Graphs And Relations Practice Quiz! Test

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2. 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?

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.

Explanation

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.

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3. For the line of the equation below, the gradient is negative

True

False

find the gradient using 'makesubject'

Explanation

find the gradient using 'makesubject'

4.

I have completed some calculations and filled them in red.For the set of points above, what is the value of 'n'

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=0.25

Explanation

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=0.25

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5. A graph of the equation below would show a negative gradient.

True

False

use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?

Explanation

use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?

6. For the line of the equation below, y will increase as x decreases

True

False

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 positive

Explanation

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 positive

7. A graph of the equation below would show a negative gradient.

True

False

use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?

Explanation

use App makesubject - it puts the equation in gradient-yintercept form - so you can just read off the gradient. Is it positive or negative?

8.

Which App is the most efficient way to find the point of intersection between these two lines?

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.

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.

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9.

Which App will find the equation for the line above most efficiently?

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 axies

Explanation

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 axies

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10.

What are the coordinates for the point of intersection for red and blue lines? One decimal place.

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.

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.

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11. The point (3, -3) falls in the region define by the inequality below.

True

False

pointtest

Explanation

pointtest

12. The point (4, 4) sits on the same line created by the equation below.

True

False

pointtest

Explanation

pointtest

13. The cost equation for a surf board manufacturer is C = 5200 + 150x.How much does it cost to produce 200 boards

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 ..

Explanation

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 ..

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15. For the line of the equation below, y will decrease x decreases

True

False

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 positive

Explanation

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 positive

16. 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 relationship

The cost of recovering copper from the ocean at a distance of 50 metres underwater is $5000. What is the value of 'k'?

use pointn2equ because you are given values for one point ... (50, 5000) and you have a value for 'n' - its 2.

Explanation

use pointn2equ because you are given values for one point ... (50, 5000) and you have a value for 'n' - its 2.

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17. 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?

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.

Explanation

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.

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18.

Which App will find the equation for the line above

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 axies

Explanation

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 axies

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19. 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

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.

Explanation

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.

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23. The point (4, 0) sits on the same line created by the equation below.

True

False

pointtest

Explanation

pointtest

24.

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)

To find the speed of the train on the way home, we need to determine the distance traveled and the time taken. From the graph, we can see that the train started its journey home at the 8-hour mark and arrived back home at the 10-hour mark. This means the journey home took 2 hours.

The distance traveled on the way home is the difference between the distance at the 8-hour mark and the distance at the 10-hour mark. From the graph, the distance at the 8-hour mark is 200 km, and the distance at the 10-hour mark is 0 km. Therefore, the distance traveled on the way home is 200 km.

Now, we can calculate the speed using the formula:

Speed = Distance / Time

Speed = 200 km / 2 hours = 100 km/h

Therefore, the train was traveling at a speed of 100 km/h on the way home.

Explanation

To find the speed of the train on the way home, we need to determine the distance traveled and the time taken. From the graph, we can see that the train started its journey home at the 8-hour mark and arrived back home at the 10-hour mark. This means the journey home took 2 hours.

The distance traveled on the way home is the difference between the distance at the 8-hour mark and the distance at the 10-hour mark. From the graph, the distance at the 8-hour mark is 200 km, and the distance at the 10-hour mark is 0 km. Therefore, the distance traveled on the way home is 200 km.

Now, we can calculate the speed using the formula:

Speed = Distance / Time

Speed = 200 km / 2 hours = 100 km/h

Therefore, the train was traveling at a speed of 100 km/h on the way home.

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25. 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?

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.

Explanation

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.

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26.

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.

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 1

Explanation

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 1

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27.

Which App will find the equation for the line above

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 axies

Explanation

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 axies

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29. 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?

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.

Explanation

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.

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30. When graphed, the equation below would pass through the origin.

True

False

pointtest - the origin is (0,0)

Explanation

pointtest - the origin is (0,0)

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32. A negative gradient is when y decreases as x increases

True

False

decrease and increase is negative gradient (in either order). increase increase is positive gradient. decrease decrease is positive gradient.

Explanation

decrease and increase is negative gradient (in either order). increase increase is positive gradient. decrease decrease is positive gradient.

33. 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?

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 page

Explanation

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 page

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35. When graphed, the equation below would pass through the origin.

True

False

pointtest - the origin is (0,0)

Explanation

pointtest - the origin is (0,0)

36.

Which App will find the equation for the line above

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 axies

Explanation

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 axies

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38. 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?

breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.

Explanation

breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.

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41.

Which App will find the equation for the line above most efficiently?

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 axies

Explanation

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 axies

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42.

Which App will find the equation for the line above most efficiently?

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 axies

Explanation

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 axies

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44. The point (3, -3) falls in the region define by the inequality below.

True

False

pointtest

Explanation

pointtest

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48. 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?

breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.

Explanation

breakeven app - 5200 fixed, 150 varied, 700 retail.
The tenth board is the break even board. Every additional board makes $550 profit per board.

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49.

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?

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.

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.

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50.

What is the equation for the relationship between x and y as shown in the graph above?

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 0.125

Explanation

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 0.125

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