WorksheetsMID TERM
Total questions: 70
Worksheet time: 2hrs 42mins
Solve for x : -12x +8 +5x = 36
4
-1/4
1/4
-4
Solve for k: 8k - (6k-4) = 10
-3
-5
3
5
Solve for y: -2y + 4 = 8y - 6
-1/2
1/2
-1
1
Solve for w: 13w - 2(4w + 1) = w - 58
14
-0.14
-14
0.14
Solve the equation below:
y =
(a)
Arjun, Aria, and Kai are working on a software project for their computer science class. They are trying to identify the line of code that is causing their program to crash. Can you help them identify which line contains the error?
Line 2
Line 3
Line 4
Line 5
Solve the equation below for h
h=V/(pi r^(2))
h=(V)(pi r^(2))
h=(pi r^(2))/V
h=V+(pi r^(2)
Solve the equation below for a.
w = 7a + 4b
(a)
The larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, what are the two numbers? type the numbers separated by the word and
(a)
The length of a rectangle is five inches less than twice its width. If the rectangle has a perimeter of 80 inches, find the length and width.
w=15
l=25
w=25
l=15
w=-15
l=-25
w=-25
l=-15
Evaluate the expression below if x = -7 and y = 4.
(a)
Michael, Mia, Mason, Daniel, Benjamin, and Harper are on a treasure hunt. They found a clue that says '2 - (2x - 4) > -4'. They believe this clue will lead them to the treasure. Can you help them solve and graph this inequality to find the treasure?
A
B
C
D
Elijah, Abigail, and Ethan are working in a chemistry lab at their school. They are studying the properties of gases and come across the ideal gas law, PV=nRT, where P is the pressure of the gas, V is the volume of the gas, n is the amount of the gas, R is a constant, and T is the temperature of the gas. They start discussing the equation and make some statements. Can you identify which of these statements about the ideal gas law are true?
Elijah says: 'If we divide both sides of the equation by V, we get an equation solved for P.'
Abigail suggests: 'Dividing both sides of the equation by R results in an equation solved for T.'
Ethan thinks: 'Subtracting P from both sides of the equation results in an equation solved for V.'
Elijah proposes: 'Subtracting PV from both sides of the equation and then dividing both sides of the equation by nT-PV results in an equation solved for R.'
Solve
x=
(a)
Anika, Zoe, and Nora are on a treasure hunt. They found a map with a line equation and a clue that says 'Find the equation of the line that is parallel to this one and goes through the origin (0,0)'. Can you help them solve this clue?
A. y=13x+4
B. y=-3x+4
C. y=-3x
D. y=13x
Sophia, Ethan, and Maya are planning a surprise party and they need a plumber for some work. The plumber charges $25 for a service call in addition to $50 per hour for service. Can you help them figure out the cost? Write an equation for the cost of service using c for cost and h for hours.
A. h = 50c+25
B. c=50 + 25h
C. c=25+50h
D. h = 50 + 25c
Grace and Harper are on a treasure hunt. They found a map with a line that passes through two points: (-2, -3) and (4,3). Michael, being a math whiz, needs to write the equation of this line in slope-intercept form to help them find the treasure. Can you help Michael?
A. y = x +1
B. y = -x + 1
C. y = x - 1
D. y = -x - 1
Avery, Priya, and Charlotte are having a race up a hill. If you were to graph their progress, what type of slope would the graph have?
A. Positive
B. Negative
C. Zero slope
D. Undefined
Grace, Benjamin, and Abigail are running a toy factory. They found out that the cost c, in dollars, to produce n toys can be modeled by the linear equation c=6.5n+1500. Can you help them figure out the c-intercept and what it means in this context?
A. The c-intercept is 6.5. This means the cost increases by $6.50 for each toy they produce.
B. The c-intercept is 6.5. This means the number of toys they can produce increases by about 6.5 for each $1 increase in cost.
C. The c-intercept is 1500. This means it costs $1500 to run the factory even if no toys are produced.
D. The c-intercept is 1500. This means the factory can produce 1500 toys at no cost.
The linear equation p=2,376t + 73,219 estimates the number of college seniors p who graduated with a bachelor's degree in psychology t years after 2000. The linear equation b=2,376t + 56,545 models the number of college seniors b who graduated with a bachelor's degree in biology t years after 2000. Indicate by putting a checkmark in the appropriate column of the table whether each statement is true or false according to the given model.
Separate answer with backslash.
(a)
Liam and Grace are having a friendly debate. Liam says the equations y=3x+2 and y=3x-3 represent the same line, while Grace thinks otherwise. Evelyn, their math whiz friend, says these lines are _________. Can you help them figure it out?
perpendicular
the same line
parallel
neither
Scarlett, Daniel, and Priya are on a treasure hunt. They found a map with a clue that says 'Find the line that passes through the point (-3,4) and is perpendicular to y=32x+6'. Which of the following lines could be the one they are looking for?
A. y=32x +6
B. y=-23x-2
C. y=23x+3
D. y=-23x+2
Nora, Arjun, and Jackson are on a treasure hunt. They found a map with a graph and a riddle. The riddle says: 'The treasure is hidden at the y-intercept ________ ( Responses: (-3 , 0), (0, -3), (0, 4), (4,0) ) and to get there, you need to follow the slope _________ ( Responses: -4/3, -3/4, 3/4, 4/3) . Can you help them find the treasure?
(a)
Henry and Abigail are on a treasure hunt. They found a map with a clue that says 'Find the equation of the line when the slope (m) is 2 and it passes through the point (-1,5)'. Can you help them solve this clue?
(a)
Noah and Aiden are trying to solve the following system of equations to determine the number of apples each of them has. If the equations are:
y=4x+1
How many solutions will they find?
One Solution
No Solution
Infinitely Many Solutions
Cannot tell without graphing
Which system of linear equations has no solution?
Which system of equations has one solution?
Evelyn, Anika, and Isla are working on a project to map out the city's subway system. If they end up with a map that has infinitely many solutions, what does that mean about the subway lines they've drawn?
The lines are the same
The lines are parallel and never touch
The lines cross in one place
Aiden and Mason are trying to solve a system of equations to find the coordinates of a treasure in a treasure hunt game. What is the solution to their system of equations?
(0,3)
(-3, 1)
(1, 3)
Infinitely Many Solutions
No Solution
Isla, Abigail, and Aria are trying to find the coordinates of a treasure based on a map. They came up with the following system of equations. What is the solution to their system of equations?
(5,2)
(2, 5)
(0,3)
Infinity Many Solutions
No Solutions
Isla, Rohan, and James are trying to find the location of a treasure based on a map. The map has a system of equations that leads to the treasure. What is the solution to this system of equations?
(0,3) - At the top of a hill
(0,0) - At the starting point
(-3,0) - Inside a cave
Infinity Many Solutions - Everywhere
No Solution - The map is misleading
Abigail, Aiden, and James are trying to find the coordinates of a treasure based on a map. They have narrowed down the possible locations to four coordinates. Which of these could be the correct location of the treasure?
(0, 3)
(1, -1)
(-3, 1)
(1, 3)
Daniel, Anika, and Samuel are trying to solve a system of equations but they find that it has no solution. What does the graph of their equations look like?
intersecting lines
parallel lines
skew lines
intersecting lines
Anika and Ethan are trying to solve a system of equations to figure out the number of apples (x) and oranges (y) they have. They know that 5 apples and 4 oranges together make a total of -14. They also know that the number of oranges is equal to -7 times the number of apples minus 15. Can you help them solve this system by substitution?
(-2, -1)
(1, -2)
(-2, 1)
(-1, -2)
Isla is planning a party and she needs to figure out the number of guests she can invite. She has two equations to help her decide:
The number of guests (x) plus twice the number of pizzas (y) she orders should be equal to 2.
The number of guests (x) should be equal to 2 minus four times the number of pizzas (y) she orders.
Can you help Isla solve this system by substitution?
Isla can invite -3 guests and order 0 pizzas
Isla can invite 0 guests and order 2 pizzas
Isla can invite -3 guests and order -2 pizzas
Isla can invite 2 guests and order 0 pizzas
Abigail, Scarlett, and Jackson are trying to solve a system of equations to figure out the coordinates of a treasure in a treasure hunt game. They have the following equations representing the coordinates:
y = -6x + 5
-2x + y = 5
Can you help them find the treasure by solving this system by substitution?
(-3, -6)
(-6, 3)
(0, 5)
(-3, 5)
Abigail, Sophia, and Ava are trying to solve a system of equations to figure out the coordinates of a treasure in a treasure hunt game. They have the following equations representing the coordinates:
6x + y = -1
y = -3x - 4
Can you help them find the treasure by solving the system by substitution?
(3, 1)
(1, 7)
(-3, 1)
(1, -7)
David, Elijah, and Priya are trying to split 28 apples and 28 oranges equally. If David gets 4 apples and 9 oranges, and Elijah gets -4 apples and -1 orange, how many apples and oranges does Priya get?
Represent Priya's share as (apples, oranges).
(-7,0)
(6,0)
(-6,0)
(7,0)
Grace, Isla, and Aria are trying to solve a problem. They have two equations representing the number of apples (x) and oranges (y) they have:
3x+7y=23
-3x-7y=-17
They want to find the solution by elimination. What is the solution?
No solution
(0, 3)
(-3,3)
(3,3)
Lily, Benjamin, and William are trying to solve a problem using the elimination method in their math class. They are given the following equations:
4x-6y= -6
-2x-12y= -12
Can you help them find the solution?
(0,1)
(1,0)
(1,1)
(0, 2)
David and Daniel are trying to split their earnings from their summer job. They find that if David earns 2x and Daniel earns 3y, they have a total of $12. On the other hand, if David earns 5x and Daniel loses y, they have a total of $13. How much did each of them earn?
David: -3, Daniel: -2
David: 1.5, Daniel: 2
David: 3, Daniel: 0
David: 3, Daniel: 2
Aria and Rohan are trying to solve a system of equations. They want to know if (-2,4) is a solution to the system they are working on. Is it a solution?
Solution
Not a solution
Benjamin, Grace, and Kai are playing a treasure hunt game. They found a map with coordinates for the treasure. Which point is the correct location of the treasure?
(0, 6)
(-3, 4)
(1, 0)
(-4, 3)
Ethan, Anika, and Emma are trying to find a location for their picnic. They have a system of inequalities to represent the possible locations. Which of the following coordinates is not a solution to their system of inequalities?
(0,-1)
(0,3)
(4,0)
(6,-2)
Evelyn, Zoe, and Nora are planning a big party at the Country Buffet restaurant. The restaurant has tables that seat 6 people and booths that can seat 4 people. They counted 38 seating units in total, which can accommodate 188 people. They started a fun challenge to figure out the number of tables, t, and the number of booths, b, at the restaurant. Can you help them solve this challenge?
4t=386 b=188
t+b=38 6t+4b=188
t+b=188 6t+4b=38
t+b=38 4t+6b=188
Imagine this, Nora, Avery, and Daniel are playing a game of 'Treasure Hunt'. Nora finds a treasure chest filled with quarters and dimes amounting to $6.80. Avery notices that the number of dimes is 3 times the number of quarters. Can you help Daniel figure out a system of equations to find 'q', the number of quarters, and 'd', the number of dimes, in the treasure chest?
q=3+d 0.25q+0.10d=6.80
d=3+q q+d=6.80
q=3d 0.25q+0.10d=6.80
q=3d q+d=6.80
Graph to solve the systems of equations y=-2x+4y=x-2 The solution is ( _________ , _________ )
Aiden, Ethan, and Aria were having a friendly competition to solve a problem using substitution. Suddenly, they noticed an error in one of the steps. Can you help them identify which line contains the error?
Line A
Line B
Line C
Line D
Our friends Liam, Zoe, and Anika were watching Belinda solve a system of equations. Suddenly, they noticed an error! Can you spot which line contains the mistake?
Line C
Line D
Line A
Line E
Line B
Imagine you're in a detective club with Ava, Nora, and Henry. Mrs. Ochoa just handed you a piece of work to investigate. Can you spot where the mystery student might have made a mistake?
Line D
Line A
Line B
Line C
Line E
Abigail, Sophia, and Lily are on a treasure hunt. They found a mysterious note with two equations: 3x+2y=8 and 4y=-6x+16. They believe solving these equations will lead them to the treasure. Can you help them figure out if these equations have:
1 solution
no solution
many solutions
David, Aiden, and Mason planned a fun movie night. They bought 9 tickets in total for $54. Adult tickets were priced at $8 each, while the child tickets were $3.50 each. Can you guess how many adult tickets they bought?
2 adult tickets
3 adult tickets
4 adult tickets
5 adult tickets
Two burgers and one hotdog cost $4.82. At the same price, one burger and two hotdogs cost $3.70. How much does a hotdog cost?
Olivia, a budding chemist, has two acid solutions at her disposal. One is a 25% solution and the other is a 50% solution. She needs to create a 200ml solution with 35% acid concentration for her science project. How much of each solution should she use?
80ml of the 50% solution and 120ml of the 25% solution
150ml of the 50% solution and 50ml of the 25% solution
60ml of the 50% solution and 140ml of the 25% solution
50ml of the 50% solution and 150ml of the 25% solution
Graph. y = 2/3x - 3
Graph. y = -4
Graph. x = 1
(10, 1) and (5, 2)
Write the equation for the line in slope-intercept form
y=-2/3x+5
y=2/3x+5
y=-3/2x+5
y=3/2x-5
Write the linear equation for the graph.
y=-1/3x-2
y=1/3x+2
y=1/3x-2
y=-1/3x+2
Write the equation given the points (2, 4) and (0,3)
y=-1/2x+3
y=1/2x+3
y=2/1x+3
y=-2/1x+3
