Algebra I Second Semester Exam Review—Due the day of your exam—
Worth 15% of your exam grade.
Follow the directions for each question. You must do the work neatly on a
separate paper and show all work. If you turn it in on this paper, you will not
receive any credit.
1. Solve the following equation: 2x  3  5x  9
x3 x2

2. Solve the following equation:
5
10
5
r
3. Simplify this expression: 0 4
sr
4. Find the value of this expression: 7.4 108
5. Simplify this expression:
 7g 
3 3
6. Simplify this expression: ( f 4 k 2 )5
2
 6x 2 
7. Simplify this expression:  3 
 y 
8. Add the following polynomials: 2r 3  2r  9  5r 3  2r 2  4r 
9. Subtract the following polynomials:
x
4
 3   8 x 4  4 x  12 
10. Multiply the following polynomials: 10bc 2 10b 7 c 2  b 
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Square the following polynomial: d  15
Multiply the following polynomials: 12x  6x  1
What is the GCF of the monomials 25a 3b 6 and 15a 5b ?
Factor the polynomial 4 x 3  12 x .
Factor the polynomial x 2  4 x  21 .
Factor the polynomial 2 x 2  5 x  12 .
Factor the polynomial 9 x 2  16 .
Factor the polynomial 4 x 2  12 x  9 .
Factor the following polynomial completely: 3 x 4  6 x 3  45 x 2
Which of the following graphs is a quadratic graph?
2
a.
b.
c.
d.
21. Use this graph for each of the questions below.
a. What is the vertex?
b. What is the axis of symmetry?
c. What are the zeros?
d. Is the vertex a minimum or maximum?
22. What is the vertex of this quadratic graph: y  x 2  8x  5
23. What are the three differences between the graphs of y  2 x 2  3 and y  x 2 ?
24. This is the graph of the equation y  x 2  2 x  3 :
What are the solutions to that quadratic?
25. What are the solutions to this equation:  x  5 x  3  0 ?
26.
27.
28.
29.
30.
Solve this equation using square roots: 3x 2  2  14 .
Solve this equation using the Quadratic Formula: 2 x 2  7 x  2  0 .
Solve the following equation using any effective method: x 2  3x  10  0
Solve the following equation using any effective method: x 2  x  12  0
Which of the following graphs is an exponential graph?
a.
c.
b.
d.
31. The number of students in the book club is increasing at a rate of 15% per
year. In 2001, there were 9 students in the book club. Find the number of
students in the book club in the year 2008.
32. The population of a small town is decreasing at a rate of 4% per year. In
1970, the population was 24,500. Find the population in the year 2020.
33. You invest $3000 in a bank with a 4% interest rate, compounded monthly.
How much money will you have in 10 years?
34. Simplify 18 .
35. Simplify 128 x 2 y 5 .
8
.
18
37. Add 6 7  3 7 .
38. Subtract 50 x  2 x  12 x .
39. Multiply 3 5 2 6 .
36. Simplify
40. Simplify
41. Solve
5
.
3
x  6  3.
A bag of marbles has 12 red marbles, 8 blue marbles, and 5 green marbles.
42. If you draw a marble at random, what is the probability it is green?
43. If you draw a marble at random, what is the probability it is not red?
44. You roll a 6-sided die and flip a going. List the sample space.
45. A standard deck of cards contains 4 queens and 52 cards. If you draw two
cards, what is the probability that you will draw two queens if:
a) you replace the first card before you draw the second card
b) you don’t replace the first card before you draw the second card
46. How many different four digit numbers are there that have an odd first digit
and an even last digit?
47. You and your friends are having a sleepover and you have 7 different
movies to choose from. You are going to watch three of them. How many
different ways can this happen if:
a) you don’t care what order you watch them in?
b) you do care what order you watch them in?
Important Formulas for the Exam:
Quadratic Formula
x
b  b  4ac
2a
2
Axis of symmetry
formula
b
x
2a
Exponential Growth /
decay
t
y  a 1  r 
Y = final amt.
a = starting amt.
r = rate as a decimal
t = time
Compound interest
nt
 r
A  P 1  
 n
A = final amt.
P = principle
r = rate as a decimal
n = # of comp. per year
t = time in years