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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.
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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.
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3.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation use App simequations
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4.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation use App simequations
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5.
For the equations above, give the coordinates of the point of intersection ie. (3, 5)
Explanation use App simequations
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6.
A graph of the equation below would show a negative gradient.
A.
True
B.
False
Correct Answer B. False
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?
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7.
A graph of the equation below would show a negative gradient.
A.
True
B.
False
Correct Answer A. True
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?
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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. True
Explanation pointtest
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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. True
Explanation pointtest
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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. True
Explanation pointtest
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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. False
Explanation pointtest
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12.
When graphed, the equation below would pass through the origin.
A.
True
B.
False
Correct Answer A. True
Explanation pointtest - the origin is (0,0)
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13.
When graphed, the equation below would pass through the origin.
A.
True
B.
False
Correct Answer A. True
Explanation pointtest - the origin is (0,0)
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14.
A negative gradient is when y decreases as x increases
A.
True
B.
False
Correct Answer A. True
Explanation decrease and increase is negative gradient (in either order). increase increase is positive gradient. decrease decrease is positive gradient.
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15.
For the line of the equation below, the gradient is negative
A.
True
B.
False
Correct Answer A. True
Explanation find the gradient using 'makesubject'
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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. False
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
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17.
For the line of the equation below, y will decrease x decreases
A.
True
B.
False
Correct Answer B. False
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
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18.
Which App will find the equation for the line above
Correct Answer twopoints
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.
Which App will find the equation for the line above
Correct Answer twopoints
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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20.
Which App will find the equation for the line above
Correct Answer twopoints
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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21.
Which App will find the equation for the line above most efficiently?
Correct Answer intercepts
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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22.
Which App will find the equation for the line above most efficiently?
Correct Answer intercepts
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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23.
Which App will find the equation for the line above most efficiently?
Correct Answer intercepts
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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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=1/8x
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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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^2
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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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+.5n
Explanation fixed is Flagfall, variable is 50c ... BUT it is in a different unit of measure.
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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+3n
Explanation $10 is a fixed charge, and $3 is a variable. the cost equation is c=fixed +variable x n
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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 $1
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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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.
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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 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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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 $2
Explanation no apps for this one. remember, and open circle means 'not included' and a closed means 'included'
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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, 400kilometres
Explanation no apps for this one. this is an 'up and back' journey, so if you said 200, you fell for it.
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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/h
Explanation no apps for this one. this is an 'up and back' journey, so if you said 200, you fell for it.
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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 $90
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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35.
Using the data above, what is the value of x at the point 'B'?
Correct Answer 30
Explanation use twopoints to find the equation, then find the value when y=0, the x intercept.