Review Systems of Equations Standard: A.CED.3; A.REI.6

Transcription

1 Name: Review Systems of Equations Standard: A.CED.3; A.REI.6 Hour: Fundamentals 1. The solution of a system is a. Line Coordinate Point Plane 2. For a point to be a solution to a system, it must make equation(s) true. One Both Neither 3. Graphically and visually, the solution to a system is the of the two lines. Y-Intercepts X-Intercepts Slope Intersection 4. Parallel lines have solution(s). One Two No Infinitely Many 5. Infinitely many solutions means that the two lines are. Parallel Intersecting the same 6. There are 3 ways to solve a system:,, and. S Examples Circle the error in each problem. Explain why it is incorrect and what should have been done. You do not need to solve all the way. 7. Elimination x + 2y = 18 3x 5y = Substitution 3y = 3x 5 2x = y + 8 3y = 48 y = 16 3x + 2( 16) = 18 3x 32 = 18 3x = 50 x = 50 3 ( 50 3, 16) y = 3(y + 8) 5 y = 3y y = 3y y = 19 y = x = x = 3 2 x = 3 4 ( 3 4, 19 2 ) 9. Graphing y = 1 x 6 2 2y 3x = 6 ( 2, 6)

2 Practice Solve each system using the method indicated. If no method is indicated, you may choose any method empty coordinate planes are provided at the end. Check your answers by plugging your solution point back in. When possible, verify your answers using the intersection feature of the graphing calculator (Graph functions, 2 ND, Trace [Calc], Intersect, Enter 3 times) 10. Substitution x = 3y + 1 2x 3y = Elimination 5x + y = 10 x + y = Graphing y = 2x 8 y = 2 3 x

3 13. y = 3 x y = 3x x + 4y = 24 y = 3 4 x x 3y = 6 2x + y = 12

4 Word Problems Write and solve a system for each situation. 16. Jack and Jill went up the hill to fetch some pails of water. Jack s pail holds twice what Jill s pail holds. Together, they can carry 9 gallons of water. How much water do Jack and Jill s pails each hold? 17. Benny is going to the bakery to pick up 37 desserts, cookies and cupcakes, which he ordered for $63. How many cupcakes and cookies did Benny purchase if cookies cost $1.50 and cupcakes cost $2? 18. On Tuesday Johnny and Susie bought a hot chocolate and two apple turnovers for $4.75. The following week, they bought 2 hot chocolates and an apple turnover for $5. How much does an apple turnover and hot chocolate each cost? Solutions Determine if the given point is a solution to the system. 19. (2, 4) y = 2x 2x = 3y (13, 10) 2x + y = 16 3y = 9 3x Extra Coordinate Planes

5 Name: Review Inequalities Standard: A.CED.3; A.REI.1; A.REI.3; A.REI.12 Hour: Fundamentals 1. > 2. < Flip the inequality sign when you or by a. 6. These signs have an open dot, or dashed line: & 7. These signs have a closed dot, or solid line: & 8. Plug in a to determine where to shade. I Examples Identify the error in each problem. Explain why it is incorrect and what should have been done. You do not need to solve the entire problem. 9. 5x 2x 12 3x 12 x y + 8 > 20y 16 8 > 8y > 8y 3 > y 11. y 4 3 x x + 3y < 24 3 Practice Solve and graph each inequality on the number line or coordinate plane provided x + 9 > 4 3 x x (4 + x) 7x + 10

6 < x < x y 3x x 6y < y < y > 3 2 x + 1 y 2x + 5 Write an inequality for each graph

7 Word Problems Write and/or solve and graph an inequality or system of inequalities for each situation. 23. You can be no more than 48 tall to play in the play place. 24. The temperature of meat must be at least 165 degrees for safe consumption. Inequality: Inequality: 25. The budget for the party you are having is $60 and you need to provide pizza and breadsticks. Pizzas are $5.00 each and breadsticks are $2.50 each. (When graphing consider, which values are possible? Positive? Zero? Negative?) 26. Valentine s Day is coming up and you want to get a gift for each of your 9 friends. Chocolates are 75 cents each and cards are $1.25 each. But you only have $10 left from Christmas. (System of Inequalities) 27. Circle all points that are a solution to the system of inequalities. y 2 x 8 3 4x y < 18 ( 5, 7) (1, 9) (0, 0) (5, 2)

8 Name: Review Functions & Families Standard: F.IF1; F.IF2; F.IF.7 Hour: A significant part of this review is accessed via Quizlet (digital flashcards and study aids). If you do not have access to Quizlet (smartphone or computer), let Ms. Heizer know. Function Families Fundamentals 1. A relation is a function if it passes the test. 2. In a table, there should be exactly y-value for every x-value, even if the x-values repeat. 3. Another way to represent y is to write. 4. In the example f(3 a), the input is. 5. To create a table in your calculator, first enter the function into Y=, then press (table). 6. functions have a common first difference. 7. Quadratic functions have a common. 8. functions have a common ratio. F Examples Identify the error in each problem. Explain why it is incorrect and what should have been done. You do not need to complete the entire problem. 9. f(x) = 3 x + 11; f(6) 2 f(6) = 3 (6) f(6) = f(6) = f(x) = 3x 1; f(x) = 14 f(14) = 3(14) 1 f(14) = 42 1 f(14) = f(x) = 2(x + 1) + 7; f(4 a) f(4 a) = 2(4 a + 1) + 7 f(4 a) = 8 a f(4 a) = 8 a + 8 f(4 a) = 16 a 12. Jimmy says that the following relation is a function because none of the y-values repeat. x f(x)

9 Practice Determine whether each of the following relations is a function or not x f(x) x f(x) {(1, 2), (2, 2), (3, 4), (4, 4)} 18. {(7, 1), (0, 7)} Evaluate. 19. f(x) = 2x 7; f( 5) 20. g(x) = 2 x + 8; g(15) h(x) = 3x 6 ; h( 3) 22. f(x) = 2x 2 + x; f(4) 23. g(x) = 4x 12; g(6a) 24. h(x) = 2x; h(5 2a)

10 25. g(x) = 7 x; g(3a + 8) 26. f(x) = 3(x 8) 9; f(6 2a) Solve for x. 27. f(x) = 2x 8; f(x) = h(x) = 3 x + 13; h(x) = g(x) = 3x; g(x) = g(x) = (x + 8) + 3; g(x) = h(x) = 2x + 8; h(x) = 3x 32. f(x) = 9 4x; f(x) = 7x = 2x 2 + x ( 1 3 )x = 1 81

11 Determine whether each table is a linear, quadratic, or exponential function or neither x y x y x y 38. x y Word Problems 39. A cross country runner runs at 9 miles per hour, whose distance is represented by M(h) = 9h. Find M(3). 40. At a frozen yogurt shop, the cost is determined by the weight (in ounces) and is represented by C(w) =.49w Find the weight of the frozen yogurt if C(w) = Over break you earned some extra money by working at your job. Explain what P(36) = 288 means.