a system (linear –quad or quad) algebraically.

Unit 12: Quadratic Functions

o Learning Target 1: Solve quadratic equations

o Learning Target 2: Find the vertex of a quadratic algebraically

o Learning Target 3: Find the roots of a quadratic algebraically

o Learning Target 4: Graph a quadratic from a table or from the vertex and roots

o Learning Target 5: Understand the relationship between the value of a and the shape of the graph

Describe the relationship between the value of a and the parabola

when will the parabola be up like a cup?_________________________________________________

when will the parabola be down like a frown?_____________________________________________

when will the parabola be skinny? ______________________________________________________

when will the parabola be wide?________________________________________________________

Learning Target 6: Solve quadratic equations using the quadratic formula:

Unit 11 Algebraic Fractions / Rational Expressions

o Topic 1: Algebraic Fractions

Learning Target 1: evaluate an algebraic fraction for a given value

Learning Target 2: find the excluded values

Learning Target 3: simplify an algebraic fraction by factoring and canceling

Learning Target 4: Adding and subtract algebraic fractions.

Learning Target 5: Multiply and Divide algebraic fractions

Unit 10: Factoring

Topic 1: 1 Step Factoring:

Learning Target 1: Factor polynomials that have a greatest common factor (gcf)

Learning Target 2: Factor quadratic trinomials (diamond and dots)

Learning Target 3: Factor quadratic trinomials when a does not equal one (acgc)

Topic 2: Two Step factoring

Learning Target 1: Factor polynomials with multiple factors (two step factoring)

Unit 9:Shapes

o Topic 1: Compound Shapes

Learning Target 1: Find the area and perimeter of compound shapes

Learning Target 2: Find the volume and surface area of three dimensional shapes

Learning Target 3: Find the values of the Mathematical Error of given values: absolute, relative and percent

a. Sally guesses that she weighs 135 but the doctor tells her she weighs 131. Find the absolute,

relative and percent error of her weight.

b. Mick estimate the dimensions of his yard to be 25ft by 40 ft. After measuring he sees that the

actual measurements are 28ft by 37 ft. Find the absolute, relative and percent error of the area of

the yard.

c. John thinks that his fish tank holds 25 cubic feet of water. He measured the tank dimensions and

got : l =- 4.5 ft, w= 2 ft and h = 1.1 ft. Find the absolute, relative and percent error for the volume of

the fish tank.

Unit 8: Polynomials

o Topic 1: Polynomials

Learning Target 1: Name polynomials by the number of terms and degree

Learning Target 2: Add and subtract polynomials

Learning Target 3: Multiply and Divide polynomials

7: Exponents

o Topic 1: Exponent Laws

Learning Target 1: Simplify an exponential expression using the 5 exponent laws

o Topic 2: Exponential Growth and Decay

Learning Target 1: Use the growth/decay formula to solve problems.

1. The bacteria count increases exponentially at a

rate of 11.5% an hour. If a piece of candy has 9

bacteria on it now, now many where there be

in:

a. 12 hours?

b. 2 days?

2. The value of a boat depreciates at a rate of 8%

a year. If the boat was originally worth $18,500

how much will it be worth in:

a. 3 years?

b. A decade?

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Unit 6: Systems Part 1

o Topic 1: Solving Systems of Equations

Learning Target 1: solve a system of equations using substitution

Learning Target 2: solve a system of equation using elimination

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Learning Target 3: decide which method of solving is more appropriate

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o 2: Graph Linear Systems

Learning Target 1: Graph a system of equations and identify the solution

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Learning Target 3: Find the solution of a linear system using a graphing calculator

Learning target 4: graph a system of linear inequalities and identify the solution

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o Topic 3: Modeling with Systems

Learning Target 1: create a model of linear equations that models a given situation

Unit 5: Rates

o Topic 1: Basic Rates:

Learning Target 1: Use the formula d=rt to solve rate problems.

a) Lance biked 50 miles in 7 hours. What is his

rate in miles per hour?

b) Michael swam at a rate of 1.1 m/sec for 100

seconds. How far did his swim?

c) Amy walked 1200m at 50 meters per minute.

How long was she walking for?

d) Chris is a cross country runner. If he ran 25

miles at an average rate of 4.5 mi/hr how long

was he running?

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Learning Target 2: Find or use the unit rate for a given situation.

a) A large pizza from Papa’s Pizza has 12 slices and

costs $15.99. Find the unit rate.

b) The unit rate for bottled water is $0.35 a

bottle. If a case of water bottles has 24 bottles

in it, how much will it cost?

o Topic 2: Converting Rates

Learning Target 1: Convert a value using conversion factors

a. 5 gal = ________ tbs b. 150 cm = _____in

c. 15,000 feet = _______ km d. 200 tsp = ______ cups

Learning Target 2: Convert a rate using conversion factors

a) Jim can run 10 km/hour. Convert this to feet

per minute. (round your answer to the nearest

whole number)

b) A bird can fly 12 feet per second, convert this

speed to miles per hour. Round to the nearest

hundredth.

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Unit 4: Inequalities

o Topic 1: 1 Variable Inequalities

Learning Target 1: Solve and graph one variable inequality

Learning Target 2: Solve and graph one variable compound inequality

Learning Target 3: Write the equation of a one variable inequality given its graph.

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o Topic 2: 2 Variable Inequalities

Learning Target 1: Graph a two variable inequality given the equation of the inequality in any form.

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Learning Target 2: Write the equation of a two variable inequality given its graph

o Topic 3: Modeling Inequalities

Learning Target 1: Write an inequality that models a realistic situation.

1. Tommy is saving up to buy a new car. He already has

$600 saved up and is working afterschool to earn extra

money. He gets paid $14 an hour and needs $3500 for

the car. How many hours does he need to work to have

enough to buy the car?

a. Write an inequality that describes this

situation. Be sure to define your variables

b. Solve your inequality to answer the question. Be

sure your answer is in sentence form.

2. Sally is going on a shopping spree and has a $250

budget. She already spent $98 on a new dress and

$34on a pair of jeans. She also wants to buy a few

shirts that cost $28 each. What is the maximum

number of shirts she can buy and still be in her budget.

a. Write an inequality that describes this

situation. Be sure to define your variables

b. Solve your inequality to answer the

question. Be sure your answer is in sentence form.

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Unit 3: Graphing Lines

o Topic 1: Graphing Lines:

Learning Target 1: Graph a line given two points on the line:

a. The points (-4,1) and (0,-2) are on a line. b. The points (5,-3) and (-2,-3) are a line.

Plot the line: plot the line:

Learning Target 2: Graph a line given one point and the slope of the line.

a. A line has m = -2 and the point (-3,2) is on the line b. A line has m = 2/3 and the point (-4,0) is on the line

Plot the line: plot the line:

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Learning Target 3: Graph a line given the equation of the line in slope –intercept form.

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Learning Target 4: Graph a line given the equation not in slope intercept form.

Learning Target 5: Find the slope of the line given the graph of the line.

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Learning Target 6: Find the slope of the line given two points.

o Topic 2: Writing the equations of Lines:

Learning Target 1: Write the equation of the line given its graph.

Learning Target 2: Write the equation of the line give one point and the slope of the line.

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Learning Target 3: Write the equation of the line give two points on the line.

Unit 2: Solving Equations

o Topic 6: Solving Equations:

Learning Target 1: Be able to solve any equation of one variable

Combining like terms

Variables on both

sides of the equals

sign

Cross multiplication

Distribution

Equations with

fractions

See solving equations practice sheet at the end of the packet for problems

Learning Target 2: Solve a literal equation for a given variable.

a. the formula for the perimeter of a rectangle is

P = 2l+2w. Solve the formula for w.

b . Consider the equation

Solve the

equation for a.

o Topic 7:Modeling Equations:

Learning Target 1: Write and solve an equation that models a realistic situation.

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o Topic 8: Properties:

Learning Target 1: Identify and use the properties of real numbers using integers and

variables.

Unit 1: Beat the Basics

o Topic 1: Signed Numbers and Order of Operations

Learning Target 1: Be able to perform mathematical operations with positive and negative numbers.

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Learning Target 2: Be able to simplify multistep expressions using order of operations

o Topic 2: Fractions

Learning Target 1: simplify improper fractions

Learning Target 2: perform all mathematical operations with fractions

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Learning Target 3: complete problem solving that involves fractions.

o Topic 3: Decimals and Percents

Learning Target 1: perform mathematical operations with decimals

Learning Target 2: convert decimals to percents and visa versa

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Learning Target 3: complete problem solving that involves decimals and percents

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SOLVING EQUATIONS: