Checkpoint 1 Simplifying Like Terms and Distributive Property

Transcription

1 Checkpoint 1 Simplifying Like Terms and Distributive Property Simplify the following expressions completely ( 2) (8x 5) + (4x 6) 7. (6t + 1)(t 2) 8. (2k + 11) (4 7k) 9. (x 2 x + 9) (5x 2 + 5x 7) 10. (w + 4)(w 6) 11. (3r 5) (2a 4b)(a + 5b) 13. 4x 2 (3x 2 x + 2) 14. 2a 3(a + 5)

2 15. (2a 2 + 3)(5a 2 2) 16. x (2a 5)(a 2 4a + 1) 18. If the length of a rectangle can be represented as 2x 3 and the width is 4x + 5, write an expression that represents the perimeter of the rectangle. 19. Write the expression that represents the area of the rectangle above. 20. Kurtis is building a walkway that surrounds a rectangular garden. The shaded area in the picture represents this walkway. x + 6 Write an expression that represents the area of the walkway using the information provided. x 3x 3x Suppose the width of the garden is 4 feet and the length of the garden is 12 feet. The walkway is to be 3 feet wide all the way around the garden. If bricks for the walkway sell at $1.50 per square foot, what would be the total cost of bricks for the walkway.

3 Solve the following equations. Checkpoint 2 Solving Equations = 3x 2. x 6 = x = = 3x x < x = y 8. 5 = 5 2x = 3x x 2 3 = x 13 x = a 13 = 7a

4 x 4 x 14. 5(2 x) 3 2x 7 3x x = 6x = 4(2f 3) 3f 17. 5(3y + 2) 6 > 15y Solve the following formulas for the variable indicated. 18. y = mx + b; solve for x 19. x m z ; solve for x 18. s The volume of a pyramid is given by the formula V b h, where V is the volume of the 3 pyramid, b is the length of one side of the base, and h is the height of the pyramid. Rewrite the equation so that it would give you the height of the pyramid, for a known volume and base length

5 Checkpoint 3 Graph and Write the Equations of Lines Graph the following functions. 1. y = 3x 7 2. y = 2 x f(x) = x m = m = m = b = b = b = 4. g(x) = x x 10y = y = 2x m = m = m = b = b = b =

6 7. 3x 4y = y = x = 16 m = m = m = b = b = b = Write the equation of a line given the following information

7 13. The line with slope = 3 passing through (6, 2) 14. The line with slope = 3 passing through (5, 1) 15. A line with m= -2 passing through (0,2) 16. The line that goes through (6, 1) and (3, 3). 17. A line passing through the origin and (8, 2) 18. A line passing through (-1, 3) and (-1, 5) 19. A line passing through (0, 10) and (-5,0) 20. A with an x-intercept of -2, and a y-intercept of 6

8 Checkpoint 4 Solve Systems by Graphing and Substitution Solve the following systems of equations by graphing. 1. y = x 1 and x + y = 3 2. y = 2x and 2x + 5y = 12 Solve the following systems of equations by substitution. 3. y = 4x and x + y = 5 4. x = 4y and 3x + 2y = x y = 4 and 2x 3y = 9 6. x + 3y = 8 and 2x 4y = 9

9 7. x + 14y = 84 and 2x 7y = x y = 11 and 3x 6y = x 2y = 60 and 5x 3y = y + 2x = 2 and y + x = 1

10 Checkpoint 5 Solve Systems by Elimination Solve the following systems of equations by graphing. 1. x + 2y = 12 and x + 6y = x y = 9 and x + y = x + 5y = 14 and 4x + 5y = 8 4. x + 3y = 7 and 2x 3y = 4 5. x + y = 1 and x 2y = x + 5y = 3 and x + 3y = 7

11 7. y = 2x + 8 and y = 3x x y = 6 and 2x + y = x + 7y = 2 and 2x 7y = y = 9x 35 and 5x + 8y = x + 8y = 29 and 7x + 3y = x + 8y = 7 and 18x 15y = 14

12 Checkpoint 6 Solve Systems of Equations with 3 Variables Tell whether the given ordered triple is a solution to the system. 1,4, 3 6,0, x y z 5 x 4y 2z 12 5x 2y 2z 19 3x y 4z 6 x 3y z 5 x 3y z 9 Solve the following systems of equations. 3. 2x y 2z 7 x 2y 4z 5 x 4y 6z 1

13 4. x 5y 2z 1 x 2y z 6 2x 7y 3z x y z 6 x y z 2 3x y 4 6. x 3y z 12 2x 4y 2z 6 x 2y z 6

14 Checkpoint 7 Domain and Range Given the following information, find the domain and range for the following. 1. (1,6), (2, 7), ( 1,8), (8, 3) 2. (7,7), (2,6), ( 4, 3), (11, 8) 3. ( 8,8), (7,0), ( 6, 7), (1,4), (0,5) Find the domain and range of each function 4. Domain: 5. Domain: 6. Domain: Range: Range: Range: 7. Domain: 8. Domain: 9. Domain: Range: Range: Range:

15 10. Domain: Range: 11. Domain: Range: 12. Domain: Range: 13. Domain: Range: 14. Domain: Range: 15. Domain: Range: 16. Eric wants to buy T-shirts for homecoming. It costs $20 for a design fee, and each T-shirt is $5. Eric knows that the amount of money it costs to produce the homecoming T-shirts is dependent on the number of T-shirts he orders. Write a function for Eric, and then state the domain and range of that function.

16 Checkpoint 8 Notation Given the following graph, write the domain and range in inequality, set, and interval notation. Also, describe using words. 1. D R Words Inequality Set Interval 2. D R Words Inequality Set Interval 3. D R Words Inequality Set Interval 4.

17 D R Words Inequality Set Interval 5. D R Words Inequality Set Interval A movie theater seats 200 people. For any particular show, the amount of money the theater makes is a function of the number of people, n, in attendance. If a ticket costs $4.00 A) Write a function that illustrates the amount of money made by the movie theater. B) Sketch a rough graph

18 Checkpoint 9 Piecewise Functions part 1 Evaluating the piecewise functions given the following domains 1. when x = 3 2. when x = 4 3. Find f(5) 4. Find f(2) 4x if x 2 f x 2x 10 if 2 x 5 2 if 5 x 10 Graph the following functions: 2 f x = x 1, if x f x = 4x 5, if x f x = x if -6 x 0 2 f x = 2 x 4, if 2 x 6 8.

19 f x = 2 if 3 x f x = x 1 +2 if x A gourmet coffee store sells the house blend of coffee beans at $9.89 per pound of coffee for quantities up to and including 5 pounds. For each additional pound after the 5 pounds, the price is $7.98 per pound. a. Write a function that relates the cost and the number of pounds of coffee beans being purchased. b. Determine the cost for 3 pounds of coffee beans c. Determine the cost for 7 pounds of coffee beans. d. Determine the cost for 5.5 pounds of coffee beans.

20 Checkpoint 10 Piecewise Functions part 2 Graph the following functions: 1. 2x 1, if x f x = x 1, if x 2 x 1, if x 0 f x = 2 f 3x 7, if x 2 x x 9, if 1 x 2 = 3 x 5, if 2 x if x , if 2 x 1 f x = 2 x, if 1 x 3 4 x, if 0 x 2 f x = 2, if 1 x 4 1 f x = 2x 10, if 2 x 5 5, if 4 x 7 x 7, if x 3 3 2, if 5 x 10

21 For #7-8 Write and Graph the piecewise function described using the domain 3 x Rounding Function. The output f x is the input x rounded to the nearest integer. If the decimal part of x is 0.5, then x is rounded up when x is positive and x is rounded down when x is negative. 8. Greatest Integer Function. The output f x is the greatest integer Less than or equal to the input x.

22 9. An air-conditioning salesperson receives a base salary of $2850 per month plus a commission. The commission is 2% of the sales up to and including $25,000 for the month and 5% of sales over $25,000 for the month a. Write a function that relates the salesperson s total monthly income with his or her sales for the month. b. Determine the salesperson s total monthly income if his or her sales were $19,500 for the month. c. Determine the salesperson s total monthly income if his or her sales were $43,000 for the month d. Graph the piecewise function.