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1 Algebra 1 Name _______________________________ Semester 1 Review Date __________________ Fill in the following information (Concept Review) 1. How would you describe the slope of a line? 2. What is the formula to find slope given two points of the line? 3. How do you find the slope of a line from an equation in standard form? 4. What is the equation of a horizontal line? b. State its slope. 5. What is the equation of a vertical line? b. State its slope. 6. What two pieces of information are needed to write the equation of a line? a. b. 7. What is true about parallel lines in regard to their slope? 8. What is true about perpendicular lines in regard to their slopes? 9. Define a function and describe a “test” that can be used to identify a function. 10. When solving inequalities, we use solving equation skills to get the solution set. What “extra” rule must we remind ourselves of when solving inequalities? 11. How do you solve a system of equations? 12. What is the x-intercept for a graph? 13. What is the y-intercept of a graph? 14. Define the domain for a graph: 15. Define the range for a graph: 1 2 Functions and Relations Review: 1. 2. Determine whether the relation is a function. Antonio’s age (years) 11 12 13 14 15 16 Antonio’s height (inches) 60 61 62 67 69 69 Give the domain and range of the relation. x y 2 5 8 17 0 0 –3 –5 3. a. f(3) Given that f(x) = 2(1 – x) and g(x) = b. g(-3) 2 , find: 1 x c. g(1) d 3 f( ) 4 f. Find x if f(x) is ‒6 e. If f(x) = 4, find x. Matching Match each vocabulary term with its definition. a. domain b. x-axis c. range d. relation e. dependent variable f. independent variable g. y-axis h. function ____ 4. a type of relation that pairs each element in the domain with exactly one element in the range ____ 5. a variable whose value determines the value of the output, also known as the input of a function ____ 6. the set of output values of a function or relation ____ 7. the set of input values of a function or relation ____ 8. a set of ordered pairs ____ 9. a variable whose value depends on the value of the input, also known as the output of a function Linear Equations Review: Graph and label key points: x and y intercepts. 1. ‒2x + 4y = ‒8 2. y = 5x 3. x = 5 4. y = ‒3 5. y = ‒0.6x + 8 2 3 Write each equation in slope- intercept. 3 6. m = , y intercepts (0, ‒ 2) 4 7. through (−3, 4) and (2, −1) Write and equation in standard form (ax + by = c) for each line described: 8. passes through (−3, 2), and a zero slope 9. x-intercept is -1 and y-intercept is 3 10. parallel to 𝑥 – 2𝑦 = 5 and passes through (2, −1) Find the x-intercept and the y-intercept of a line from its linear equation. Graph a line by finding and connecting its x and y-intercepts. 11. Find the x and y-intercepts 12. Find the x and y-intercepts and graph 3x 4 y 8 . 2 of y x 12 . 5 Calculate slope given two ordered pairs. Find slope by counting from point to point on a linear graph. 13. Find slope between (−1, 5) and (−7, 9). 14. What is the slope of the line sketched below? Solve for x or y given slope and two ordered pairs with one x or y missing. 15. Find y such that the slope between (2, 𝑦) and (5, −3) is 7. Know special cases of slope for horizontal and vertical lines. 16. What is the slope of a vertical line? 17. What is the slope of y 4 . 3 4 Systems: See the other review and the one for the quiz on 12/12 Mixed Review Simplify each expression. 1. 15 12 32 21 3. -5x 2 (3x 3 y 4 ) 2 2. 8m – 3[2(-3m 2 + 5m + 8) + 2m] – (6 – 3m + m 2 ) 4. (2c – 3)(c 2 - 2c + 5) 5. (5 – 3a) 2 Evaluate the expression if x = ‒6, y = 4, and z = ‒2 6. x + 2y 7. z – x 8. x 9. 2x + y 10. x y 11. y 2 z 2 Solve each of the following: 12. 7 – 2x = 3 13. 3(4 – 3x) = x – 8 15. 2(x – 1) = 5 – (3 – 2x) 16. ‒3[2a +3(5 – 2a)] = a – [6 – 4a] 14. 3 a + 3 = 2a – 11 5 Simplify: 17. 4 x 2 y(3 y 2 4 xy 3 ) 18. (c – 2)(2c – 3) 20. (10n + 3)(10n – 3) 21. 7 4 32 35 22. −2[8 – (−3) 2 ] + 2 + 2 3 23. 8𝑚 – 3[2(−3𝑚 + 8) + 2𝑚] + 6 19. (5 – 3a) 2 4 5 Graph the following and label x-intercepts and y-intercepts. 2 26. ‒2x + 4y = 8 27. f(x) = x ‒3 3 Domain: Range: Domain: Range: 28. x = ‒3 Domain: Range: 29. y = 2 Domain: Range: 5