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WorksheetsThe Climb: Level 2
Total questions: 138
Worksheet time: 6hrs 9mins
An equation is...
a statement in algebra that says that two expressions are equivalent
a statement in algebra that says that two or more expressions are equivalent
a statement in algebra that says that two expressions are similar
a statement in pre-calculus that says that two expressions are equivalent
A linear equation is...
an equation in which the highest power on any variable is 1
an equation in which the highest power on any variable is 2
an equation in which the highest power on all variables is 2
an equation in which the lowest power on any variable is 1
To isolate a variable in a linear equation, you...
use inverse operations to "undo" whatever is being done to the variable, remembering to do the same thing to both sides to keep them equal
use inverse operations to "undo" whatever is being done to the variable, remembering to do the same thing to both sides to keep them different
use similar operations to "undo" whatever is being done to the variable, remembering to do the same thing to both sides to keep them equal
use inverse operations to "undo" whatever is being done to the number, remembering to do the same thing to both sides to keep them equal
How would you solve the following ?
8x=5
Multiply both sides by 8
Multiply both sides by 5
Divide both sides by 8
Multiply both sides by x
Identify the proper order for solving linear equations:
1) Eliminate any fractions
2) Collect and combine like terms
3) Divide to leave the desired variable by itself
3) Eliminate any fractions
2) Collect and combine like terms
1) Divide to leave the desired variable by itself
2) Eliminate any fractions
1) Collect and combine like terms
3) Divide to leave the desired variable by itself
1) Eliminate any fractions
3) Collect and combine like terms
2) Divide to leave the desired variable by itself
What's the first step in isolating "x" given the desire to eliminate any fractions?
31(x+11)=21(4x−6)
Multiply both sides by 6
Divide both sides by one-third
Divide both sides by one-half
Divide both sides by (x+11)
Divide both sides by (4x-6)
Solve
31(x+11)=21(4x−6)
Which represents a linear equation in slope-intercept form?
y=mx+b
x2−x1y2−y1
y2−y1=m(x2−x1)
y=bx+m
Which does "m" represent in slope-intercept form?
y=mx+b
The slope of the line
The y-intercept of the line
The x-intercept of the line
The x-value of the y-intercept
Which could "m" represent in slope-intercept form in a real-world scenario?
y=mx+b
Miles per hour
Money put into a bank account
Words typed per minute
Wins per season
Salary earned in year one
Which could "b" represent in slope-intercept form in a real-world scenario?
y=mx+b
Miles per hour
Money put into a bank account
Words typed per minute
Wins per season
Salary earned in year one
The rate of change (slope) for a linear relationship is constant (does not vary)
y=mx+b
True
False
What's the slope formula?
m=y2−y1x2−x1
m=x1−x2y1−y2
m=x2−x1y2−y1
m=y1−y2x1−x2
Which describes a "positive slope"?
Goes up from left to right
Goes down from left to right
Goes up from right to left
Goes down from right to left
Which describes a "negative slope"?
Goes up from left to right
Goes down from left to right
Goes up from right to left
Goes down from right to left
A line with a slope of zero...
Goes up from left to right
Goes down from left to right
Goes up from right to left
Goes down from right to left
Is horizontal
The slope of a vertical line...
Goes up from left to right
Is undefined
Goes up from right to left
Goes down from right to left
Is horizontal
The slope of parallel lines...
go up from left to right
are undefined
are the same
go down from right to left
are horizontal
The slope of perpendicular lines...
have positive reciprocal slopes
are undefined
are the same
have negative reciprocal slopes
are horizontal
Which are true about linear equations in standard form?
Two variables
Three constants
Two of the constants may equal zero
Two of the constants may not equal zero
All constants must be integers
SE.1
Kindly solve for x and enter the numerical value only:
2x+3=7+x
(a)
SE.2
Kindly solve for x and enter the numerical value only:
−2x+4=5x−10
(a)
SE.3
Kindly solve for x and enter the numerical value only:
(4x+5)−(−2x+11)=x+4
(a)
SE.4
Kindly solve for x and enter the numerical value only:
21x+1=3x−4
(a)
SE.5
Kindly solve for x and enter the numerical value only:
(a)
SE.6
Kindly solve for x and enter the numerical value only:
(a)
SE.7
Kindly solve for x and enter the numerical value only:
(a)
SE.8
Kindly solve for x and enter the numerical value only:
(Simplify fractions as much as possible, enter your response using simplified fractions, and list your termed-variables in alphabetical order)
(a)
SE.9
Kindly solve for x and enter the numerical value only:
x=y−27−4y
x=y−27+4y
x=7+4yy−2
x=y−24y−7
SE.10
Kindly solve for x and enter the numerical value only:
(a)
TD.1
Translate from English to math as an equation:
"The number of subscribers is 4 less than 3 times the number of followers"
S=3F-4
F=3S-4
S=3F+4
S=-4-3F
TD.2
Translate from English to math as an equation:
"After a 15 percent decrease in the original purchase price, a certain stock is worth $92 per share"
$92=.85P
$92=P-.15
$92=.85/P
$92=.15P
TD.3
Translate from English to math as an equation:
"Average speed in "miles per hour" if the total distance traveled in two and one-half hours is D miles."
A.S. = 2.5D
D = 2.5A.S.
A.S. = D2.5
A.S. = 2.5D
TD.4
Translate from English to math as an equation:
"The product of x and y is equivalent to their sum increased by 5."
xy=(x+y)+5
yx=(x+y)+5
xy=(x+y)−5
xy=x+y+5
TD.5
Translate from English to math as an equation:
"Jose's age in 5 years will be 1 year more than double what Beatrice's age was 2 years ago."
J+5=1+2(B-2)
J+5=(1+2B)+2
J+5=(1+2B)-2
J+5=1+(2B-2)
TD.6
Translate from English to math as an equation:
"If 2 more blue chips are added to a pile, the ratio of blue to red chips will be 3:1"
13=R2B+R
13=R2+B
13=R2B+B
3=R2B+R
13=B2B+R
TD.7
Translate from English to math as an equation:
"The total of the ages of Rachel's siblings if she has one sibling that is 3 years younger and three siblings that are 2, 4, and 5 years older."
Total Ages =
(R-3)+(R+2)+(R+4)+(R+5)
Total Ages =
(R+3)+(R+2)+(R+4)+(R+5)
Total Ages =
(R-3)-(R+2)+(R+4)+(R+5)
Total Ages =
(R+3)+(R-2)+(R-4)+(R-5)
TD.8
Translate from English to math as an equation:
"If the number of dimes in a piggy bank is decreased by 2, then 3 out of every 5 coins in the piggy bank will be dimes."
53=CD−2
53C=D−2
53=DC−2
53D=C−2
53=CD+2
TD.9
Translate from English to math as an equation:
"The product of x decreased by y and one-third the sum of x and half of y."
(x−y) (31(x+21y))
x−(y(31(x+21y)))
(x−y) (31x+21y)
(x−y) (31(21x+21y))
TD.10
Translate from English to math as an equation:
"If the value of Martine's assets increased by $10,000, then the combined assets of Martine and Angela would be twice what Martine's assets would be if they were increased by half."
(M+10,000)+A=2(1.5M)
(M+10,000)+A=2(M+.5M)
(M+10,000)=2(M+.5M+A)
(M+10,000)+A=2(1.5M)+A
(M+10,000)=2(M+.5M)
SI.1
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
(a)
SI.2
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
(a)
SI.3
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
(a)
SI.4
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
y=131x−3138
y=131x+3138
y=121x−3127
y=121x+3127
SI.5
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
If fractions persist, rewrite them in decimal form
(a)
Kai is playing video games at the mall arcade.
The amount of money Kai has remaining
can be found using the equation
y = 20 − 0.50x, where x is the number of
games Kai has played. How many games
can Kai play if he spends all his money?
(a)
Which of the following situations is best represented by the equation y = x + 15?
Each student begins the candy hunt with 15 pieces of candy in their bag.
Emery earns $15 per hour babysitting
Joshua spent $15 of his money at the movie theater.
Each homeroom class has at least 15 students
Two students write the equations below:
Sarah: y = 3x
Camille: y = x + 3
Mrs. Jeffery states that in Sarah’s equation, y is three times as much as x, and in Camille’s equation, y is _____________.
3 less than x
3 more than x
3 times as much as x
the same as the value of x
y = 2x
y = x + 2
A factory is able to make 14 toys every hour. The equation they use to find out how many toys they can make over time is y = 14x. Which coordinate point below could be a part of this pattern?
(0, 14)
(3, 42)
(14, 1)
(42, 3)
A copier machine can produce 500 copies per minute. This can be modeled by C(m) = 500m. The copier can only run for 4 hours (240 mins) before needing a break.
What does the DOMAIN represent?
Copies made
minutes on
500
4 hours
A copier machine can produce 500 copies per minute. This can be modeled by C(m) = 500m. The copier can only run for 4 hours (240 mins) before needing a break.
What is the smallest/largest the Domain can be?
0≤x≤240
0≤x≤500
4≤x≤500
240≤x≤500
Starting at sunrise, the temperature rose 2.5⁰ every hour. After 8 hours, the temperature was 67⁰. Write an equation in point-slope form to model the temperature, y, after x hours after sunrise. If sunrise was at 6:00 AM, what is the temperature at noon?
y+67=2.5(x+8) ; the temperature was 62⁰ at noon
y−67=2.5(x−8); the temperature was 62⁰ at noon
y−67=2.5(x−8); the temperature was 77⁰ at noon
y−8=2.5(x−67); the temperature was 77⁰ at noon
The table shows the relationship between y, the cost to rent a boat, and x, the amount of time the boat is rented. Which graph best represents the relationship between x and y shown in the table?
The equation is solved for y.
y = 1/2x - 5
Which is the graph of this equation?
y + 1 = -3(x - 5),
the line contains the point (5, -1) and has a slope of?
(4, -7); m = -1/4
(-2, -3), (4, 3)
Slopes of parallel lines are...
opposite reciprocals.
opposites.
identical.
always 7.
m = 4
m = 5/8
y = 5/7x - 30
These lines are...
y = 3/2x + 9
These lines are...
Are the two linear equations parallel, perpendicular, or neither?
Parallel
Perpendicular
Neither
3x + 8y = 24
5x - 3y = 15
Which situation can be represented by
y = 12x + 4 ?
The number of people, y, arriving at party, if there are 12 cars with 4 people in each car
The cost, y, of buying x movie tickets that sell for $12 each, plus $4 for popcorn
The cost, y, of buying 12 candy bars that sell for $ 4 each.
The number of cookies, y, if there are 12 cookies per box and you ate 4
A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:
y = 2.75x + 4.25
What does 2.75 represent?
The total cost of the fixed fee plus charge per mile
The charge per mile
Miles
The fixed fee
The equation y = 2.50x + 225 represents the purchase of posters for a fundraiser where x represents the number of posters ordered and y represents the total cost. If Nick wanted to order 400 posters, what would be the total cost?
$625.00
$750.00
$1000.00
$1225.00
The equation y = 120x + 250 represents the cost for renting an event hall where x represents the number of hours a customer rents the hall and y represents the total cost. If Alan paid $790.00, how many hours did he rent the hall?
4 hours
4.5 hours
5 hours
5.5 hours
The equation y = 120x + 250 represents the cost for renting an event hall where x represents the number of hours a customer rents the hall and y represents the total cost. If Alan wants to rent the hall for 3 hours, what will be his final cost?
$610.00
$870.00
$1,110.00
$360.00
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. What is the y-intercept for this situation?
(0,15)
(0,2)
(0,17)
(0,13)
In order to join an online course, there is a $20 startup fee and a $5 monthly fee. What is the rate of change(slope) for this situation.
$20
$5
$25
$15
A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. What does the slope mean in this situation?
Every t-shirt costs $8
Every t-shirt costs $25
The initial fee is $25
The initial fee is $8
Your new job is at the Custom T Shop, where T Shirts are printed to order. For each order, Custom T Shop charges $8 per shirt plus a one time set up fee of $15, represented by the equation y=8x+15
How much would 50 shirts cost?
y= 40
y= 400
y= 415
y= 65
y= 390
The rental rate at Rent A Wreck is $30 per day plus $0.25 per mile driven.
How much would a 100 mile rental cost?
$45
$55
$23
$100
Who is growing faster?
Mochi, because he is gaining 2 lbs/month
Mochi, because he is gaining 4 lbs/month
Kappa, because he is gaining 3.5 lbs/month
Kappa, because he is gaining 5 lbs/month
A 100-point test has x questions worth 2 points apiece and y questions worth 4 points apiece.
Which equation matches the situation?
2x + 4y = 100
100 + 2y = 4y
x + y = 100
y = 2x + 100
A 100-point test has x questions worth 2 points apiece and y questions worth 4 points apiece.
If you have 24 questions worth 4 points apiece, how many questions will be worth 2 points apiece?
24
2
5
0
You are selling drinks at the carnival to raise money. You sell lemonade for $2 per cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of lemonade and y be the number of orange drinks.
If you sold 60 cups of lemonade, how many cups of orange drink did you sell?
60
40
10
120
Dexter's Gym charges a one-time registration fee of $40 and $20 each month. The total fee after x months is $340. Which equation models this situation?
40x + 20 = 340
20x + 40 = 340
20x - 40 = 340
20 + 340 = 40x
A plumber charges $50 to make a house call. He also charges $25 per hour for labor.
How much would it cost for 2.5 hours of labor?
$100
4.50
$112.50
$65.00
$123.45
The rental rate at Rent A Wreck is $30 per day plus $0.25 per mile driven.
How much would a 100 mile rental cost?
$45
$55
$23
$100
A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.
The additional fee of $8.
The initial fee of $25.
The additional fee of $25.
The initial fee of $8.
Your four-month bill for the gym comes to $221. That includes the cost per month of $50 plus the one-time membership fee. How much is the membership fee?
$21
$171
$4.42
$15.50
SOE.1
What is a System of Equations
A collection of linear equations, where the number of equations matches the number of variables, allowing for an algebraic solution.
A set of two or more variables that usually contains multiple equations
An equation that usually contains multiple variables
A set of three or more equations that usually contains multiple variables
A set of two or more equations that usually contains the same variables
SOE.2
When you are given a situation involving "n" variables, you need a system of "n" equations to arrive at fixed values for those variables.
"n" represents the number of constants
True
False
SOE.3
The following is a system of equations:
y=x+3
y=z-2
True
False
"Commercial Break"
Solve
6k+8=5
(a)
Kindly copy into your notes and type "Done" when finished
(a)
SOE.4
The solution of a system of equations will always be a...
number
coordinate
x-value
y-value
variable
SOE.5
Solving a system of equations means finding...
the appropriate x-value
the appropriate y-value
the slope
the y-intercept
a way to get out of doing the work in the first place
SOE.6
How many solutions does the following system have?
One
None
Infinitely many
SOE.7
How many solutions does the following system have?
One
None
Infinitely many
SOE.8
Kindly solve the system and enter your answer as a coordinate with parenthesis, a comma separating the x and y values, and no spaces.
y=6x+2
y=5x+15
(a)
LE.PS.4
43(8x+12)+5=8x+12
Based on the equation above, what is the value of 5x+1?
Kindly enter numeric value only.
-No hints 😎-
(a)
SOE.9
Kindly solve the system and enter your answer as a coordinate with parenthesis, a comma separating the x and y values, and no spaces.
y=7x+3
y=6x+16
(a)
LE.PS.5
A line that passes through the origin in the coordinate plane has a slope of 37 . Which of the following is a point on the line?
(-14,-6)
(-6,-14)
(-6,14)
(14,6)
LE.PS.8*
A line passes through the origin and points (-4,c) and (c,-9). What is one possible value of c?
4
6
9
12
LE.PS.9
w=240+1.2d
The weight of a flask containing a solution can be modeled by the equation above, where w is the weight in grams and d is the number of drops of solution that are in the flask. What is d when w is 300?
(a)
SE.3
Kindly solve for x and enter the numerical value only:
(4x+5)−(−2x+11)=x+4
(a)
SE.8
Kindly solve for x and enter the numerical value only:
(Simplify fractions as much as possible, enter your response using simplified fractions, and list your termed-variables in alphabetical order)
(a)
TD.5
Translate from English to math as an equation:
"Jose's age in 5 years will be 1 year more than double what Beatrice's age was 2 years ago."
J+5=1+2(B-2)
J+5=(1+2B)+2
J+5=(1+2B)-2
J+5=1+(2B-2)
TD.6
Translate from English to math as an equation:
"If 2 more blue chips are added to a pile, the ratio of blue to red chips will be 3:1"
13=R2B+R
13=R2+B
13=R2B+B
3=R2B+R
13=B2B+R
SI.4
Write the equation for the line that passes through each set of points without spaces and beginning with "y="
y=131x−3138
y=131x+3138
y=121x−3127
y=121x+3127
SOE.10
Solve the following system using substitution:
y=x+2
x+y=6
(a)
SOE.11
Solve the following system using substitution:
y=x-2
2x-y=6
(a)
SOE.12
Solve the following system using substitution:
x=y-2
2y-x=6
(a)
SOE.13
Kindly solve the following system using elimination:
y=2x+3
y=x-5
(a)
SOE.14
Solve the following system using elimination:
x+y=2
x-y=1
(a)
SOE.14a
Kindly solve the system below
-3x - 8y = 20
-5x + y = 19
(a)
SOE.15
What is the solution to the system of equations below?
x + y = 10
x - y = 2
(a)
SOE.15a
Kindly solve the system below:
-4x + y = 6
-5x - y = 21
(a)
SOE.16 (Stop here for the day)
What is the solution to the system of equations below?
x - 3y = -13
-x + 4y = 15
(a)
SOE.17
What is the solution to the system of equations below?
-4x - 2y = -2
5x + 2y = 4
(-3, 2)
(-3, 3)
(2, -3)
(2, 3)
SOE.18
What is the solution to the system of equations below?
-x + 2y = 12
x + 6y = 20
(-4, -6)
(-4, 4)
(2, 7)
(8, 2)
SOE.19
What is the solution to the system of equations below?
4x + 3y = -9
-4x - 8y = 4
(-7, 3)
(-5, 2)
(-3, 1)
(-1, 0)
SOE.20
What is the solution to the system of equations below?
-5x + 2y = -3
5x + y = -9
(-4, 11)
(-1, -4)
(3, 6)
(6, 3)
SOE.21
What is the solution to the system of equations below?
10x + 5y = -5
7x - 5y = 5
(-1, 0)
(0, -1)
(0, 1)
(1, 0)
SOE.22
What is the solution to the system of equations below?
2x - 2y = 2
6x + 2y = -18
(-3, -2)
(-1, -2)
(-2, -3)
(-2, -1)
SOE.23
What is the solution to the system of equations below?
6x + 6y = -24
6x - 6y = -36
(-5, 1)
(-5, 3)
(-5, 5)
(-5, 7)
SOE.24
What is the solution to the system of equations below?
2x + 3y = 18
15x - 3y = 33
(-3, -4)
(-3, 8)
(3, -4)
(3, 4)
SOE.25
Kindly solve the system using the method of your choice:
y = 6x - 11
-2x - 3y = -7
(a)
