Graphs And Relations Practice Quiz! Test
What is a graph? The representation of a relation on a quadrangular coordinate plane is called a graph. A relation is any curve graphed on a rectangular coordinate plane and represents a set of ordered pairs. A graph is a configuration amounting to a set of objects in which some objects are somehow‘ related. ’ For this quiz, you will be shown algebraic equations, and it is up to you to determine the answer. Good luck.
Questions and Answers
- 1.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. Write a profit equation for the business, where P is the profit and 'x' is the number of sales.
Explanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
The Profit Equation is scrolled up.Rate this question:
- 2.
I have two points on a line, (0,10) and (1, 5). What is the x-intercept for this line in coordinate form?
Explanation
use the app twopoints, then go across to page 1.6 to see the x intercept. WRITE IT IN COORDINATE FORM.Rate this question:
- 3.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation
use App simequationsRate this question:
- 4.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation
use App simequationsRate this question:
- 5.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation
use App simequationsRate this question:
- 6.
A graph of the equation below would show a negative gradient.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?Rate this question:
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- 7.
A graph of the equation below would show a negative gradient.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?Rate this question:
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- 8.
The point (3, -3) falls in the region define by the inequality below.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
pointtestRate this question:
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- 9.
The point (3, -3) falls in the region define by the inequality below.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
pointtestRate this question:
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- 10.
The point (4, 4) sits on the same line created by the equation below.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
pointtestRate this question:
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- 11.
The point (4, 0) sits on the same line created by the equation below.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
pointtestRate this question:
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- 12.
When graphed, the equation below would pass through the origin.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
pointtest - the origin is (0,0)Rate this question:
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- 13.
When graphed, the equation below would pass through the origin.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
pointtest - the origin is (0,0)Rate this question:
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- 14.
A negative gradient is when y decreases as x increases
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
decrease and increase is negative gradient (in either order). increase increase is positive gradient. decrease decrease is positive gradient.Rate this question:
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- 15.
For the line of the equation below, the gradient is negative
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
find the gradient using 'makesubject'Rate this question:
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- 16.
For the line of the equation below, y will increase as x decreases
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
find the gradient using 'makesubject'
negative gradients are 'y increases as x decreases' OR 'y decreases as x increases' Different is negative
positive gradients are 'y increases as x increases' OR 'y decreases as x decreases' Same is positiveRate this question:
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- 17.
For the line of the equation below, y will decrease x decreases
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
find the gradient using 'makesubject'
negative gradients are 'y increases as x decreases' OR 'y decreases as x increases' Different is negative
positive gradients are 'y increases as x increases' OR 'y decreases as x decreases' Same is positiveRate this question:
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- 18.
Which App will find the equation for the line above
Correct Answer
twopointsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 19.
Which App will find the equation for the line above
Correct Answer
twopointsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 20.
Which App will find the equation for the line above
Correct Answer
twopointsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 21.
Which App will find the equation for the line above most efficiently?
Correct Answer
interceptsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 22.
Which App will find the equation for the line above most efficiently?
Correct Answer
interceptsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 23.
Which App will find the equation for the line above most efficiently?
Correct Answer
interceptsExplanation
twopoints is best when the line doesn't pass through whole numbers on the x and y axies.
intercepts is best when the line passes through whole numbers on BOTH the x and y axiesRate this question:
- 24.
What is the equation for the relationship between x and y as shown in the graph above?
Correct Answer
y=0.125/x, y=1/8xExplanation
pointn2eqn - but the graph here has been LINEARISED where n=1
When the graph is linear, make sure you observe the x axis values which linearise a NON LINEAR equation.
This problem is a linearised version of y=k/xn, and the value for 'k' is 1/8 or 0.125Rate this question:
- 25.
What is the equation for the relationship between x and y as shown in the graph above?Write squared as x^2 in your equation, and k as a decimal.
Correct Answer
y=1.2x^2Explanation
pointn2eqn - but the graph here has been LINEARISED where n=2
When the graph is linear, make sure you observe the x axis values which linearise a NON LINEAR equation.
This problem is a linearised version of y=k/n, and the value for 'k' is 1Rate this question:
- 26.
A taxi driver charges $5 flag-fall, and 50c per km for a ride. Write the cost equation for a trip where C is the cost and 'n' is the number of kms travelled
Correct Answer
c=5+0.5n, c=5+.5nExplanation
fixed is Flagfall, variable is 50c ... BUT it is in a different unit of measure.Rate this question:
- 27.
A surf club charges $10 to hire a boardl, and $3 per hour. Write the cost equation for a surf where C is the cost and 'n' is the number of hours hired
Correct Answer
c=10+3nExplanation
$10 is a fixed charge, and $3 is a variable. the cost equation is c=fixed +variable x nRate this question:
- 28.
A grocer sells three apples and five oranges for $4.50, and then sells two oranges and four apples for $3.20. How much is does it cost for two apples?
Correct Answer
$1Explanation
simequations - 3a+5b=4.50 and 2b+4a=3.20 ... solve THEN READ QUESTION AGAIN. One apple is 50 cents, so two apples are a dollar.Rate this question:
- 29.
The graph above shows the feasible region for a linear programming problem. Find the maximum value given the objective function is : P=2x+3y. At what point does the maximum occur?
Correct Answer
(48,20), (48, 20)Explanation
use the app objectfunction to find the values. 156 is the maximum value, but the question asks what is the POINT, not what is the value.Rate this question:
- 30.
The relationship between the cost of recovering copper from under the sea (C) and the distance in metres the copper is underwater (d) is given by the relationshipThe cost of recovering copper from the ocean at a distance of 50 metres underwater is $5000. What is the value of 'k'?
Correct Answer
2Explanation
use pointn2equ because you are given values for one point ... (50, 5000) and you have a value for 'n' - its 2.Rate this question:
- 31.
I enter a parking lot and stay for exactly one hour, then leave and return for exactly two hours. How much have I saved in comparison to staying for 3 hours without exiting the parking lot?
Correct Answer
$2Explanation
no apps for this one. remember, and open circle means 'not included' and a closed means 'included'Rate this question:
- 32.
The line graph above shows a day trip to the beach, where the x axis is the time taken in hours, and the y axis is the distance from home in km. What is the total distance travelled on the day.
Correct Answer
400km, 400 km, 400 kilometres, 400kilometresExplanation
no apps for this one. this is an 'up and back' journey, so if you said 200, you fell for it.Rate this question:
- 33.
The line graph above shows a day trip to the beach by train, where the x axis is the time taken in hours, and the y axis is the distance from home in km. How fast was the train travelling on the way home? Include the unit of measure (km/h)
Correct Answer
200km/h, 200 km/hExplanation
no apps for this one. this is an 'up and back' journey, so if you said 200, you fell for it.Rate this question:
- 34.
My plumber uses a cost equation where C = ax + b, where a is the rate he charges me per hour, and b is the call out fee.He charges me $290 for 6 hours of work, then the next week he returns to do 8 hours of work for $370.If I want him to return to replace a few tap washers - for one hour - how much will he charge?
Correct Answer
$90Explanation
this looks like a simequation, or cost equation question and would work that way, but twopoints works better.
(6, 290) and (8, 370) gives you the equation for the line ... y=50+40x
then, you can just substitute x = 1 (1 hour) into the equation and you have the answer.Rate this question:
- 35.
Using the data above, what is the value of x at the point 'B'?
Correct Answer
30Explanation
use twopoints to find the equation, then find the value when y=0, the x intercept.Rate this question:
- 36.
Using the data above, what is the value of y at the point 'A'?
Correct Answer
60Explanation
use twopoints to find the equation, then find the value for the y interceptRate this question:
- 37.
Which App is the most efficient way to find the point of intersection between these two lines?
Correct Answer
interceptsExplanation
twopoints will work, but then you have to type in the two equations to the simequations app.
intercepts allows you to type in the x and y intercepts for each line and it will give the solution for both lines.Rate this question:
- 38.
What are the coordinates for the point of intersection for red and blue lines? One decimal place.
Correct Answer
(2.7, 3.7)Explanation
twopoints will work, but then you have to type in the two equations to the simequations app.
intercepts allows you to type in the x and y intercepts for each line and it will give the solution for both lines.
They are given as fractions, so convert to a decimal, then put in coordinate form.Rate this question:
- 39.
The cost equation for a surf board manufacturer is C = 5200 + 150x.How much does it cost to produce 200 boards
Correct Answer
$35200Explanation
while it looks like a breakeven or profitloss, the reality is it is just two equations :
the cost equation, and a second equation to sub in. You can do this one manually by subbing in 200 where 150 is in the equations
C=5200+150*200 ..Rate this question:
- 40.
The cost equation for a surf board manufacturer is C = 5200 + 150x.There is a capital injection of $50,000. How many complete boards will this make?
Correct Answer
298Explanation
while it looks like a breakeven or profitloss, the reality is it is just two equations :
the cost equation, and a second equation to sub in. You can do this one manually by subbing in 50000 where the 'C' is ...
50000=5200+150x ... solve that on your calc, or use simequations and you get the same answer.
complete boards ... you don't round it up.Rate this question:
- 41.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. How many boards need to be made to break even
Correct Answer
10Explanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
While the number is 9.45, the break even happens after the 10th sale. You have to round UP not down for break even.Rate this question:
- 42.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. How much profit is made on the 15th board sold?
Correct Answer
$550Explanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.Rate this question:
- 43.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. How much revenue has been taken by the time the company breaks even?
Correct Answer
$7000Explanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.Rate this question:
- 44.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. Write a profit equation for the business, where P is the profit and 'x' is the number of sales.
Correct Answer
P=550x-5200, P=-5200+550xExplanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
The Profit Equation is scrolled up.Rate this question:
- 45.
The cost equation for a surf board manufacturer is C = 5200 + 150x. The boards are selling for $700 each. What is the profit if 75 boards are sold in a month?
Correct Answer
$36050Explanation
breakeven app - 5200 fixed, 150 varied, 700 retail.
profitloss App with 'unit's as the value you are entering. The cost and revenue equations are already imported from breakeven, and the units should be '75' ... the profit is shown at the bottom of the pageRate this question:
- 46.
I have two 150g letters, both going to the same place. How much do I save if I put them together in the same envelope and send them as a single letter?
Correct Answer
$1, $1.00Explanation
up to - means including, because the next value is 'over' ... over means not including.Rate this question:
- 47.
I have completed some calculations and filled them in red.For the set of points above, what is the value of 'n'
Correct Answer
2Explanation
plotpoints will help you determine the type of graph you have - parabola (n=2) or cubic(n=3).
use pointn2equ to match the 'y' values with the ones given.
Use the 'settings' App to plot points that are fractional, making the xmin=0, xmax=2 and the step=0.25Rate this question:
- 48.
This is a table of values in a non-linear form:What is the value of 'k' in the equation for the table of data above?
Correct Answer
16Explanation
choose a point, use pointn2eqn and it will give you 'k'.Rate this question:
- 49.
I have a cost equation for a product of C=2500+15n. What is the cost to produce 100 units?
Correct Answer
$4000Explanation
this is a simple substitution, or simequations App. c=2500+15n, and n=100 will give the answer.Rate this question:
- 50.
I have a revenue equation for a product of R=750n. I have made revenue of $15000 over the past month. How many items did I sell?
Correct Answer
20Explanation
simple substitution or the app simequations can solve this one. The two equations are : r=750n and r=15000. That will give you n=20.Rate this question:
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Mar 18, 2023Quiz Edited by
ProProfs Editorial Team -
Jun 10, 2015Quiz Created by
Anthony Nunan
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