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WorksheetsAlgebra 1 Full Year Review
Total questions: 140
Worksheet time: 6hrs 14mins
The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. What is the cost per lesson?
$11.71 per lesson
$11.10 per lesson
$10 per lesson
Cannot be determined
To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $102.00 The cost for 8 tickets is $150. What are the two points that we could use to find a linear equation for cost, C, of t tickets?
(5,8) & (102, 150)
(8,5) & (150,102)
(5,102) & (8,150)
(102,5) & (150,8)
The temperature where Cally lives is 73℉ and is falling 2℉ per hour. Which of the following equations can be used to determine how many hours (h) it will take for the temperature to drop to 65℉?
73 - 2h = 65
73 - 65 = 2h
65 - 2h = 63
2h - 73 = 65
A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:
f(x) = 2.75x + 4.25
What does 4.25 represent?
The total cost of the fixed fee plus charge per mile
The charge per mile
Miles
The fixed fee
Karma
A car is driving down from the top of a Colorado mountain. The elevation at the top of the mountain is 13,500 feet. Every minute of driving, the car’s elevation decreases by 150 feet. Write an equation to represent the given situation.
y = 150x - 13,500
y = 13,500 - 150x
y= 150x + 13,5000
y = -150x - 13,500
Write the linear equation in y = mx + b form using the given points.
y = 2/3x - 2
y = 3/2x - 2
y = -2/3x + 2
y = x + 2
Write the equation of the line passing through the points (1, -2) and (4, 1).
y = x + 3
y = x - 3
y = -x + 3
y = -x - 3
y= 3x - 3
y= -1/3x - 3
y = 1/3x - 3
y= -3x - 3
STANDARD FORM:
2x - 5y = -10
What is the slope?
−52
21
23
STANDARD FORM:
2x - 5y = -10
What is the y-intercept?
3
5
2
Which equation in standard form represents this graph?
-3x +2y = -6
3x + 2y = 6
-3x - 2y= 12
-3x + 2y = -12
Graph. x = 4
A
B
C
D
A
B
C
D
3x + 8y = 24
Consider the given function that represents the balance in a bank account.
b(x)=850(1.025)x
What is the initial balance in the account?
(a)
A small private school with a graduating class of 40 students in the year 2019 predicts that its graduating class will increase by 5% each year.
What function best represents this situation?
f(x)=40(0.95)x
f(x)=40(1.05)x
f(x)=5(0.60)x
f(x)=5(1.40)x
The value of a new video game is $40. The value is expected to decrease by 5% each year.
What function best represents this situation?
f(x)=40(0.95)x
f(x)=40(1.05)x
f(x)=5(0.60)x
f(x)=5(1.40)x
Write the equation of the exponential function for the given graph.
y = 2(2)x
y = 2(1)x
y = 1(1/2)x
y = 2x
Write the equation of the exponential function for the given graph.
y = 3x
y = 2(1/3)x
y = (1/3)x
y = -1(1/3)x
Write the equation of the exponential function for the given table.
y = 2(1/3)x
y = -2(1/3)x
y = 1/3(2)x
y = 2(-1/3)x
Write the equation of the exponential function for the given table.
y = 1(4)x
y = 1(1/4)x
y = 4(4)x
y = 1/4(1)x
The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.
Which function models the amount of cola in gallons after h hours?
f(h) = 75(-5)h
f(h) = -5(75)h
f(h) = .95(75)h
f(h) = 75(.95)h
Given the following table of values, construct the function that represents the sequence.
y = 3(4)x
y = 3x + 4
y = 4(3)x
y = 4x + 3
Suppose a bacteria is introduced to two different solutions in separate petri dishes. The bacteria in the first solution grow at a rate modeled by the function G(t) = (1.40)t. The bacteria in the second solution grow in accordance with the data displayed in the table.
Which statement best describes the growth rates exhibited within the two different solutions?
The bacteria grow at the same rate in both solutions.
The bacteria grow at a slower rate in the first solution.
The bacteria grow at a faster rate in the first solution.
The bacteria decay in the first solution and grow in the second solution.
Leonard compared the cost of purchasing a gallon of gas at two different gas stations.
The function C(g) = 3.25 + 0.07x models the average cost of a gallon of gas at the first gas station after x months. The table below shows the average cost of a gallon of gas at the second gas station after different numbers of months.
Which statement is true?
The first station had a higher initial price per gallon and increased at a greater amount per month than the second station.
The second station had a higher initial price per gallon and increased at a greater amount per month than the first station.
The first station had a higher initial price per gallon but increased at a smaller amount per month than the second station.
The second station had a higher initial price per gallon but increased at a smaller amount per month than the first station.
Jason invested money into two different accounts. He deposited $75 into the first account which earns 6% interest annually. The value of the second account after different amounts of time is shown in the table.
Which statement is true?
Jason started with $4 less in the second account than the first account.
Jason started with $5 less in the second account than the first account.
Jason started with $4 more in the second account than the first account.
Jason started with $5 more in the second account than the first account.
The function C(m) = 0.55m + 3.75 models the cost to take an m mile-long taxi ride from Quick Cabs. The table shows the cost to take a cab different distances from Get You There Cabs.
Which statement is true about the two cab companies?
Quick Cabs costs less per mile but has a higher fixed fee than Get You There Cabs.
Quick Cabs costs more per mile but has a lower fixed fee than Get You There Cabs.
Quick Cabs costs less per mile and has a lower fixed fee than Get You There Cabs.
Quick Cabs costs more per mile and has a higher fixed fee than Get You There Cabs.
What is the growth/decay rate if the function is f(x)=20(1.7)x ?
70%
7%
0.7%
0.07%
170%
What is the growth/decay rate if the function is f(x)=5,829(0.8)x ?
8%
80%
2%
20%
0.8%
What is the growth/decay rate if the function is f(x)=850(1.04)x ?
4%
40%
0.4%
104%
0.04%
What is the solution to this system of equations?
x = 7 - 2y
2x + y = 5
(-1,4)
(1,3)
(4,-1)
(3,1)
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. Which would be the correct system of equations for this story?
T + M = 100
3T + 11M = 100
T + M = 20
3T - 11M = 100
T + M = 20
3T + 11M = 100
T - M = 20
3T + 11M = 100
The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Which system of equations represents this situation?
5q + 2z = 1.32
1z = 0.75
5q + 2z = 1.32
3q + 1z = 0.75
q + z = 1.32
q + z = 0.75
5q + 2z = 0.75
3q + 1z = 1.32
3x + 2y = 315
2x + 4y = 450
3x + 2y = 450
2x + 4y = 315
2x + 2y = 315
3x + 4y = 450
3x + 2y = 315
4x + 2y = 450
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?
1s + 3c = 38
2s + 3c = 52
3s + 1c = 38
3s + 2c = 52
s + c = 38
s + c = 52
3s + 3c = 38
1s + 2c = 52
Solve by elimination:
7x + y = -9
-3x - y = 5
Write your solution as an ordered pair without spaces (x,y)
(a)
Solve by elimination
-8x + 5y = -17
9x - 4y = 24
Write your solution as an ordered pair without spaces (x,y)
(a)
Given:
f(x)=6x
Find x when f(x)=−24
x=−4
x=4
x=−144
x=−6
Given the graph,
find:
f(2)f(2)=5
f(2)=4
f(2)=3
f(2)=0
Given the graph,
find:
f(4)f(4)=3
f(4)=1
f(4)=2
f(4)=0
Given the graph,
find the value of x when:
f(x)=0x=1
x=0
x=7
x=2
Given the graph,
find the value of x whenf(x)=2
x=7
x=1
x=5
x=4
Given the function
f(x)=x+3
Evaluate:
f(−2)
f(−2)=−1
f(−2)=1
f(−2)=5
f(−2)=−5
Interpret d(8)=300 in context.
Interpret W(5)=75
Number of steps taken per day and number of kilometers walked per day. r=.92
strong positive
strong negative
weak positive
weak negative
Car weight and distance traveled using a full tank of gas. r=−.86
strong positive
strong negative
weak positive
weak negative
Score on science exam and number of words written on the essay question. r=.28
strong positive
strong negative
weak positive
weak negative
Based on the scatterplot, which of the following conclusions about the relationship between her height and weight is true?
There is a negative relationship between height and weight
There is a positive relationship between height and weight
There is a constant relationship between height and weight
There is no relationship between height and weight
Which expression represents the simplified area of the rectangle?
x2 + 9x + 20
x2 + 9x - 20
x2 + x - 20
x2 - x - 20
Which expression is the simplified area of a rectangle with a length of (3x – 1) and a width of (x + 5)?
3x2 + 4x + 5
3x2 + 4x - 5
3x2 + 14x + 5
3x2 + 14x - 5
Subtract (2x + 8) from (5x + 1)
7x2 + 2x + 9
10x2 + 42x + 8
3x - 7
-3x + 7
What is the difference between (3- 2x + 2x2) and (4x -5 +3x2)?
x2 + 6x + 8
2x2 + 5x - 7
-x2 -6x + 8
-2x2 + 11x - 4
Simplify (x - 4y)2
X2 - 16y2
X2 +8xy -16y2
x2 - 8xy +16y2
x2 + 4y2
Simplify (2x - 8)2
4x2 + 64
4x2 -16x + 64
4x2 + 16x - 64
4x2 - 64
Find the axis of symmetry for
f(x) = x2- 8x + 15. Type your answer with no spaces.
(a)
Find the vertex of
f(x) = -x2 - 4x + 12. Type your answer with no spaces.
(a)
The graph of y=-2x2+3 will have a:
minimum
maximum
neither
Which graph represents y=-x2+4
Will the function x2 + 3x - 4 have a minimum or maximum?
Minimum
Maximum
Will the function -2x2 + 3x - 4 have a minimum or maximum?
Minimum
Maximum
Find the vertex:
( 4 , 8 )
( -4 , -8 )
( 4 , -8 )
( -4 , 8 )
Find the vertex:
( 4 , 6 )
( -4 , -6 )
( 4 , -6 )
( -4 , 6 )
Which equations matches the graph above?
h(x)= (x+1)2−4
h(x)=−(x+1)2−4
h(x)=(x+4)2−1
h(x)=−(x+4)2+1
Which equation is graphed above?
y=−(x−1)2+4
y=(x−1)2+4
y=−(x−4)2+1
y=(x−4)2+1
y=−3(x+5)2−4
Convert the equation from vertex form to standard form.
y = 9x2 - 15x + 21
y = -3x2 - 75x - 4
y = 9x2 + 90x + 221
y = -3x2 - 30x - 79
y=−5(x+2)2−10
Convert the equation from vertex form to standard form.
y = -5x2 - 20x - 30
y = -5x2 - 4x - 10
y = 25x2 + 100x + 90
y = 25x2 - 10x - 30
What causes the graph of y = x2 to be narrower (vertical stretch)?
multiply the x2 by a fraction/decimal between 0 and 1
multiply the x2 by 0
multiply the x2 by a negative number
multiply the x2 by a number greater than 1
What causes the graph of y = x2 to be wider (vertical compression)?
multiply the x2 by a fraction/decimal between 0 and 1
multiply the x2 by 0
multiply the x2 by a negative number
multiply the x2 by a number greater than 1
Which points are on the parabola represented by
y = x2 - 6x + 3
Select all that apply.
(0, 3)
(1, -2)
(2, -5)
(-1, 3)
What is the maximum height of the hovercraft?
9 meters
81 meters
27 meters
108 meters
324 meters
What causes the graph of y = x2 to open downward?
multiply the x2 by a fraction/decimal between 0 and 1
multiply the x2 by 0
multiply the x2 by a negative number
multiply the x2 by a number greater than 1
In the vertex form f(x) = a(x - h)² + k , what does the 'a' value do?
Shifts the function left or right
Changing 'a' value has no affect on the parent function
Vertical stretch or compression
Shifts the function up or down
Reflects the parabola across the x-axis
Given f(x) = ax² , if 0 < a < 1 , the graph will transform by
becoming wider or vertically compressed
becoming narrower or vertically stretched
Given f(x) = ax² , if a > 1 , the graph will transform by
becoming wider or vertically compressed
becoming narrower or vertically stretched
In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?
Shifts the function left or right
Reflection over the x-axis
Vertical stretch or compression
Shifts the function up or down
In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?
Shifts the function left or right
Reflects over the x-axis
Vertical stretch or compression
Shifts the function up or down
Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?
Horizontal shift left 6, vertical shift up 2
Horizontal shift left 6, vertical shift down 2
Horizontal shift right 6, vertical shift down 2
Horizontal shift right 6, vertical shift up 2
What steps transform the graph y = x2 to y = (x-4)2
Shifted down 4 units
Shifted left 4 units
Shifted right 4 units
Shifted up 4 units
What type of function describes the story below?You have $5 and triple your money every day.
Linear
Quadratic
Exponential
Which function best models the amount of money you earn when you get paid an hourly wage?
Linear
Quadratic
Exponential
Which statement below is TRUE regarding the two functions?
Both functions are linear
Both functions are increasing
Both functions have a y-intercept of 1
Both functions are exponential growth
Which of the following statements is true about the functions f(x) and g(x)?
The y-intercept of the function f(x) is less than the y-intercept of the function g(x).
The y-intercept of the function f(x) is greater than the y-intercept of the function g(x).
The y-intercept of the function f(x) is equal to than the y-intercept of the function g(x).
The y-intercepts cannot be determined.
-2x ≥ 22
5 ≥ x
-5m < 10
6 > x
Which graph represents the inequality, y ≤37x−2 ?
A
B
C
D
If the inequality symbol is ≤ or ≥, the line will be ___________.
solid
dotted
If the inequality symbol is < or >, the line will be _________.
solid
dotted
Are the points on the boundary line part of the solution set?
No, they are NOT part of the solution set
Yes, they are part of the solution set
Which point below is NOT part of the solution set?
(0,0)
(-10,20)
(3,5)
(3,0)
Consider the inequality, y < 2x + 3. Which is true?
The line would be solid with shading above.
The line would be dotted with shading above.
The line would be solid with shading below.
None of the above
Is (0,0) a solution to the inequality, y > -x +1?
Yes
No
What is the graph of the linear inequality:
x+y>−4What is the graph of the linear inequality:
What is the graph of the linear inequality:
7x−2y>−4
Which of the following is NOT a solution to the systems of inequalities?
(0, 0)
(3, -2)
(3, -4)
(4, -4)
y>-2x+3
y≤-2x+3
y≥-2x+3
y>2x+3
y < 2
y < 2
y < 2
y < -2
Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?
x + y ≥ 6
32x + 20y ≤ 150
x + y ≥ 632
x + 20y ≥ 150
x + y ≤ 6
32x + 20y ≤ 150
x + y ≤ 6
32x + 20y ≥ 150
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing
x + y ≤ 300
7.5x + 5.5y ≥ 2000
x + y < 300
7.5x + 5.5y ≥ 2000
x + y ≤ 300
7.5x + 5.5y ≤ 2000
x + y > 2000
7.5x + 5.5y ≤ 300
Jonah is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00. He needs to buy at least 20 candles and cannot spend more than $80.
Write a system of linear inequalities that represents the situation.
x+y≤20
3.5x+5y≥80
xy≥20
3.5+5y≤80
x−y≥20
3.5x+5y≤80
x+y≥20
3.5x+5y≤80
What is the median commute time?
30 min
25 min
35 min
40 min
What percentage of the temperatures is below 71 degrees?
75%
50%
25%
0%
Which class has a higher median?
1st Period
2nd Period
Which class has the highest test score?
1st Period
2nd Period
25 %
50%
75%
100%
How many trees are at least 15 feet tall?
12 trees
2 trees
9 trees
41 trees
Which way is the data display skewed (tail)?
Left
Right
No Skew
Which way is the data display skewed (tail)?
Left
Right
No Skew
What is the y-intercept of
f(x)=2x2 + 4x + 6. Type your answer as an ordered pair with no spaces.
(a)
Which function has a greater y-intercept, f(x) or g(x)?
f(x) = 4x2+8x +5
f(x)
g(x)
They're the same
The y-intercepts cannot be determined.
Which function has an axis of symmetry further to the left, f(x) or g(x)?
f(x) = 4x2+8x +5
f(x)
g(x)
They're the same
The axis of symmetries cannot be determined.
Which function has a higher vertex, f(x) or g(x)?
f(x) = 4x2+8x +5
f(x)
g(x)
They're the same height
The vertices cannot be determined.
7 ⋅ 7 = ?, which is ?
rational
irrational
4π − 4π = ?, which is ?
rational
irrational
35+25 = ?, so the result is ?
510, irrational
55, irrational
65, irrational
610, irrational
Is 161+43 rational or irrational?
Rational
Irrational
If the discriminant is positive, then the solution could be....
(select all that apply)
one real solution
two real rational solutions
no real solutions
one real irrational solution
two real irrational solutions
______________
How many solutions does it have?
