ANSWER KEY Name: Algebra 1 Benchmark Review study guide is due on test day! Test Date: A-Day 2/7 Checklist Do I understand? Unit 1 Solving Equations and Inequalities Two Step Equations Properties of Real Numbers Proofs for Equations Solving Multi-Step Equations Solving Linear Inequalities Solving & Graphing Compound Inequalities Unit 2 Word Problems Word Problems with Proportions Word Problems with Equations Word Problems with Inequalities Set Up and Solving Answer must be in sentence form or have appropriate units! Unit 3 Literal Equations Solving Literal Equations Function Form y as a function of x Unit 4 Functions and Linear Graphs Introduction to Functions Vertical Line Test Functional Notation Graphing with a Table of Values Graphing using X & Y Intercepts - Cover Up Method Slope remember formula! Graphing in Slope-Intercept Form (y=mx+b) Unit 5 Writing Equations of Lines Given Slope and Y-Intercept y= mx + b Using Point-Slope Form y y1=m(x - x1) Using Standard Form Ax + By = C Parallel same slope Perpendicular opposite reciprocal slope Unit 6 Direct and Inverse Variation Direct Variation know formula! Inverse Variation know formula! Solving for a missing variable of a direct or inverse variation Writing the equation of a direct and inverse variation Word problems using variation Unit 7 Solving Systems of Equations and Inequalities Graphing Systems Using Substitution Using Elimination Word Problems set up and solve! Answer key to study guide can be found here or on my website! Extra practice can be found here! Answers to extra practice can be found here!
You must fill in this information on your own! I will be checking for it when you turn your review sheet in to me! Formulas to know! To find slope: Point-Slope: Parallel lines have the slope. Perpendicular lines have slopes! Horizontal lines have a slope of. Vertical lines have an slope. Slope-intercept form: Standard form: When multiplying or dividing an inequality by a negative you must! Domain represents the - values and range represents the - values. A relation is NOT a function if the repeat. Direct Variation: y = k = Inverse Variation: y = k =
Algebra Benchmark Review HW The benchmark is a cumulative summative, meaning it covers all material that we have learned in quarters 1 and 2! It is an indicator of how well you will do on the SOL exam in May. 1. Simplify the following expression if x = 1 3 x 2 + 2x 4 2. Find the solution to the following system using elimination. 3x + 5y = 11 { 4x 3y = 5 3. Examine the inequality that has been solved below: Step 1: 10 < x + 6 Step 2: 10 + ( 6) < x + 6 + ( 6) Step 3: 4 < x + 0 Step 4: 4 < x What property was used between step 1 and 2? 4. What is the slope of the line? 1 y = x + 7 3 The slope is NOT 1 3 or 1! 5. What is the slope of the line? 4x + 6y = 3 The slope is NOT 4! 6. Solve for x. Make sure you get an integer answer! 3(x 6) + 4 = 25 6(x + 2)
7. Graph the following inequality: 2x + 3y 6 8. Solve the following inequality and write two solutions. 3(x + 6) > 2(x 4) 9. Emma has 36 coins worth $7.00 in quarters and nickels. Write a system and solve for how many coins of each type Emma has. 10. Given the following system of inequalities, which points would work as a solution? y < 2x + 5 { 3x y 7 (0,0) (3, 2) (4, 3) ( 2, 1) ( 2, 6) ( 3, 0) 11. What is the slope of the graph below? 12. Solve the following equation for p. (Hint: Backwards PEMDAS!) K = p+c 2 2k = p + c 2k c = p p = 2k c
13. Write the equation of the graphs below. 14. Solve the following equation for x. 3x 6 7 = 12x+6 14 15. Write an equation in slope intercept form that goes through the given two points. a. ( 4, 3) and ( 4, 2) Undefined slope, use VUX! x = -4 b. (6, 2) and ( 7, 4) m = 6 13 y 4 = 6 (x 7) 13 16. a. What is a root of an equation? A root is an x-intercept, or the point(s) where the graph crosses the x-axis. Therefore, we let y=0. b. Find the root of f(x) = 2 x + 6. 3 y = 6 10 x + 13 13 17. When f(x) = x 2 + 2x + 6 find f( 4). 18. Solve and graph the inequality below: 8 < x 4 5 Be careful because x is negative!
19. Given 5x + 7y = 4, write the equation of one line that would be parallel and one line that would be perpendicular. Answers will vary. 20. The points below represent a direct variation. Write the direct variation equation. {(2, 12), ( 3, 18), (1, 6)} Parallel: Your equation must have a slope of 5 7. Perpendicular: Your equation must have a slope of 7 5. 21. Determine the domain and range for each relation. Then, determine if it is a function. a. {( 3, 5), (5, 5), ( 3, 2), (5, 3)} 22. Name the x-intercept and y-intercept for all the graphs shown below. a. b. b. c. c. d. d. e.