# Chapter 7 Review Problems ```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
(-3,7)
(0, 0)
3. Solve graphically:
x y 2
x y 0
4. Solve the system algebraically:
y2  2 y  x  0
(1, 1)
5. Solve the system of equations:
3x  2 y  z  17
x  y  z  4
x yz 3
(inconsistent system)
x y 0
(-3, 3) and (0,0)
6. Find the equation of the parabola
y  ax 2  bx  c that passes through the points:
(0,-5),(1,-2),(2,5)
(𝑎 = 2, 𝑏 = 1, 𝑐 = −5)
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
𝐴 𝐵𝑥 + 𝐶
𝐷𝑥 + 𝐸
+ 2
+ 2
𝑥 𝑥 + 2 (𝑥 + 2)2
𝐴
𝐵
𝐶
(𝑥 + 𝑥 2 + 𝑥−5)
9. Write the partial fraction decomposition of the rational
10. Write the partial fraction decomposition of the rational
4 x2
x3  x 2  x  1
2
x
2
x  2 x  15
expression:
1
(1 + (
9
8 𝑥−3
−
25
𝑥+5
expression:
)
(
2
𝑥−1
+
2𝑥+2
𝑥 2 +1
)
There can also be word problems like anything you will find on page 516 or page 529 in your text book.
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