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WorksheetsAlgebra 2 Semester 1 Practice Final 2020
Total questions: 110
Worksheet time: 2hrs 50mins
Find the slope of the line.
1/2
-1/2
2/1
-2/1
What is the y-intercept of this graph?
(0,1)
(0,-2)
(0,0)
(0,3)
Which of these lines has a slope of -3?
A
B
C
D
Given the graph choose all correct statements
The slope of the line = 0
The slope of the line is undefined
y = -2
x = -2
y = -2x
Write the slope intercept form of the equation graphed.
y = -2x + 3
y = 1.5x + 2
y = 2x - 3
y = -1.5x - 2
Write the equation for the line.
y= -1x+3
y= 4x+3
y=1/4x+3
y= -4x+3
Write the equation of the line.
y= -1x + 3
y= 3x - 1
y= -1/3x - 1
y= -3x - 3
Which point below is NOT part of the solution set?
(0, 0)
(5, 1)
(-1, -3)
(20, -5)
Which of the following equations match the given graph?
y ≤ -5/4 x + 3
y ≥ -5/4 x + 3
y < -5/4 x + 3
y > -5/4 x + 3
Select the correct graph for each inequality.
A
B
C
D
What is the solution to the system of linear equations graphed below?
No Solution
Infinitely Many Solutions
One Solution: (3, 1)
One Solution: (1, 3)
What is the solution to the system of linear equations graphed below?
No Solution
Infinitely Many Solutions
One Solution: (0 , 4)
One Solution: (0, -6)
Which graph represents a system of equations with no solution?
None of the above
What is the solution to the system of linear equations graphed below?
No Solution
Infinitely Many Solutions
One Solution: (0, 2)
One Solution: (2, 6)
Which of the following is not a solution to this system of inequalities?
(0,-1)
(0,3)
(4,0)
(6,-2)
Which system of inequalities matches the graph?
y > 2x - 4
y < 2
y < 2x - 4
y < 2
y > 2x - 4
y < 2
y < 2x - 4
y < -2
6(n + 2) < -72
n < -14
n < 35/3
n < -10
∞
Select all which are solutions to the given inequality.
-3x + 2 > 8
-2
2
-5
0
-10
5(v + 3) - 10v > -10
Solve.
z + 3(2 + 4z) = 6(z+1) + 5z
0
2
No solution
All real numbers
10x + 2x + 5 = 8x + 4x + 7
6x - 2(x-3) =4(x + 1) + 4
Solve the following system of equations using the elimination method:
(-2, 1)
no solutions
(-2, 0)
(-1, -3)
infinite solutions
If you solve a systems of equations by substitution and your substituted equation is 3y=3y+6, how many solutions does the systems have?
No Solutions
1 Solution
2 Solutions
Infinitely Many Solutions
Not enough information to know
What is the solution to the systems:
y=-3x-2
6x+2y=-4
(6,2)
(-1,-5)
(-2,-8)
Infinity Many Solutions
No Solution
What is the solution to the systems:
3x+y=11
y=x+3
(4,7)
(0.5,3.5)
(-2,17)
(2,5)
No Solution
How many solutions does the system of equations below have?
One Solution
No Solution
Infinitely Many Solutions Infinitely Many Solutions
How many solutions does the system of equations below have?
One Solution
No Solution
Infinitely Many Solutions Infinitely Many Solutions
How many solutions does the system of equations below have?
One Solution
No Solution
Infinitely Many Solutions Infinitely Many Solutions
Solve the system of equations.
(-6, 1)
(-12, -12)
(1, -6)
No solution
Infinite solutions
Solve the system of Equation (Elimination Method)
5x + y = 9
10x − 7y = −18
What is the value of y?
y=-4
y=-1
y= 1
y= 4
y does not have a solution
Solve the system of Equation (x,y)
−4x + 9y = 9
x − 3y = −6
What is the value of x
x=-9
x=-5
x=5
x=9
There is no solution for x
Which of the following could be a correct first step in solving the system shown? Select all that apply.
Multiply the first equation by 2, then add the result to the third equation.
Multiply the second equation by 2, then add the result to the third equation.
Add the first and second equation.
Add the first and third equation.
Add the second and third equation.
x + y + z = 4
x = -2y
z = -3y
Solve:
-4x - 5y - z = 18
-2x - 5y - 2z = 12
-2x + 5y + 2z = 4
(4, 0, -2)
(-4, 0, -2)
Many Solutions
I did not get any of the answers above so I am assuming none of the above.
Solve the system of equations:
x+y+z=2
2x+2y+2z=4
−3x−3y−3z=−6
x=0, y=0, z=0
x=1, y=1, z=2
No solution
Infinite solutions
Solve the system of equations:
x−y−2z=4
4x−4y−z=2
−x+y+2z=−3
x=1, y=−1, z=0
x=0, y=0, z=1
No solution
Infinite solutions
f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)
16
4
-4
None of these.
9 - √17
4
2
√8
Given f(x) = 2x and g(x) = x2+3 , find f(g(x)).
x2+2x+3
4x2+3
2x2+3
2x2+6
Find the inverse of f(x) = -4x - 12
f-1(x) = 4x - 3
f-1(x) = -1/4x - 3
f-1(x) = 1/4x + 3
f-1(x) = -4x - 3
Find the inverse of f(x) = x2 - 5
f-1(x) = √(x) + 5
f-1(x) = ∛(x-5)
f-1(x) =√(x+5)
f-1(x) = x2 - 5
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
D: {1, -3, -4,}
R: {0, 1, 2, -4}
D:{0, 1, 2, -4}
R:{1, -3, -4}
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
Is this graph a function or not a function?
Function with a range -3≥y≥3
Function with a range -3≤y≤3
Function with a domain -5≤x≤2
Function with a domain -5≥x≥2
Not a Function
Is this graph a function or not a function?
Function with a range y≤3
Function with a range y≥3
Function with a domain -4≤x≤5
Function where the domain and range are all real numbers
Not a Function
Give the domain and range. Tell if it is a function.
D: {-4, -2, 0, 2}
R: {-2, -2, 1, 1}
Function
D: {-4, -2, 0, 2}
R: {-2, 1}
Function
D: {-4, -2, 0, 2}
R: {-2, -2, 1, 1}
Not a Function
D: {-4, -2, 0, 2}
R: {-2, 1}
Not a Function
Not enough information to determine range and domain.
Check ALL information that is true about the graph.
Function
Not a Function
Continuous Graph
Discrete Graph
Which of these mappings sets represents a function, choose all that apply?
Which of the following tables represent could be a function of x? Check ALL that apply.
None of the tables have values that could represent a function
Which of the following could be the graph of a function of x? Check ALL that apply!
Given f(x) = -4x - 10 and f(x) = 10. Find x
x = -5
x = 5
x = -50
x = 30
Ms. Law is on leave from work and she has a savings account. She is not getting any extra income and her bills are $899 a week. Her account can be represented by the following equations
y = 11,000 - 899x
where x is the number of weeks and y is the amount left in the account. What is a reasonable domain for this situation?
{0, 1, 2, 3, 4, 5}
{11000, 10911, 10822, 10733, 10644, 10555}
0 ≤ x ≤ 5
10555 ≤ f(x) ≤ 11000
What is the equation of this graph?
f(x) = (x + 2)2 - 3
f(x) = (x - 2)2 - 3
f(x) = |x + 2| - 3
f(x) = |x - 2| - 3
What is the equation of this graph?
f(x) = (x + 2)2 - 2
f(x) = (x - 2)2 - 2
f(x) = |x + 2| - 2
f(x) = |x - 2| - 2
y = Ix + 2I - 1
y = -Ix + 2I - 1
y = -Ix - 2I - 1
y = -Ix + 1I - 2
Describe the transformation from the parent graph
Reflect over x, right 3, down 4
Reflect over y, right 3, down 4
Reflect over x, right 3, up 4
Reflect over y, left 3, down 4
Which of the following is the correct equation for the given graph?
f(x) = -(x + 2)2 - 4
f(x) = -(x - 2)2 - 4
f(x) = -3(x - 2)2 - 4
f(x) = -3(x + 2)2 - 4
Up 2
Up 2
Down 2
Down 2
g(x)=(x=3)2
g(x)=x2-3
g(x)=x2+3
g(x)=3x2
The blue is f(x)=|x|, red must be
|v + 8| − 5 = 2
{-1,-15}
{-1,-5}
{-15,15}
No Solution
| n + 2 | - 3 ≥ -6
No Solution
All Real Numbers
n ≤ -5 or n ≥ 1
-5 ≤ n ≤ 1
| x + 3 | ≤ 2
No Solution
All Real Numbers
-5 ≤ x ≤ -1
1 ≤ x ≤ 5
|6 - 2f| = -5
11/2, 1/2
-5, 5
1, 3
⊘ No solution
When x is less than or equal to 2, what equation is shown in the graph?
f(x) = 3
f(x) = x
f(x) = | x |
f(x) = | x - 1 |
What is g(7) if:
-17
-13
13
17
Which piecewise function corresponds to this graph? (Take your time)
f(x) = { x if x < 4; -x+1 if x ≥ 4
f(x) = { x if x ≤ 4; -x+1 if x > 4
f(x) = { -x+1 if x < 4; x if x ≥ 4
f(x) = { -x+1 if x ≤ 4; x if x > 4
What are the domain restrictions for the green piece of this function?
-2 < x ≤ 1
-1 < x ≤ 0.5
x > -2
x ≤ 1
A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.
How much does he earn for a 70 hour week?
$1020
$1140
$840
He works for free!
Which graph matches:
-x+4 if x<2
2x-6 if x>=2
A
B
C
D
Pick the correct graph
A
B
C
D
What is the RANGE of the function?
(-∞, +∞)
(-∞, 4]
(-∞, 4)
[0, 4]
All Real Numbers
Find x if y = 1
x = -1
x = 0
-2 < x < 1
x = -3
x = 2
The zeros of the function f(x)=3x2-3x-6 are
-1 and -2
1 and 2
1 and -2
-1 and 2
If 4x2-100=0, the roots of the equation are
-25 and 25
-5 and 5
-25, only
-5, only
What are the solutions to the equation x2-8x=10
4±√10
4±√26
-4±√10
-4±√26
Keith determines the zeros of the function f(x) to be -6 and 5. What could be Keith's function?
f(x)=(x+5)(x+6)
f(x)=(x-5)(x+6)
f(x)=(x+5)(x-6)
f(x)=(x-5)(x-6)
If the quadratic formula is used to find the roots of the equation x2-6x-19=0, the correct roots are
What are the roots of the equation x2+4x-16=0
What are the solutions to the equation x2-8x=24
x=4±2√10
x=-4±2√10
x=4±2√2
x=-4±2√2
x2 - 8x + 15
Factor: x2 + 2xy – 3y2
(x - 2y)(x + y)
(x + y)(x - 3y)
(x + 2)(x - y)
(x - y)(x + 3y)
(x + 2y)(x - y)
What are the factors of
25x2 - 81y2?
(5x - 9y)(5x + 9y)
(5x - 9)(5x - 9)
(5x + 9)(5x + 9)
Cannot be factored
(5x - 9y)(5x - 9y)
Factor 4b5+4b3+16b2
4b3(b4+b2+4b)
4b3(b4+4b+5)
4(b5+b3+4b2)
4b2(b3+b+4)
Factor completely.
3x2 + 10x - 8
(3x + 2)(x + 4)
(7x + 5)(x + 2)
(3x - 2)(x + 4)
(7x - 3)(x - 4)
Factor completely.
5x2 - 7x + 2
5(x - 2)(x + 1)
(5x - 2)(x + 1)
(7x - 1)(x - 4)
(5x - 2)(x - 1)
Factor and solve:
14=2x²- 12x
x=7,1
x=-7,1
x=-1,7
No solution
What are the green dots called?
axis of symmetry
vertex
parabola
roots or x-intercepts
What is the green dot on the parabola called?
maximum
minumum
roots
zeros
vertex
What is the green dashed line called?
roots or x-intercepts
parabola
axis of symmetry
line of dashes
Which variable, when negative, can cause the parent function to reflect across the x-axis (face downwards)?
f(x) = a (x-h)2+k
a
h
k
f(x)
x
