CHAPTER 1 REVIEW
ALGEBRA 2/TRIG
Show work on a separate piece of paper if necessary.
1. Model the following situation with an equation and a graph. A taxi charges $6.00 for a fare
plus $1.50 per mile.
2
2. Graph the equation y   x  2 .
5
3. Write the slope-intercept form of an equation of the line that passes through the point (9, 7)
2
and has the slope m = .
3
4. Find the slope-intercept form of the line passing through the point (-2, -3) and parallel to
the line 3x + 4y = 9.
5. Write an equation in slope-intercept form for the line that contains the point (3, -6) and is
1
perpendicular to y  x  7 .
2
6. Solve the proportion:
z2 z
 .
7
6
1
7. Solve the proportion:
m2 m2

.
15
6
Solve the literal equation for the indicated variable.
8. m 
1
(a  b), for b.
2
9. V 
1
Bh for h.
3
10. R = 3mn + 3mc – 3mp, solve for m. Write your answer as one term.
11. Solve the compound inequality. Then graph the solution on a number line.
1
( x  9)  4 or 3  2 x  5
3
12. The distance between the moon and Earth varies depending on where the moon is in its
orbit. The closest (perigee) the moon comes to Earth is 225,700 miles and the farthest
(apogee) is 252,000 miles. Write an absolute value inequality that represents the range of
distances between the moon and the Earth.
13. Use a graphing calculator to create a scatter plot of the data in the table. Describe the
correlation as positive, negative, or no correlation. Then find an equation for the line of best
fit in slope intercept form.
x 0 2 5 9
Y 5 9 15 23
2
Solve the inequality and graph the solution on a number line.
14. 6x + 2 ≥ 3(x – 3)
15. -3x – 6 < 12 and 1 – 2x ≤ 17.
16. 4x < -20 OR 5x – 2 ≥ 3
17. Determine if the table represents a linear relationship between x and y. If the relationship
is linear, write the next ordered pair that would appear in the table.
x 0 1 2 3
y 1 6 11 16
18. Find the slope and y-intercept of the line 12x – 7y = 24.
19. Write an equation in slope-intercept form for the line containing the
points (-7, -1) and (5, 7).
20. Write an equation in slope-intercept form for the line containing the
points (0, 13) and (4, -11).
3
21. Solve for r: r 
1 7

5 10
Solve the following absolute value inequalities.
22.
3x  7  2
23.
4x  3  2  4
24. The Opera House wants to sell tickets to a play. It plans on selling 200 reserved seat
tickets and 350 general admission tickets. The price of a reserved seat ticket is $3 more
than a general admission ticket. The organization wants to collect at least $6650.
a. Write an inequality in one variable that best describes this situation.
b. What is the minimum price it can charge for a reserved-seat ticket?
25. If y varies directly as x, find the constant of variation, and write an equation of direct
variation that relates the two variables when y = 65 and x = 13.
26. The Real Peanut Company’s money earned, or revenue R, from selling x units of peanuts
is R = 72x. The cost of producing x units of peanuts is C = 38x + 544. In order to make a
profit the revenue must be greater than the cost.
a. Write and solve an inequality in one variable that describe this relationship between
revenue and cost.
b. How many bags of peanuts must the company sell in order to make a profit?
4