Part A: Linear Equations and Inequalities

Transcription

1 Part A: Linear Equations and Inequalities 1. Solve 2(1 x) -5x 2 for x. 2. Solve. 3. The formula represents the area of a circle where A represents the area, r is the radius. Solve this formula for r A. B. C. D. 4. The equation below was solved incorrectly. Study the work below. 5x - 5 = -2(x 8) Step 1: 5x - 5 = -2x -8 Step 2: 7x = -3 Step 3: x = Describe the mistake in the work shown above and find the correct solution to the equation. 5. At Jiffy Lube, Tony earns $100 every week plus $15 for every oil change he performs. Write an equation that can be used to determine Tony s weekly salary (T) given the number of times he changes the oil (C). Answer What is the minimum number of oil changes Tony must perform to earn a weekly salary of $500? Answer 1

2 Part B: Relations and Functions 1. What is the domain and range of the relation shown in the table below? x y Domain Range Is the relation in the table above a function? (circle one) YES NO 2. Sketch a graph of the following situation on the axes below. Marco grew at a steady rate from age 4 to age 12. He then grew at a much faster rate until age 14. He then didn t grow at all until age 16, when he grew at a very slow rate until 18. At age 18 he reached his adult height and never grew again. Label carefully. 3. What is the y-intercept of the graph of -2y = x 4? A. -4 B. -2 C. 2 D Which is an equation of a line with a slope of 2 that passes through the point (-4, 3)? A. y = -2x 5 B. y = -2x 4 C. y = 2x + 3 D. y = 2x Graph 2

3 Part C: Pairs of Linear Equations and Inequalities (Systems) 1. Solve the system of equations below. -5y + 3x = 16 10y + 4x = Solve the system of equations below. What is the value of y in the solution? x = -9y 3x + 6y = -7 A. -3 B Juliet bought 4 tacos and 3 sodas for $7.23. Romeo bought 6 tacos and 1 soda for $7.03. What is the cost for 1 taco? 4. Tommy is 7 years younger than Dominique. The sum of their ages in years is 63. What is Tony s age in years? 5. Graph the system of linear inequalities to the right. -x + 2y > -6-2y 6x 8 3

4 Part D: Polynomials 1. Multiply (2x 1) (4x + 2). 2. Which of the following is equivalent to? 3. Which expression is equivalent to (g 5 h 2 ) 4? A. 4g 20 h 8 B. 4g 9 h 6 C. g 9 h 6 D. g 20 h 8 4. Factor. 5. Factor. 4

5 Part E: Quadratic and Radical Equations and Functions 1. Solve 2x 2 = -2x + 84 A. x = -6, -7 B. x = -6, 7 C. x = -7, 6 D. x = 7, 6 2. Solve (x+3) 2 = What are the x-intercepts of the graph of y = 2x 2-7 x 4? 4. Solve 5. The height (h) of a certain insect, in feet, that jumps straight up into the air is modeled by the equation h = -16t 2 +tv, where t is the time in seconds after the insect jumps, and is the initial upward velocity of the insect. What is the maximum height (h) of the insect, in feet, after t seconds, if the insect s initial upward velocity is 12 feet per second. 5

6 New Released Items for Solve: 2. Describe how to estimate the solution to a pair of equations graphed on a coordinate plane. Then, explain how to determine if there is one solution, no solution, or infinitely many solutions to the pair of equations. 3. Factor 4. Joe ran from his home to school at a constant speed. He immediately turned around and ran back home, but at a slower constant speed. Joe ran along a straight path to and from his school. Which graph best represents Joe s distance from his home over time? 6

7 5. The graph below represents the total number of times a website was visited over a 5-day period. What is the slope of the line segment and what does it represent in terms of this situation? Write an equation that represents the total number of times this website is visited, V, after d days. Answer If this trend continues, how many times will the website be visited in 30 days? Answer 7