1617 GSE Alg. I Reasoning w/linear Equalities & Inequalities Touchstone

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1 High School HS Algebra GSE Alg. I Reasoning w/linear Equalities & Inequalities Touchstone 1. A number of apples were shared evenly among 4 students. Each student was also given 2 pears. Each student received a total of 6 pieces of fruit. Let a represent the total number of apples. Which equation can be used to find the total number of apples? A. B. a / 4-2 = 6 a/ 4 +2 = 6 C. 4a + 2 = 6 D. 4a - 2 = 6 2. A tour bus driver takes home 75% of the salary he earns and gives 60% of his tips to the tour guides on the bus. He took home $980 last week from salary and tips. Let s represent the driver's salary and t represent the total amount of tips the driver earns. Which equation can be used to find the possible amounts of his salary and tips the driver took home last week? A. 0.75s + 0.4t = 980 B. 0.75s 0.4t = 980 C. 0.75s t = 980 D. 0.75s 0.04t = Nicole gets paid $120 each week and $35 for every iphone that she sells. Which of the following equations represents her weekly income? A. y = 120x + 35 B. y = x C. y = -35x D. y = 35x Which BEST describes the system? -3x + y = 12 y = 3x - 2 A. The system cannot be solved B. One solution; lines intersect C. Two solutions; lines are parallel D. No solution; lines are parallel

2 5. Solve the equation for y. 2x - 4y = 4 A. y = 2x - 2 B. y = 1 / 2 x - 1 C. y = 1 / 2 x + 2 D. y = x Which of these properties correctly justifies the missing step in solving the equation above? A. Distributive Property B. Commutative Property of Addition C. Commutative Property of Multiplication D. Division Property of Equality 7. Solve for x in the following equation: y = mx + b A. x = y - m / b B. x = y / m + b C. x = y-b m D. x = y + b / m 8. Solve the inequality 4-5x < 14. A. x < -2 B. x > -2 C. x < -50 D. x > -50

3 9. Which of the following would be the most appropriate first step if you wanted to solve this system of equations using elimination? 2x + y = 11 x + 3y = -18 A. Multiply the second equation by 2 B. Multiply the second equation by -2 C. Multiply the second equation by 3 D. Multiply the second equation by What is the solution to the linear system? y = -x + 7-2x + 2y = 6 A. (-2, 9) B. (2, 5) C. (2, 9) D. No solution 11. Ed and Greg are working on their math homework. Ed says (2, 0) is a solution to y < 4x - 8. Greg disagrees. Who is correct and why? A. Ed is correct because when he plugged (2, 0) into the expression it resulted in a true statement, 0 = 0. B. Ed is correct because when he graphed the expression, (2, 0) was on the boundary line so it is a solution. C. Greg is correct because when he plugged (2, 0) into the expression it resulted in a false statement 0 < 0. D. Greg is correct because when he graphed the expression, (2, 0) was not on the boundary line so it is not a solution.

4 12. The graph represents the prices of 2 taxis. According to the graph, when does it make more sense to take the Atlanta Taxi Inc. cab and why? A. You will take the Atlanta Taxi Inc. cab when you are going less than 3 miles because it will be faster. B. You will take the Atlanta Taxi Inc.cab when you are going more than 3 miles because it will cost less. C. You will take the Atlanta Taxi Inc. cab when you are going less than 3 miles because it will cost less. D. You will take the Atlanta Taxi Inc. cab when you are going more than 3 miles because it will be faster.

5 13. Which graph represents the solution to the system of linear inequalities? 3x - 4y 16 4x + 3y < 9 A. B. C. D.

6 14. An arithmetic sequence has a common difference of 4 and the 3rd term is 10. What is the 6th term? A. 14 B. 22 C. 34 D A function is given a recursive form of a n = a n with a first term of 25. Which function represents the sequence? 16. A. f (x) = x - 3 B. f (x) = 25x - 3 C. f (x) = -3x + 22 D. f (x) = -3x + 28 Determine the range of the function. A. y -2 B. x -2 C. No solution D. All real numbers

7 17. Describe the end behavior of the function. A. As x -, y As x, y B. As x -, y - As x, y C. As x -, y - As x, y - D. As x -, y - As x -, y The function h (n) represents the number of hours it takes to assemble n engines in a factory. What is a reasonable domain for the function h (n)? A. The nonnegative rational numbers B. The nonnegative real numbers C. The nonnegative integers D. The real numbers

8 19. Compare the following functions to determine which has a greater rate of change. A. Function1 B. Function 2 C. The functions have the same rate of change D. The functions do not have a rate of change 20. Given the arithmetic sequence 2, 5, 8, 11,... find a n A. a n = 3n + 1 B. a n = 3n - 1 C. a n = -3n + 5 D. a n = 2n Which of the following does NOT represent an arithmetic sequence? A. 3, 4, 5, 6, 7 B. -1, 1, 3, 5, 7 C. 2, 4, 8, 16,... D. 10, 6, 2, The ordered pair (5, 9) is a solution to which linear system? A. x + y = 14 -x + 2y = 11 B. -x + y = 4 2x - y = 9 C. -x + y = 4 2x + y = 19 D. x + y = 14 2x - 2y = 14

9 23. You are taking a test worth 100 points. There are a total of 32 questions consisting of five-point questions and two-point questions. How many five-point questions are on the test? A. 10 B. 12 C. 15 D What is the x-coordinate at the point of intersection for f (x) and g (x)? f (x) = 3x + 50 g (x) = 2x 18 A. -35 B. 3 C. -68 D For the given linear function, what are the intercepts? A. (0, 6) and (-6, 0) B. (5, 0) and (-5, 0) C. (0, 5) and (-5, 0) D. (6, 0) and (-5, 0)

10 26. Two sisters are saving money for summer vacation. Above represents the growth of each sister's savings account. Comparing the growth of each account as lines on a graph, in which week will the lines intersect? A. Week 4 B. Week 6 C. Week 10 D. Week If a system of linear equations has no solution, what do you know about the graphs of the equations? A. The graphs coincide B. The graphs intersect C. The graphs are parallel D. The graphs are perpendicular

11 28. What is the solution to the system of equations? A. (1, 0) B. (0, 3) C. Infinitely many solutions D. No solution 29. Which of the following expressions represents A = 4πr 2 solved for r 2? A. r 2 = A/ 4π B. r 2 = 4A/ π C. r 2 = 4πA D. r 2 = 4π/ A 30. {4, 6, 8, 10,...} What is the function notation form of the sequence? A. f (x) = 2x B. f (x) = x + 2 C. f (x) = 2x + 2 D. f (x) = 4x + 2