Algebra 2
1st nine weeks exam review
1.
y
Use the graph to find these function
values:
5
4
3
f  1 = ___________
2
1
-5
f  0  = ____________
-4
-3
-2
-1
x
1
-1
2
3
4
5
-2
-3
f 1 = ____________
-4
-5
2. Compare these representations for a function. Which has the largest y value when x = 2?
_________
y
Graph:
Table:
4
3
x
-2
-1
-1
0
1
2
2
1
-4
-3
-2
x
-1
1
2
3
4
-1
-2
-3
-4
Formula:
f  x   x2  3
f(x)
-4
-1
2
5
8
3. Compare the average rate of change for the graph of each function over the interval 0,3 . Which
has the greater rate of change over the given interval?
y
y
9
9
Graph A
8
Graph B
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
-1
x
1
2
3
4
5
-1
x
1
-1
2
3
4
5
Graph the linear equation given below and identify some of its key features.
4 . x  2y  6
y
Slope: ___________________
5
4
y-intercept: _______________
3
2
1
-5
-4
-3
-2
-1
-1
x-intercept: _______________
x
1
2
3
4
5
domain: _________________
-2
range: ___________________
-3
-4
If x = 10, then y = ___________
-5
5. The table below illustrates the world growth in Internet use. Let x represent the number of years
that have passed since 2001, and let y represent the number of internet users worldwide ( in millions).
Draw a scatterplot to represent the data set, and your calculator to answer the following questions.
Year, x
Number of Internet Users (in
millions), y
2001, 0
494.1
2002, 1
679.8
2003, 2
790.1
2004, 3
935.0
2005, 4
1047.9
2006, 5
1217.0
2007, 6
1402.1
2008, 7
1542.5
2015, 14
?
USERS, millions
1400
1200
1000
800
600
YEAR, x
1
2
3
4
5
6
7
8
a) Equation of Median Fit line: ______________
d) Prediction value for 2015
b) Correlation: ____________________________
_______________________________________
c) Correlation coefficient: ___________________
6. Use your calculator to find the value of the correlation coefficient when an equation for the line of
best fit is determined. Based on your results, would the equation for the line of best fit be a good
predictor for future outcomes for this data set? Why or why not?
x
1
2
3
4
5
6
7
8
9
y
3
8
-2
4
6
-3
2
7
-1
Correlation coefficient for the linear regression:
__________________________________________________________________________________
__________________________________________________________________________________
________________
Find the area of each figure drawn below.
7.
8.
3 3 4
ab c
4
8a 3b 2
12a 2b 4 c 2
9.
Simplify each expression.
10.
6x
3
 4 x  3  8 x 2  7 x  1
11.
x
3
 4 x 2  11   x 2  4 x  5 
8m  3
Factor each expression completely.
12. 14 xy 2  2 xy
13. 25x 2  y 2
15. 3 y 2  27
16. 20 x 3  35 x 2  8 x  14
14. 6 x 2  4 x  16
Find each quotient.
2 x 2 y  xy  2 xy 2
17.
xy
6 x 4 y  11xy 5
18.
3xy 2
19.
x
4
 2 x 2  3x  1   x  1
20. Is  x  4  a factor of the polynomial 3x 2  11x  4 ?
Simplify each expression.
21.
24.
27.
16m8
4
2 3 24  6 3 2  3 375
22.
25.
6
192

2 2 5

23.
5 12  3 75
26.
1  3  2  6 
5
3x
Write in simplest radical from of each expression.
28.
1
4
3
4
5 x y
7
4
29.
1
3
9 9
5
3
Write each radical expression using rational exponents.
30.
4
16z 2
31.
4
81x 6 y 5
Solve each radical equation. Be sure to check for extraneous solutions.
x 5 3  0
32.
33.
2w  1  11  18
34.
4  9  7i   6  5 10i 
37.
3
4
y  2  14  9
Simplify each expression.
35.
3 4 8
9

36.
 3  6i  4  8i 
Solve each of the following by factoring or using the quadratic formula.
38.
x 2  7 x  13  0
41.
Using the equation 3x 2  16 x  35  0 , determine each of the following:
A.
B.
C.
D.
E.
39.
3x 2  5 x  6  0
40.
4 x 2  32 x  15  0
What is the quadratic term?
What is the linear term?
What is the constant term?
What is the discriminate?
What is the nature of the roots?
Write the quadratic equation with the given roots:
42.
2, 1
43.
-3, 4
44.
-1, -7
Solve each rational equation. Check for extraneous solutions.
45.
x
1

x3 4
Write the equation in vertex form. Identify the vertex, focus, axis of symmetry, directrix, and
direction of the opening for each parabola:
46.
y  2 x2  8x  7
1
on the coordinate plane given below. Determine the horizontal and
x3
vertical asymptotes.
47. Graph y 
y
6
5
4
3
2
1
-6
-5
-4
-3
-2
-1
x
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
48.
The total area of the parallelogram below is (8x3 - 18x2 - 41x + 21) . What is the expression
that BEST represents the length of the base of the parallelogram?
(2x - 7)
Determine the remainder for each given below:
49.
(2 x3 15x2  2 x  120);
 x  5
50.
 g  3
(8g 3  19 g 2 12 g  9);
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
 x  7
( x3  8x2  x  42);
53.
Which point corresponds to a zero of the function f(x) = x2 + 2x - 15?
A.
54.
(0, 3)
B.
52.
(3, 0)
(2 x3  x2  41x  20);
 x  4
51.
C.
(0, -3)
D.
(-3, 0)
Which of the following statements is NEVER true about a cubic function?
A.
The end behavior is down and up.
B.
The function has 3 zeros.
C.
The function has 3 turning points.
D.
The function has complex roots.
E.
The function has an odd degree.