ALGEBRA 1 SEMESTER 1 STUDY GUIDE NAME _________________________

1. Solve each of the following equations for x:

a) -4(-3 + 2x) = -28 b) 4(x – 7) = -2x – 4

2. Write an equation for each graph below:

3. If f ( x )=x2+2 x+4 , find f (−2 ) .

4. Evaluate f ( x )=−3x−2 at x = 4.

5. If f ( x )=−x+5 ,find f (2a ) .

6. Explain what slope is and how to find it.

7. Find the slope of the line passing through the coordinates (2,-1) and (6,-9).

8. Find the slope of the line graphed below.

9. Sam earns $400 per week plus $20 for each item he sells. Write an equation that models the relationship between his pay p per week and the number of items n he sells.

10. A cup of coffee is initially at a temperature of 110°. Sitting on the table its temperature decreases by 4 degrees per minute. Write an equation describing the temperature of the coffee as a function of time.

11. Tickets to the football game cost $4.00 for students and $6.00 for adults. Last night’s game made $640 in admission tickets. Write an equation that models the number of tickets sold at the game.

12. Give the slope of the following equation: y=−4 x+7.

13. Find the y-intercept of the following linear equation: y−1=3 ( x+2 ) .

14. Write a function that best describes the following relation:

x y

0 3

1 6

2 9

3 12

15. Graph the equation 3x + 2y = 6.

16. Graph the equation y = -2x + 3.

17. Graph the equation y = -2. 18. Graph and solve the system of equations:

y = 12x−1

-2x + 4y = -4.

19. During a sale at a local department store, you buy 3 sweatshirts and 2 hats for $60. Later you return and buy 3 sweatshirts and 4 hats for $90. What is the price of each sweatshirt and hat?

20. Solve y = 3x x + 2y = 7

21. Solve x + y = 9

6x + 5y = 51

22. Sam buys fresh fruit twice over a one-week period. On Monday, he buys 2 apples and 3 bananas for $3.20. On Wednesday, he buys 3 apples and 5 bananas for $5.10. Write and solve a system of linear equations to determine how much each type of fruit costs.

Multiply:

23. 2a(4a) 24. 3 x (x+5)

25. Make an x 🡪 y table to draw a graph for the rule y=x2+2 x−1.

26. Complete each of these Diamond Problems:

27. Study the tile pattern.

a. Draw Figure 4 and Figure 5. Explain how the pattern grows.

b. Write an equation (rule) for the number of tiles in the pattern.

c. Explain how the growth factor appears in your equation.

28. Chris had the following multiple-choice question on a recent test: Each point on the graph below represents a different kind of hamburger. Chris had to select the statement that most accurately described the graph. Chris picked choice (2). Was this a good choice? If not, which is the best choice? Explain your reasoning.

a. All burgers have different prices and different calorie counts.

b. As the calories increase, so does the price for all burgers.

c. Burger D is high in calories and has the lowest price of all the burgers.

d. Burger A is low in calories and has a low price.

29. Write an algebraic equation for each figure below to express the relationship, "Area as a product equals area as a sum."

a) x +7 b)

3x x2 6x

-4 2x 12

30. For each graph below, state whether it is a function or a relation. Then state the domain and the range for each of the graphs.

31. Simplify each expression.

a. 12 47

+4 614 b. 5

34−4 2

9

c. (−3 38 )(5 2

9 ) d. −1 19÷(2 6

7 )

32. What is the equation for a line that has a slope of –2 and passes through the point (–11, 17)?

33. Graph the line that has a slope of 25 and a y-intercept of –4.

Then write the equation of that line.

34. Simplify the following expressions. No negative exponents in your final answers.

a. (2 x4 )4 b. a6b9

a8b3 c. 6 g3h2∙3 gh4 d. 5x−2

y−3

35. Solve each equation:

a. −2 (b−4 )=−7b+3 b. 8 (1−3m )−2=−15−3m

36. Use generic rectangles to multiply each of the following:

a. (− y−2)(8 y−9) b. (x+4 )(−5x2−9x−2)