| |
| |
1. |
Use substitution to solve the system of equations given below. 8x - 4y = 16 2x - y = 4 |
| |
|
A. |
infinitely many solutions |
B. |
(0, -4) |
| |
|
C. |
(2, 0) |
D. |
no solution |
| |
|
Hint |
|
| |
2. |
Simplify (3a4b5c)4. |
| |
|
A. |
81a16b20c4 |
B. |
7a16b20c4 |
| |
|
C. |
3a16b20c4 |
D. |
12a8b9c5 |
| |
|
Hint |
|
| |
3. |
Determine whether the number is rational or irrational. |
| |
|
A. |
rational |
B. |
irrational |
| |
|
C. |
neither |
D. |
both |
| |
|
Hint |
|
| |
4. |
What is the equation of the graph shown? |
| |
|
 |
| |
|
A. |
f(x) = -2x2 + 2x - 1 |
| |
|
B. |
f(x) = 2x2 + 2x + 1 |
| |
|
C. |
f(x) = -2x2 + 2x + 1 |
| |
|
D. |
f(x) = 2x2 - 2x + 1 |
| |
|
Hint |
|
| |
5. |
Find the equation that has direct variation. |
| |
|
A. |
y = 4x |
B. |
y = –3x – 1 |
| |
|
C. |
y = 5x + 1.3 |
D. |
y = 0.8x + 9 |
| |
|
Hint |
|
| |
6. |
Which characteristic describes a graph that is linear and has direct variation. |
| |
|
A. |
Variables x and y are not proportional. |
| |
|
B. |
The equation has the form y = mx. |
| |
|
C. |
The graph does not pass through (0, 0). |
| |
|
D. |
The equation has the form y = mx + b. |
| |
|
Hint |
|
| |
7. |
Find the situation that is linear but does not have direct variation. |
| |
|
A. |
At the beginning of the summer, Dina had $0 in the bank. She earned $50 mowing lawns the previous week and deposited the money in the bank. |
| |
|
B. |
At the beginning of the summer, Dina had $200 in the bank. She started a job and deposited $10 per week. |
| |
|
C. |
At the beginning of the summer, Dina had $200 in the bank. She withdrew $30 to buy a new pair of shorts. |
| |
|
D. |
At the beginning of the summer, Dina had $0 in the bank. She started a job and deposited $10 per week. |
| |
|
Hint |
|
| |
8. |
Pam's mother gives Pam $20 each week for lunch to be bought at the school cafeteria. Lunches cost $4 per day. Draw a graph showing the amount Pam has left decreasing very slowly. Suppose you graph the time in days on the horizontal axis and the amount Pam has left on the vertical axis. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
9. |
Which way does the graph of y = –2x2 open? |
| |
|
A. |
up |
B. |
down |
| |
|
C. |
right |
D. |
left |
| |
|
Hint |
|
| |
10. |
Describe how the graph of y = (x + 1)2 differs from the graph of y = x2. |
| |
|
A. |
the graph of y = (x + 1)2 moved 1 unit to the left |
| |
|
B. |
the graph of y = (x + 1) 2 moved down 1 unit |
| |
|
C. |
the graph of y = (x + 1)2 moved up 1 unit |
| |
|
D. |
the graph of y = (x+1)2 moved 1 unit to the right |
| |
|
Hint |
|
| |
11. |
Find a quadratic equation for the table. |
| |
|
 |
| |
|
A. |
y = 5x2 – 2 |
B. |
y = 5x2 + 1 |
| |
|
C. |
y = x2 – 5 |
D. |
y = 5x2 – 1 |
| |
|
Hint |
|
| |
12. |
Find the equation of the following graph. |
| |
|
 |
| |
|
A. |
y = x3 |
B. |
y =  |
| |
|
C. |
y =  |
D. |
y = x2 |
| |
|
Hint |
|
| |
13. |
What is the reciprocal of –20? Evaluate it in decimal form. |
| |
|
A. |
–0.05 |
B. |
–0.20 |
| |
|
C. |
–0.02 |
D. |
–0.50 |
| |
|
Hint |
|
| |
14. |
What is true of the second differences for the equation x2 – 6x + 12? |
| |
|
A. |
they increase by 12 |
| |
|
B. |
they increase by 1 |
| |
|
C. |
they decrease by 1 |
| |
|
D. |
they are constant |
| |
|
Hint |
|
| |
15. |
What type of relationship does the equation have if its first differences are constant? |
| |
|
A. |
quadratic |
B. |
cubic |
| |
|
C. |
constant |
D. |
linear |
| |
|
Hint |
|
| |
16. |
Find a solution to the equation by doing the same thing to both sides. 8p + 14 = 2p – 22 |
| |
|
A. |
p = –6 |
B. |
p = 6 |
| |
|
C. |
p = –1 |
D. |
p = 1 |
| |
|
Hint |
|
| |
17. |
How could you use the graph of h = 20t – 6t2 to estimate the solution(s) of 20t – 6t2 = 7, where h stands for height and t stands for time? |
| |
|
 |
| |
|
A. |
Draw a vertical line at t = 7 and find where it intersects the curve. |
| |
|
B. |
Draw a vertical line at t = 20 and find where it intersects the curve. |
| |
|
C. |
Draw a horizontal line at h = 20 and find where it intersects the curve. |
| |
|
D. |
Draw a horizontal line at h = 7 and find where it intersects the curve. |
| |
|
Hint |
|
| |
18. |
A ball is launched straight up from ground level modeling the equation h = 52t – 10t2, where h stands for height in meters and t stands for time. What is the approximate value of t when the ball hits the ground? |
| |
|
A. |
2.6 seconds |
B. |
6.0 seconds |
| |
|
C. |
5.2 seconds |
D. |
0 seconds |
| |
|
Hint |
|
| |
19. |
Toby needs to create a rectangular pen for his dog. He decides that the area of the pen will be 100 square feet with its length 2 feet longer than its width. As you find the width of the pen, which solution can be thrown away since the width cannot be negative? |
| |
|
A. |
–9.05 |
B. |
–12.32 |
| |
|
C. |
–11.05 |
D. |
–8.32 |
| |
|
Hint |
|
| |
20. |
Use substitution or elimination to solve the system of equations. x + 2y = 6 x – 3y = –4 |
| |
|
A. |
(–2, 2) |
B. |
(2, 2) |
| |
|
C. |
(–2, –2) |
D. |
(2, –2) |
| |
|
Hint |
|
|
|