Math 085: Review for the Final Exam
Here are the topics to study:
Chapter 5
adding, subtracting, multiplying and dividing polynomials
negative exponents
simplifying exponents
scientific notation
Chapter 6
Factoring (GCF, difference of squares, grouping, trinomials)
Solving equations by factoring
Chapter 7
Adding, subtracting, multiplying and dividing rational expressions
Solving equations with rational expressions
solving similar triangles
Chapter 8
Computing square roots, cube roots, etc
Simplifying square roots
Solving equations with square roots in them
Chapter 9
Solving quadratic equations (square root, completing the square, quadratic formula)
graphing quadratic equations
See the next page for sample questions
Sample Questions
1) Subtract: (5x2 + 4x – 8) – (2x2 – 9x + 2)
2) Multiply and simplify completely:
3) Factor completely:
4) Factor completely:
5) Solve the equation by factoring:
.
6) Consider the parabola given by the equation:
a) What are the coordinates of the vertex?
b) Is this parabola opening upwards, or downwards?
c) What is the y-intercept?
d) What are the x-intercepts?
7) A projectile is shot vertically up into the air with an initial velocity of 177 feet per
second from an initial height of 88 feet off the ground. The height of the projectile, , in
feet, seconds after it's launched is given by the equation:
Find the two points in time when the object is 119 feet above the ground. Round your
answers to the nearest hundredth of a second (two decimal places).
8) solve the equation:
4  8x  1  9
9) Solve the equation by using any method:
10) Solve the equation by factoring:
.
.
11) Make a graph of the following equation:
12) Solve using the quadratic formula:
13) Solve by completing the square:
14) Divide:
x2 – 8x + 3 = 0
30 x 7 y 5
6 xy 2
6 x 3  12 x 2  6 x
15) Divide:
6x
16) Divide by using long division: (also give the remainder):
3x 3  5 x 2  2 x  9
x3
17) Simplify the following:
a) 9-2
b) (-3)-2
c) 82/3
18) Factor completely: x3 – 3x2 + 4x – 12
19) Factor completely: 26y5 – 13y3 + 39y2
3x  9
x3
20) Reduce:
3x 2  4 x  4
21) Reduce:
x2  4
x 2  25 x 2  10 x  25
 2
2x  2
x  4x  5
22) Divide:
23) Add: 4 
24) Add:
1
x3
x
x  2 x  24
2

x
x  7x  6
2
25) Solve:
x 1
6

2x  3 x  2
26) Write using scientific notation: 0.0000502
27) The two triangles below are similar. Solve for x:
28) Simplify the following:
a)
b)
75
5
8
29) Solve by taking the square root of both sides, then simplify the result.
(x + 2)2 = 40
30) Solve using the Pythagorean Theorem: