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WorksheetsBig Review Alg. 2
Total questions: 75
Worksheet time: 3hrs 28mins
Name
Class
Date
1.
|−2n| + 10 = −50
a)
{30, -30}
b)
{20,-20}
c)
{-5,5}
d)
No Solution
2.
What is the equation of this graph?
a)
y=2|x-3|+1
b)
y=2|x-1|+3
c)
y=-2|x-1| - 3
d)
y=-2|x-1|+3
3.
Which parent function matches the graph?
a)
y = |x|
b)
y = ∛(x)
c)
y = x2
d)
y = a⋅bx
4.
What type of function is shown?
a)
absolute value
b)
quadratic
c)
linear
d)
exponential
5.
What type of function is shown?
a)
linear
b)
quadratic
c)
square root
d)
absolute value
6.
What type of function is shown?
a)
Exponential
b)
square root
c)
quadratic
d)
cube root
7.
What is the Vertex coordinates for the following parabola: 2(x-3)2+4
Hint: vertex formula is a(x-h)2+k
Hint: vertex formula is a(x-h)2+k
a)
(2,4)
b)
(3,4)
c)
(1,4)
d)
(0,2)
8.
What are the coordinates of the y-intercept?
a)
(-3, 0)
b)
(0, -3)
c)
(2, 1)
d)
y=-3
9.
What are the x-intercepts for this graph?
a)
(1,0) and (3,0)
b)
(1,0) and ( -3, 0)
c)
0 and (-3,0)
d)
(0,0) and 3
10.
If the blue function is f(x)=x2, then the red function must be
a)
g(x)=x2-5
b)
g(x)=x2+5
c)
g(x)=(x-5)2
d)
g(x)=(x+5)2
11.
g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been translated to the left one and down five.
b)
f(x) has been translated to the right one and down five.
c)
f(x) has been translated to the left one and up five.
d)
f(x) has been translated to the right one and up five.
12.
g(x)=f(x+2)-3
Describe the transformation to f(x) that results in g(x).
Describe the transformation to f(x) that results in g(x).
a)
f(x) has been translated to the left two and down three.
b)
f(x) has been translated to the right two and down three.
c)
f(x) has been translated to the left two and up three.
d)
f(x) has been translated to the right two and up three.
13.
What interval notation does the number line graph represent?
a)
[∞, -5)
b)
(∞, -5)
c)
[-5, ∞)
d)
(-5, ∞)
14.
What is the interval of decrease for this function?
a)
(-5, 3)
b)
All real numbers
c)
[-2, 6]
d)
(-2, 6)
15.
What is the domain of this function in interval notation?
a)
(1, infinity)
b)
[1, infinity)
c)
(2, infinity)
d)
[2, infinity)
16.
Which statement is true about this graph?
a)
This function is always constant
b)
This function is always increasing
c)
This function is never increasing
d)
This function is both increasing and decreasing
17.
List the types of intervals that the graph demonstrates in order.
a)
decreasing, constant, increasing, constant
b)
increasing, decreasing, constant
c)
increasing, constant, increasing, constant
d)
increasing, constant, decreasing, constant
18.
What is the absolute max?
a)
(0, 36)
b)
(−2.55, −6.55), (2.55, −6.55)
c)
(−∞, ∞)
d)
None
19.
When is the velocity decreasing?
a)
0 < t < 60
b)
40 < t < 60
c)
15 < t < 40
d)
−40 < t < 0
20.
Find the inverse of
f(x) = 1/4x - 7 (hint: Change f(x) to y, switch x and y then solve for y.)
a)
f-1(x) = 4x + 7
b)
f-1(x) = -4x + 28
c)
f-1(x) = -4x - 7
d)
f-1(x) = 4x + 28
21.
Given
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
a)
11x2 - 1
b)
5x4 + 6x2 - 1
c)
5x2 + 6x - 1
d)
5x2 + 8x - 1
22.
Given g(x)= -3x and f(x)=x2+2, find g(f(x)).
a)
g(f(x))= -3x2-6
b)
g(f(x))= -3x2+2
c)
g(f(x))=9x2+2
d)
g(f(x))= -9x2+2
23.
Given g(x)= -3x and f(x)=x2+2, find f(g(x)).
a)
f(g(x))= -3x2-6
b)
f(g(x))= -3x2+2
c)
f(g(x))=9x2+2
d)
f(g(x))= -9x2+2
24.
Given f(x) = x+3, find f(-2).
a)
-1
b)
1
c)
5
d)
-5
25.
Does the graph of the function
y = -2(x + 5)2 + 2
have a minimum or a maximum?
a)
Minimum
b)
Maximum
c)
It has neither.
d)
It has both.
26.
Identify the vertex and whether the graph opens up or down.
a)
(5, 2); opens up
b)
(5, 2); opens down
c)
(-5, 2); opens up
d)
(-5, 2); opens down
27.
Which equation has a vertex of (-3, 4)?
a)
y = 2(x+3)2 + 4
b)
y = (x+3)2 - 4
c)
y = (x-3)2 + 4
d)
y = 2(x - 3)2 + 4
28.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
29.
There are 50 donkeys and chickens on a far. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?
a)
d + c = 174
4d + 2c = 50
4d + 2c = 50
b)
d + c = 50
4d + 2c = 174
4d + 2c = 174
c)
d + c = 50
2d + 4c = 174
2d + 4c = 174
d)
d + c = 174
2d + 4c = 50
2d + 4c = 50
30.
Find the slope of the line that passes through:
(-4, 7) and (-6, -4)
(-4, 7) and (-6, -4)
a)
2/11
b)
13/2
c)
3/10
d)
11/2
31.
Solve using substitution.
2x - 2y = 2
y = -5x + 14
2x - 2y = 2
y = -5x + 14
a)
(4, 5)
b)
(2.5, 1.5)
c)
(1.5, 5)
d)
(1, 2.25)
32.
a)
A
b)
B
c)
C
d)
D
33.
point (5, 3)
Slope 2
Write in point slope form and then convert to slope intercept form
Slope 2
Write in point slope form and then convert to slope intercept form
a)
y = 2x - 7
b)
y = 2x + 3
c)
y = 2x + 13
d)
y - 3 = 2(x - 5)
34.
Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, 7); m = -1/4
(4, 7); m = -1/4
a)
y - 7 = -1/4(x - 4)
b)
y - 4 = -1/4(x + 7)
c)
y + 7 = 4(x - 4)
d)
y + 7 = -1/4(x + 4)
35.
Write the equation in point-slope form for the line that contains the points
(-2, -3), (4, 3)
(-2, -3), (4, 3)
a)
y - 3 = 1(x - 2)
b)
y + 3 = 1(x + 2)
c)
y -3 = -1(x + 2)
d)
y + 3 = -1(x - 2)
36.
Simplify
x⁵ ⁄ x³
x⁵ ⁄ x³
a)
x²
b)
x
c)
1
d)
x⁸
37.
According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: 28 / 23
Example: 28 / 23
a)
add
b)
subtract
c)
multiply
d)
divide
38.
According to exponent rules, when we multiply two powers with the same base we _______ the exponents.
Example: 56 ⋅ 54
Example: 56 ⋅ 54
a)
add
b)
subtract
c)
multiply
d)
divide
39.
According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (42)5
Example: (42)5
a)
add
b)
subtract
c)
multiply
d)
divide
40.
Evaluate the expression using the quotient rule.
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
41.
(53x2y4)0
a)
5xy
b)
1
c)
0
d)
5
42.
(2ab)3
a)
8a3b3
b)
2ab3
c)
6a3b3
d)
6ab
43.
Rewrite using a positive exponent.
w-13
w-13
a)
-w13
b)
1/w13
c)
1/w-13
d)
w13
44.
Simplify.
a)
y60
b)
1/y16
c)
y-16
d)
y4
45.
Write in exponential form
∛x⁷
∛x⁷
a)
x⁷∕ ³
b)
x3⁄7
c)
3x⁷
d)
7x³
46.
Write as a radical expression
y¹⁄ ³
y¹⁄ ³
a)
∛y
b)
y³
c)
√y
d)
1∕ 3y
47.
Simplify
x²⁄ ³⋅x¹⁄ ³
x²⁄ ³⋅x¹⁄ ³
a)
2x
b)
x²⁄₉
c)
x
d)
x²
48.
Simplify
(x²⁄ ³)²⁄ ⁵
(x²⁄ ³)²⁄ ⁵
a)
x⁴∕ ¹⁵
b)
x¹⁶∕ ¹⁵
c)
x⁶
d)
6x
49.
Which expression is equivalent to (3x2y)2 (2x4y2)2
a)
10x10y6
b)
12x24y8
c)
24x10y7
d)
36x12y6
50.
Simplify x2y-5
a)
x2/y5
b)
1/x2y5
c)
y5/x2
d)
x2/y-5
51.
Add: √20 + √45
a)
√65
b)
10√5
c)
5√5
d)
13√5
52.
Find the difference.
(3- 2x + 2x2) - (4x -5 +3x2)
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
53.
Multiply
(x2-2x+1)(x+1)
(x2-2x+1)(x+1)
a)
x3-x2-x+1
b)
x3-2x+2
c)
x3+x2+x+1
d)
x3-3x2-3x+1
54.
Multiply (p − 8)2
a)
p 2 − 16p − 64
b)
p 2 + 16p + 64
c)
p 2 − 16p − 8
d)
p 2 − 16p + 64
55.
What are the x-intercepts of the polynomial y = - (x + 1)( x )(x - 2) (x - 3)?
a)
-1, 1, 0, -2, -3
b)
1, 0, -2, -3
c)
1, 0, 2, 3
d)
-1, 0, 2, 3
56.
Match the equation to the graph.
a)
y=-(x+1)(x-2)(x-4)
b)
y=(x+1)2(x-3)(x-1)3
c)
y = 3x3 – 2x + 1
d)
y=(x+1)3(x-3)(x-1)2
57.
Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0
*a positive leading coefficient
*zeros: 9, 3, -2, 0
a)
y = x(x - 9)(x - 3)(x + 2)
b)
y = x(x + 9)(x + 3)(x - 2)
c)
y = -x(x - 9)(x - 3)(x + 2)
d)
y = -x(x + 9)(x + 3)(x - 2)
58.
Factor:
4n6 + 16n4 - 8n
4n6 + 16n4 - 8n
a)
4n(n4+4n3-2)
b)
4n(n5+4n3-2)
c)
12n(n5+4n4-2)
d)
16n(n5+4n3-2)
59.
Factor by grouping
6x2 -9x + 8x - 12
a)
(3x +4)(2x -3)
b)
(3x -3)(2x +4)
c)
3x(2x - 3)+4( 2x -3)
d)
(3x +4)+(2x -3)
60.
What is end behavior?
a)
The behavior of the graph as x approaches positive infinity or negative infinity.
b)
The behavior of the graph as y approaches positive infinity or negative infinity.
c)
The behavior of the graph as x approaches 0.
d)
The behavior of the graph as y approaches 0.
61.
(2x3 - 5x2 + 3x + 7) ÷ (x - 2)
a)
2x3 - x2 + x + 9
b)
2x2 - x + 1
c)
2x2 - x + 1 + 9/x-2
d)
2x2 - 9x - 15 - 23/x-2
62.
(3x3 + 5x - 1 )÷ (x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
63.
What 5 states touch Georgia?!?
a)
Alabama, South Carolina, North Carolina, Kentucky, Florida
b)
South Carolina, North Carolina, Florida, Louisiana, Mississippi
c)
South Carolina, Alabama, North Carolina, Tennessee, Mississippi
d)
Florida, South Carolina, Tennessee, Alabama, North Carolina
64.
Peter Parker was the real name for which super hero?
a)
Superman
b)
Spiderman
c)
The Hulk
d)
Ironman
65.
What roman numeral is X?
a)
2
b)
5
c)
1000
d)
10
66.
What word is spelled the same backwards?
a)
eye
b)
mom
c)
racecar
d)
all of the above
67.
Statue of Liberty was given to us by?
a)
France
b)
Ohio
c)
Germany
d)
Iran
68.
Which planet is the closest to the sun?
a)
Pluto
b)
Venus
c)
Mercury
d)
Earth
69.
How many states start with H
a)
10
b)
1
c)
5
d)
23
70.
If cats are feline what are Sheep?
a)
Diurnal
b)
Ovine
c)
Nocturnal
d)
Feline
71.
On a farm a kid is a baby what?
a)
cow
b)
goat
c)
cat
72.
Who painted the Mona Lisa?
a)
Michelangelo
b)
Leonardo Da Vinci
c)
Catherine Meihaus
73.
name this picture
a)
mona lisa
b)
starry night
c)
the scream
d)
moonlit hamlet
74.
who is this
a)
Peter
b)
Stewie
c)
Meg
d)
Albert
75.
Factor: 8x3 - 1
a)
(2x - 1)(4x2 + 2x + 1)
b)
(2x + 1)(4x2 - 2x + 1)
c)
(2x - 1)(4x2 - 2x - 1)
d)
(2x + 1)(4x2 +2x + 1)
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