Name____________________________________
Block: ______
Precalculus
Chapter 7 Review Sheet
1. Solve algebraically:
7 x  12 y  63
2 x  3( y  2)  21
2. Solve algebraically:
3x  2 y  0
3 x  2( y  5)  10
3. Solve graphically:
x y 2
x y 0
4. Solve the system algebraically:
y2  2 y  x  0
5. Solve the system algebraically:
y  7 x3  14 x 2  28
6. Find the equation of the parabola
y  ax 2  bx  c that passes through the points:
(0,-5),(1,-2),(2,5)
y  7 x 2  70 x  28
x y 0
7. Write the partial fraction decomposition but do
not solve for the variables.
3x  4
x3  5 x 2
8. Write the partial fraction decomposition but do
not solve for the variables.
x2
x( x 2  2) 2
9. Write the partial fraction decomposition of the rational
𝑥2
expression: 2
𝑥 +2𝑥−15
10. Write the partial fraction decomposition of the rational
11. Sketch the graph of the inequality:
12. Solve the system of equations:
(𝑥 − 3)2 + (𝑦 + 2)2 < 16
expression:
4 x2
x3  x 2  x  1
3 x  2 y  z  17
x  y  z  4
x yz 3
13. A student is working part time as a hairdresser to pay college expenses. The student may work no more
than 24 hours per week. Haircuts cost $25 and require an average of 20 minutes, and permanents cost $70
and require an average of 70 minutes.
What combination of haircuts and/or permanents will yield optimal revenue?
What is the optimal revenue?
14. A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre
of crop A and 2 days to trim an acre of crop B. There are 260 days per year available for trimming. It takes
0.4 days to pick an entire acre of crop A and 0.15 days to pick an entire acre of crop B. There are 35 days
available for picking. The profit is $180 per acre of crop A and $250 per acre for crop B.
What is the optimal acreage for each crop (Crop A, Crop B)?
What is the optimal profit?
Answer Key
1. (−3, 7)
2. (0, 0)
3. (1, 1)
4. (0, 0)𝑎𝑛𝑑 (−3, 3)
5. (0, −28), (−2, −140), 𝑎𝑛𝑑 (5, 497)
6. 𝑦 = 2𝑥 2 + 𝑥 − 5
7.
8.
𝐴𝑥+𝐵
𝑥2
𝐴
𝐶
+ 𝑥−5 𝑜𝑟
𝐵𝑥+𝐶
𝐴
𝑥
𝐵
𝐶
+ 𝑥 2 + 𝑐−5
𝐷𝑥+𝐸
+ 𝑥 2 +2 + (𝑥 2 +2)2
𝑥
1
9
25
9. 1 + 8 (𝑥−3 − 𝑥+5)
2
2𝑥+2
10. 𝑥−1 + 𝑥 2 +1
11. Circle with center (3, -2) and radius of 4, graph is dashed and shaded inside
12. No solution
13. 72 haircuts and 0 perms for a revenue of $1800
14. 40 acres of crop A and 110 acres of crop B for a profit of $34,700