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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 Standard form Graph. State the slope, x- and y-intercepts. 10 5 -10 -5 5 -5 -10 10 2x + 5y = 20 Standard form Graph. State the slope, x- and y-intercepts. 10 5 -10 -5 5 -5 -10 10 3x – 2y = 5 Standard form Write the following in standard form. y = 2x + 5 Standard form Write the following in standard form. 2 y x2 3 Solving Systems of Equations: By Graphing Solve the given system by graphing. 10 5 -10 -5 5 -5 -10 10 x + y = -3 x – y = 13 Solving Systems of Equations: By Graphing Solve the given system by graphing. 10 5 -10 -5 5 -5 -10 10 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 Linear Inequalities 10 5 -10 -5 5 -5 -10 10 Graph 2x - 3y ≤ 6 Linear Inequalities 10 5 -10 -5 5 -5 -10 10 Identify the linear inequality shown. Systems of Linear Inequalities 10 5 -10 -5 5 -5 -10 10 Graph 2x + 3y ≤ 6 x – 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. 8 4 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 x x 1 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( x 4) 2 x 4 x 6 Solving Multi-step Equations 4( x 3) x 11 3x Equations with Fractions or Decimals 2 3 1 x x 3 4 2 Equations with Fractions or Decimals 6.5n 3.9 2.9n Writing Inequalities from Graphs y>0 Writing Inequalities from Graphs x≤3 Solving Inequalities 1 3x 8 x Solving Inequalities 2x x 5 3 4 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). Equations of Lines 10 5 -10 -5 5 -5 -10 10 Find an equation of the graphed line. Equations of Lines 10 5 -10 -5 5 -5 -10 10 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 1 x 1 4 5 Solving Equations 4x 3x 5x 16 Solving Multi-step Equations 5( x 30) 10 175 Solving Multi-step Equations 3 ( x 96) 7 4 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 3 2 2 2(3) 9 3 (3 4) 3 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 mean points scored by the starting players? Operations with Integers 2 2 6 2 1 2 Exploring Negative Numbers Simplify the following expression if a = -2 and b = -3. a 2ab b 2 2 Operations with Variable Expressions 3x 2 x 4 2( x 2 x 3) 2 2 Operations with Variable Expressions 3( x 4) 2( x 2) 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