Fall Final Exam Review (Revised 2013) Algebra 2CP
Algebra 2CP Fall Final Exam
Can You… Solve an equation with one variable, including absolute value equations (1.3 and 1.4)
Solve and graph inequalities, compound inequalities, and absolute value inequalities (1.5 and 1.6)
Translate an algebraic expression into a variable expression (1.3)
Solve a formula for a variable (1.3)
Set-up and solve a word problem using one or more variables (1.3)
Find the value of a function at a number and at an expression (2.1)
Find the slope, x-intercept and y-intercept of a linear equation (2.2 and 2.3)
Find the slope of a line given two points (2.3)
Write a linear equation given various information (2.4)
Graph linear equations and inequalities and absolute value equations and inequalities (2.3-2.7)
Graph and solve a system of linear inequalities (3.3)
Determine the number of solutions and solve a system of equations involving two variables (3.1 and 3.2)
Use the properties of exponents, including negative exponents, to simplify expressions (6.1)
Add, subtract, multiply and divide monomials and polynomials (6.2)
Divide polynomials by binomials, including using long division and synthetic division (6.3)
Factor polynomials (including the sum/difference of squares) using the methods demonstrated in class (6.4)
Simplify radicals by using perfect cubes, squares, etc (7.4 and 7.5)
Simplify radicals that have variables with exponents (7.6)
Simplify expressions with fractional powers and apply laws of exponents to those powers (7.6)
Graph a square root function and give its domain and range (7.3)
Add, subtract, multiply and divide with radicals, including using the conjugate to rationalize a denominator (7.5)
Solve a radical equation (7.7)
Use y = a(x – h)2 + k or y = ax2 + bx + c to find the vertex, axis of symmetry, y-intercept and a graph (5.1)
Find the zeros of a quadratic function (5.2 and 5.3)
Add, subtract, multiply and divide expressions containing i, including simplifying expressions (5.4)
Solve a quadratic eqn. by factoring, completing the square, square root property and quadratic formula (5.3-5.6)
Use the discriminant find the nature of the roots of a quadratic equation (5.6)
Solve and graph a quadratic inequality (5.8)
Determine the maximum or minimum value for a parabola (5.1)
Looking at a graph determine if the graph represents on odd-degree polynomial or an even-degree polynomial
and tell the number of real zeros and imaginary zeros (6.5)
Given a factor of a polynomial and find the remaining factors (6.9)
Find all real zeros of a polynomial using the graphing calculator an tell how many complex zeros exist (6.8-6.9)
Find the sum, difference, product and quotient of functions (7.1)
Find the composition of functions (7.1)
Find the inverse of a function and graph the function and its inverse (7.2)
Simplify rational expressions (8-1)
Add, subtract, multiply and divide rational expressions (8-1) and (8-2)
Find the asymptotes, the intercepts, and holes in the graph of a rational function (8-3)
Recognize and solve direct, joint and inverse variation problems (8-4)
Solve rational equations (remember to check for excluded values) (8-6)
Fall Final Exam Review (Revised 2013) Algebra 2CP
1) If 0.5q , 1.2r , 6s , and 5t , evaluate:
2 4 1r sq
t
2) Combine like terms: 3 2 2 6 4a b a b
3) Write an algebraic expression for the verbal
expression: Seven less than the product of 6 and
some number.
4) Solve: 8 3 5 2 1s s
5) Solve the following for the variable 1b :
1 21
2A h b b
6) If 2x and 4y , evaluate: 3xy x
7) Solve: 9 5x
8) Solve: 3 1 12y
9) Write and solve an inequality for: The sum of twice a
number and 5 is at most 17.
10) Jane has $500 in her account. She spends $140 on
groceries, $90 on a DVD player, and $35 on gas.
Write an inequality to show Jane's expenditures and
how much she has for other expenses, e.
11) Graph the solution set of 3 10 or 11x x
12) Solve: 3 1 2x
13) Solve: 5 4 6m
14) Given: 3, 1 , 1, 2 , 1, 1 , 2, 3 Determine the
domain, range, an if it's a function or not
15) Find 3f if 22 4 1f x x x
16) Write the following in Standard Form and identify the
intercepts: 3
62
y x
17) Graph the equation: 3 7 21x y
18) Find the slope between: 3, 4 and 12, 1
19) Write the slope of the line parallel to: 3 1y x
20) Find the equation of the line passes through 5, 4
and is perpendicular to 1
73
y x
21) Graph: 2 4 8x y
22) Graph: 2 3 1y x
23) Solve the system: 6 4 2x y and 2y x
24) Solve the system: 3 7 14x y and 5 2 45x y
25) Graph: 2y x and
0.5 3y x
26) Graph, find the vertices of the feasible region, and
then find the maximum and minimum values for the
region:
27) Jim has 15 bills in some combination of $1, $5, and
$20. Those 15 bills total $123. He has twice as
many $5 bills than $20 bills. Write (not solve) a
system of equations to represent this.
28) The table shows the minimum
wage from the Dept of Labor. Let t
be the number of years since 1981.
Write a prediction equation and
estimate the wage for 2012.
29) Graph: 2 4 3y x x
30) Determine whether the following
has a maximum or a minimum, then find that value: 22 8 5y x x
31) Factor: 4 6 38 2 10x x x
32) Factor: 2 12 35a a
33) Factor: 2 4 21d d
34) Factor: 216 40 25x x
35) Factor: 23 21 36x x
36) Factor: 2 216 9x y
37) Factor: 23 5 2x x
38) Factor: 3 8x
39) Factor: 38 27a
40) Solve: 23 10 8 0x x
41) Solve: 2 14 1 0x x
42) Solve: 2 6 9 25x x
43) Write an equation given the roots: 4
3,3
44) Simplify: 636m
45) Simplify: 827
46) Simplify: 34i
47) Multiply: 3 2 4 6i i
48) Divide: 6 7
3
i
i
49) Solve for m and n : 28 4 2 6m i ni
50) Solve: 2 4 20 0x x
51) What value should be added to each side to
complete the square: 2 6 1x x
t Wage
0 $3.35
9 $3.80
10 $4.25
15 $4.75
16 $5.15
5; 3
2 7
4
, 4 3
x y x
y x
y x
f x y x y
Fall Final Exam Review (Revised 2013) Algebra 2CP
52) What are the nature of the roots of the equation: 23 6 2 0x x
53) Find the vertex: 622 2 xxf
54) Graph: 2 4 2y x x
55) Solve: 2 6 5x x
56) Simplify: 3 2 62 5a b c ab
57) Simplify: 2 8
4 3
18
14
m n
m n
58) Express in Scientific Notation:
5 83.5 10 2.7 10
59) Simplify: 2 23 6 7 5 2x x x
60) Simplify: 22 3 1x x x
61) Divide: 34 3 2
2
x x
x
62) Reasonably graph: 22 4y x x
63) Simplify: 5 2 2 36 2a b a b
64) Determine whether the degree of the function is odd
or even. How many different real zeros does the
equation have?
65) Given that 2x is a
factor of
3 22 3 11 6f x x x x , find the remaining
factors.
66) List all real zeros of: 4 3 22 3 20f x x x x
67) List the possible rational zeros of the following:
3 22 3 11 6f x x x x
68) Find f g x , given: 25
43 2
xxg
xxf
69) Find f g x , given: 25
43 2
xxg
xxf
70) Find g f x , given: 25
43 2
xxg
xxf
71) Find 1f x if 24 1f x x
72) Given 3,1 , 1, 2 , 1,1 , 2, 3R , find 1R .
Is 1R a function?
73) Simplify: 5 30 2032a b
74) Simplify: 8 48 6 75 7 80
75) Simplify: 2 5
4 8
76) Simplify: 2 3
5 4x x
77) Write in radical form: 4
7m
78) Write as a rational exponent: 4 6a
79) Simplify: 3 7 59a b
80) Simplify: 3 12 2 21
81) Solve: 4 220 64 0x x
82) Solve: 1
2 6 0x x
83) Find and graph the real roots of: 2 2 8 0x x
84) Find the graph, domain, and range of 2 1y x
85) Solve: 9 11 1x x
86) Solve: 15 5x x
87) Solve: 3 1 5a
88) Simplify: 3 2 3
1 4 4
16
24
a b c
a b c
89) Simplify: 42 3
3
2
10
m n
m n
90) Simplify: 2
2
2 3
6 12
x x
x x
91) Simplify:
2
2
2 5 25
24 5
x x x
xx x
92) Simplify:
2
2
3 13 4
44 16
2
x x
xxx
93) Simplify:
2 2
3 5
2 8 12 32
x x
x x x x
94) Solve: 4
5 ss
95) Solve:
6 2 24
4 1
x x
x x
96) Solve:
2
4 4 4
42 8
x
xx x
97) Solve: 5 2
23x x
Fall Final Exam Review (Revised 2013) Algebra 2CP
98) Indicate the least common denominator of the
following: 7 3 4 9
5 8
4 3a bc a c
99) Determine the equation(s) of any asymptotes and
any hole(s) in:
2
3
4 21
xf x
x x
100) Determine the equation(s) of any asymptotes
and any hole(s) in: 22 3
1
x xf x
x
101) Some variable y varies directly with the cube of
x. If 2x when 5y , find the constant of
proportionality, k.
102) While standing on snow, the pressure (P, in
pounds per square inch) varies inversely with the
total area, A (in square inches) of the soles of your
footwear. Suppose the pressure is 0.43 pounds per
square inch while wearing 400 in2 soled snow shoes.
What would be the pressure while wearing 60 in2
soled boots?
103) If y varies jointly as x and z , and 12y
when 2.5x and 3z , then find y when 3.8x
and 14z .
104) Identify the type of function represented in each
graph:
ANSWERS
1) 11.5
2) 9 14a b
3) 6 7n
4) 4s
5) 1 22A
b bh
6) 2
7) 4 or 14x
8) 5y
9) 2 5 17; 6x x
10) 140 90 35 500e
11)
12) 1
13
x
13) 2
5m or 2m
14) D: 3,1, 1, 2 R: 1, 2, 3 ;
yes
15) 3 5f
16) 3 2 12x y ; 4, 0 and
0, 6
17)
18) 1
3m
19) 3m
20) 3 19y x
21)
22) 23) 1,1
24) 7,5
25)
26)
1, 3 , 1, 3 , 5, 6 , 5, 1
Max: 17 at 5,1 ; Min: 13 at
1, 3
27)
15
1 5 20 123
2
o f t
o f t
f t
28) 0.1071 3.1890y x
$6.51 in 2012
29) 30) Maximum; 3 at 2x
31) 3 32 4 5x x x
32) 5 7a a
33) 7 3d d
34) 24 5x
35) 3 3 4x x
36) 4 3 4 3x y x y
37) 3 2 1x x
38) 22 2 4x x x
39) 22 3 4 6 9a a a
40) 2
4,3
x
41) 7 5 2x
42) 8, 2x
Fall Final Exam Review (Revised 2013) Algebra 2CP
43) 23 5 12x x
44) 36m i
45) 6 6
46) 64i
47) 24 10i
48) 11 27
10
i
49) 1 2
;14 3
m n
50) 2 4x i
51) 9
52) 2 Real Roots
53) 2, 6
54) 55) 1 5x
56) 4 810a b c
57) 5
2
9
7
n
m
58) 39.45 10
59) 210 5 4x x
60) 3 25 7 2x x x
61) 2 364 8 19
2x x
x
62)
63) 3 22 3a b ab
64) Even; 3 different real zeros
65) 3 2 1x x
66) 5
4, , 02
x (double root)
67) 1 2 3 6 1 3
, , , , ,1 1 1 1 2 2
68) 23 5 2x x
69) 23 5 6x x
70) 215 18x
71) 1
2
xy
72) 1, 3 , 2,1 , 1, 1 , 3, 2 ;
no
73) 6 42a b
74) 2 3 28 5
75) 2 5 10
2
76) 23
20x
77) 47 4 7 or m m
78) 32a
79) 32 29a b ab
80) 36 7
81) 2, 4x
82) 9x
83) 4, 2x
84) D: 2x and R: 1y
85) 3 or 4x
86) No Real Solution
87) 1 26
3 3a
88) 4
2
2
3
a c
b
89) 5
13
8
5
m
n
90) 1
3 4
x
x
91)
5 1
1
x
x
92)
3 1
4 2
x
x
93)
2 7
4 2 8
x
x x x
94) 1, 4s
95) 1.5, 2x
96) No Real Solutions
97) 3 129
4x
98) 7 912a bc
99) Hole: 3x ;
Asym: 7x ; 0y
100) Hole: 1x
101) 5
8k
102) 2.87 psi
103) 85.12y
104) Cubic Function
Square Root Function
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