1-3 Algebraic Expressions

Chapters 1, 2, and 3 Review

Chapter 1

1-3 Algebraic Expressions

1. Write an algebraic expression to model the following

a. One less than the product of six and w

b. Four more than the quotient of 6 and m

c. Twice the difference between 5 and r

2.Write an expression to describe the situation

a. You are on a bicycle trip. You traveled 52 miles the first day. Since then, your average rate has been 12 miles per hour. Evaluate your distance for 3, 4 and 5 days.

b. You start off with $145 in your bank account. You spend $6 per week. Evaluate your account for 5, 10, 15 weeks.

1-4 Solving Equations

3. Solve the equation for each variable

a. for

b. for

c. for

1-5 Solving Inequalities

4. Solve each inequality

5. Find the solution and graph (on a number line) the inequality

a. and

6. Is the equation always, sometimes, or never true?

1-6 Absolute Value Equations and Inequalities

7. Solve each equation

8. Find and graph the solution on a number line

Chapter 2

2-1 Relations and Functions

9. Determine whether each relation is a function

a. {(3,-9), (5, 7), (7, -9), (-2, 1)}

b. {(0, 2), (1, 2), (2, 2), (3, 2)}

c. {(2, -3), (1, -5), (2, 4), (-3, 9)}

2-2 Direct Variation

10. Given y varies directly with x...

a. If y=6 when x=2, find x when y=12

b. If y=25 when x=15, find y when x=6

c. If y=5 when x=-3, find x when y= -1

2-3 Linear Functions and Slope Intercept Form

11. Write each equation in slope-intercept form. Then find the slope and y-intercept of each line

2-4 More About linear Equations

12. Write the equation of each line

a. slope =3 ; through (1, 5)

b. through (-10, 3) and (-2, -5)

c. through(-3, 1); perpendicular to -4

2-5 Using Linear Models

13. Make a scatter plot and describe the correlation

a. {0, 11), (2, 8), (3, 7), (7, 2), (8, 0)}

b. {(1, 55), (2, 38), (3, 54), (4, 37), (5, 53), (6, 40), (7, 53), (8, 36)}

c. {(1.2, 1), (2.5, 6), (2.5, 7.5), (4.1, 11), (7.9, 19)}

2-6 Families of Functions

14. Write an equation for each transformation of y=x

a. vertical stretch by a factor of 4

b. vertical shrink factor of ¼ and a shift up 3

2-7 Absolute Value Functions and Graphs

15. Graph each equation

2-8 Two-Variable Inequalities

16. Graph each inequality

17. Graph each absolute value inequality

Chapter 3

3-1 Solving systems Using Graphs

18. Solve each system by graphing

3-2 Solving Systems Algebraically

19. Solve each system using substitution of elimination

3-3 Systems of Inequalities

20. Solve each system by graphing

3-4 Linear Programming

21. A company manufactures and sells two models of lamps, L1 and L2. To manufacture each lamp, the manual work involved in model L1 is 20 minutes and for L2, 30 minutes. The mechanical (machine) work involved for L1 is 20 minutes and for L2, 10 minutes. The manual work available per month is 100 hours and the machine is limited to only 80 hours per month. Knowing that the profit per unit is $15 and $10 for L1 and L2, respectively, determine the quantities of each lamp that should be manufactured to obtain the maximum benefit.

22. Lisa has an online jewelry shop where she sells earrings and necklaces. She sells earrings for $30 and necklaces for $40. It takes 30 minutes to make a pair of earrings and 1 hour to make a necklace, and, since Lisa is a math tutor, she only has 10 hours a week to make jewelry. In addition, she only has enough materials to make 15 total jewelry items per week. She makes a profit of $15 on each pair of earrings and $20 on each necklace. How many pairs of earrings and necklaces should Lisa make each week in order to maximize her profit, assuming she sells all her jewelry?

23. The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each should be accepted to maximize income?

3-5 Systems with Three Variables

24. Solve each system using any method

3-6 Solving Systems Using Matrices

25. Solve the system of equations using a matrix (either by hand or on a calculator)