Academic Algebra 2 Unit 1 Test Study Guide
Name: ______Block: ______Date: ______
SHOW ALL WORK!
1. 2. Solve and graph:
3. Solve the inequality and graph the solution on a number line.
4. Solve the inequality and graph the solution on a number line.
5. Rewrite the linear equation in standard form. Then determine the x- and y-intercepts.
6. Rewrite the linear equation in function form. Then determine the slope and y-intercept.
7. Let
a) find and b) Find
8. Determine the equation of the line in slope-intercept form that passes through the points (2, 1) and (–4, 3).
9. Determine the equation of the line that is perpendicular to the line and passes through the point (5, 1). Write your answer in Slope-Intercept form.
10. Determine the equation of the line that is parallel to the lineand passes through the point (–2, –4). Write your answer in Slope-Intercept form.
Graph each of the following:
11) 12)
A street vender wants to sell hot dogs and pretzels. He can buy hotdogs for $8 a pack and pretzels for $5 a bag from a local distributor. He has $1200 to spend on hot dogs and pretzels.
13. Define the variables and then write an equation that represents this situation.
14. If the vender buys 30 bags of pretzels, how many packs of hot dogs can he buy?
15. If the vender buys 105 packs of hot dogs, how many bags of pretzels can he buy?
16. Determine the x- and y-intercepts of the equation. What do the x- and y-intercepts represent in the context of the problem?
Use questions 13 – 16 above to complete the following table and graph.
Quantity Name:
Unit:
Expression:
You plant a small seedling. After 2 weeks, the plant is 154 millimeters tall. After 5 weeks, the plant is 226 millimeters tall. Assume that the plant grows at a constant rate.
18. Identify the two points given in the problem statement.
19. Determine the slope of the line that represents the problem situation. What does the slope mean in the context of the problem?
20. y varies directly with x, and y = 3 when x = 2. Write an equation that relates the variables, and use this equation to find the value of y when x = 2.
21. y varies inversely with x, and y = 12 when x = –4. Write an equation that relates the variables, and use this equation to find the value of y when x = 3.
After 3 weeks the followers of a rap star’s twitter account is 5200. After 8 weeks the number of followers is 4000. Assume the number of followers drops at a constant rate.
22. Identify the two given points in the problem statement.
23. Determine the slope of the line that represents the problem situation. What does the slope represent in the context of the problem?
Unit 1 Test Study Guide Answer Key
1) x = 6, –12 2) x < –4.5 3) x < 3 and x > –2 4) x 5 and x –7
5) –x + 4y = 20 6) 7) (a) f(–1) = –3; f(12) = 23
x = –20; y = 5 (b) f -1(f(2)) = 2
8) 9) 10) y = 5x + 6 11)
12)
13) Let x = # of packs of hotdogs 8x + 5y = 1200 14) 131 packs
Let y = # of bags of pretzels 15) 72 bags
16) x = 150; y = 240; These represent when the vender buys either no hotdogs or no pretzels.
x / yPacks / Bags
8x / 5y
0 / 240
150 / 0
131.25 / 30
105 / 72
Quantity Name:
Unit:
Expression:
18) (2, 154); (5, 226) 19) 24 20) ; y = 24 21) ; –16
22) (3, 5200); (8, 4000) 23) –240