Exam Review

1st Semester

Algebra I

Topics Covered

Chapter 2 – Equations and Functions Chapter 3 – Graphing Linear Equations Chapter 4 – Solving Equations and Inequalities Chapter 7 – Systems of Linear Equations and

Inequalities

Chapter 1 – Using Algebra to Work with Data

Working with Variables and Data Order of Operations Mean, Median, Mode and Graphs Operations with Integers Exploring Negative Numbers Exploring Variable Expressions Applying Variable Expressions Working with Data

Chapter 2 – Equations and Functions

Solving Equations Solving Multi-step Equations Applying Functions Coordinate Graphs Representing Functions Using Graphs to Solve Problems

Chapter 3 – Graphing Linear Equations

Applying Rates Find Slope Equations of Lines Writing an Equation of a Line Modeling Linear Data

Chapter 4 – Solving Equations and Inequalities

Solving Problems using Tables and Graphs Solving Multi-step Equations Equations with Fractions or Decimals Writing Inequalities from Graphs Solving Inequalities

Chapter 5 –Connecting Algebra and Geometry

Ratio and Proportion Scale Measurements Similarity Perimeter and Area Probability Geometric Probability

Chapter 6 – Working with Radicals

The Pythagorean Theorem

Chapter 7 – Systems Linear Eqns and Ineqs

Using Linear Equations in Standard Form Solving Systems of Equations

Graphing Substitution Elimination (Multiplication)

Linear Inequalities Systems of Linear Inequalities

Chapter Seven

Solving Systems of Linear Equations

and Linear Inequalities

-10 -5 5 10

-10

-5

5

10

Standard form

Graph. State the slope, x- and y-intercepts.

2x + 5y = 20

-10 -5 5 10

-10

-5

5

10

Standard form

Graph. State the slope, x- and y-intercepts.

3x – 2y = 5

Standard form

Write the following in standard form.y = 2x + 5

Standard form

Write the following in standard form.

22

3y x

-10 -5 5 10

-10

-5

5

10

Solving Systems of Equations:By Graphing

Solve the given system by graphing.

x + y = -3

x – y = 13

-10 -5 5 10

-10

-5

5

10

Solving Systems of Equations:By Graphing

Solve the given system by graphing.

2x + 5y = 10

3x + y = 15

Solving Systems of Equations:By Substitution

Solve the given system by substitution.-x + 4y = 10

3x + y = 9

Solving Systems of Equations:By Substitution

Solve the given system by substitution. x – 3y = 4

3x – 2y = 6

Solving Systems of Equations:By Elimination

Solve the given system by elimination. 2x – 3y = 4

3x – 2y = 8

Solving Systems of Equations:By Elimination

Solve the given system by elimination. 5x – 2y = -9

3x + 4y = 5

-10 -5 5 10

-10

-5

5

10

Linear Inequalities

Graph 2x - 3y ≤ 6

Linear Inequalities

Identify the linear inequality shown.

-10 -5 5 10

-10

-5

5

10

-10 -5 5 10

-10

-5

5

10

Systems of Linear Inequalities

Graph2x + 3y ≤ 6x – 2y ≥ 5

Systems of Linear Inequalities

Identify the system of linear inequalities shown.

Chapter Six

Working with Radicals

Pythagorean Theorem

Find the missing leg length.

48

Pythagorean Theorem

Is a triangle with side lengths 4, 5, 6 a right triangle? Justify your answer.

Chapter Five

Connecting Algebra and Geometry

Ratio and Proportion

1 2

1x x

Ratio and Proportion

800 children a day ride on the roller coaster, but another 200 are turned away because they're not tall enough. What proportion of the total number of children are turned away?

Ratio and Proportion

At Washington High School, two out of every three students usually buys a yearbook. How many yearbooks should the school plan for if there are 1460 students at the school?

Ratio and Proportion

Methane is a compound consisting of a 1 : 4 ratio of carbon and hydrogen atoms. If a sample of methane contains 1565 atoms, how many carbon and hydrogen atoms are present?

Scale Factor

Nathan plans to include a map in his report on Africa. The map he has is 6 in. wide and 8 in. long. He wants to use a photocopier to enlarge the map so that it fills the width of the page.

What scale factor should he use to make the map 7.5 in. wide?

How long will the enlarged map be?

Similarity

A tree 48 feet high casts a shadow 36 feet long. If a flag pole casts a shadow 12 feet long, the height of the flag pole is

Perimeter and Area

The perimeters of ABC is 2 ft. The perimeter of DEF is 15 in. These two figures are similar.

Find the ratio of the corresponding side lengths.

Find the ratio of the areas.

Probability

A six sided die was rolled 60 times. 1 came up 10 times, 2 came up 9 times, 3 came up 15 times, 4 came up 8 times, 5 came up 7 times. What is the theoretical and the experimental probability of getting an even roll?

Geometric Probability

Find the area of the shaded region.

Geometric Probability

Find the area of the shaded region.

Chapter Four

Solving Equations and Inequalities

Solving Problems using Tables and Graphs

At Homecoming, 2000 tickets were sold at the football game. Adult tickets sold for $7.50 and student tickets solve for $5.00. The total revenue was $11,625.00. How many student tickets were sold? How many adult tickets were sold?

Solving Multi-step Equations

3( 4) 2 4 6x x x

Solving Multi-step Equations

xxx 311)3(4

Equations with Fractions or Decimals

2 3 1

3 4 2x x

Equations with Fractions or Decimals

6.5 3.9 2.9n n

Writing Inequalities from Graphs

y > 0

Writing Inequalities from Graphs

x ≤ 3

Solving Inequalities

xx 831

Solving Inequalities

5

43

2

xx

Chapter Three

Graphing Linear Equations

Applying Rates

How many miles per hour is 44 ft/s?

Applying Rates

How many feet per second is 100 mph?

Find Slope

Find the slope of a line that passes through (-6, -1) and (-1, 4).

Find Slope

Find the slope of a line that passes through (1, -3) and (-2, 8).

-10 -5 5 10

-10

-5

5

10

Equations of Lines

Find an equation of the graphed line.

-10 -5 5 10

-10

-5

5

10

Equations of Lines

Find an equation of the graphed line.

Writing an Equation of a Line

Find the equation of a line that passes through (-6, 2) and has a slope of -2/3.

Writing an Equation of a Line

Find the equation of a line that passes through (-4, 1) and (-6, 2) .

Chapter Two

Equations and Functions

Solving Equations

415

1x

Solving Equations

16534 xxx

Solving Multi-step Equations

17510)30(5 x

Solving Multi-step Equations

7)96(4

3x

Applying Functions

The cost of making T-shirts is $5 per shirt plus $150 for printing supplies. What is the cost of making 100 T-shirts?

Applying Functions

You have moved to a new city and plan to join the Racquet Club. The membership fee is $250 and you must pay $ 7 every time you use a court. If your bill from the Racquet Club was $630, how many times did you play racquetball?

Coordinate Graphs

In the figure, is a rectangle with center at the origin. If the coordinates of A are (3, 4), the coordinates of C are

Representing Functions

If the x-coordinate of a function is three times that of the y-coordinate, the function would be represented by

Using Graphs to Solve Problems

It took Myron 90 minutes, at an average rate of 50 miles per hour, to drive home from a business trip. Which of these graphs best represents Myron’s drive home?

Chapter One

Using Algebra to Work with Data

Working with Variables and Data

Write an algebraic expression to represent the following expression:

the difference in six times a number and nine

Working with Variables and Data

Write an algebraic expression to represent the following expression:

the sum of twice a number and three

Order of Operations

32 23

2( 3) 9 3 (3 4)3

Order of Operations

7 6(8 3)

Mean, Median, Mode, Graphs

Find the mean, median, and mode:

26, 26, 27, 27, 42, 42, 44, 44, 44, 60

Mean, Median, Mode, Graphs

What is the meanpoints scored by the starting players?

Operations with Integers

22 2 6 2 1

Exploring Negative Numbers

Simplify the following expression if a = -2 and b = -3.2 22a ab b

Operations with Variable Expressions

2 23 2 4 2( 2 3)x x x x

Operations with Variable Expressions

3( 4) 2( 2)x x

Applying Variable Expressions

The cost of making T-shirts is $3.50 per shirt plus $150 for printing supplies. What is the cost of making 250 T-shirts?

Working with Data