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Home > Mathematics > General Mathematics > Preliminary Course > Algebraic Modelling > AM2: Modelling linear relationships > Quick quiz: A sample of multiple choice questions for this topic.

AM2

1. When applying a function, the procedure follows the idea of Input – Process – Output.
    
   The cost of staging a preschool concert was calculated using the formula C = 80 + 3n, where C is the cost and n is the number of students involved.
    
   Which variable is considered to be the input for this scenario?
    
   • C, the cost.
   • n, the number of students.
   • The answers to each of the calculations.
   answer
   
    
2. The dependent variable in a linear model is w and the independent variable is b. If the gradient of the line representing this model is 2, the equation could be:
    
   • b = 2w
   • w = 2b
   • w = b + 2
   answer
   
    
3. The linear function representing the cost, C, of an excursion for a number of students, n, was given as C = 4.5n + 50.
    
   To graph this by first creating a table of values, the table could be:
    
   • 
     

     n	0	1	2	3
     C	50	95	140	185

   • 
     

     n	0	1	2	3
     C	50	54.5	109	163.5

   • 
     

     n	0	1	2	3
     C	50	54.5	59	63.5

   answer
   
    

4. To find the gradient of the line AB, Rita measured AC as 3 mm and BC as 4 mm.
    
   
    
   The gradient would be:
   • 3/4
   • 4/3
   • 5
   answer
   
    
5. This graph shows the cost of producing boxes of fudge to sell for charity.
    
   
   The gradient of this graph is 5. This gradient represents:
   • The cost per box of fudge.
   • The cost of the box to put the fudge in.
   • The cost of the fudge for each box.
   answer
   
    
6. This graph shows the cost of producing boxes of fudge to sell for charity.
    
   
   The graph meets the vertical axis at 13 in an open circle. This value of 13 represents:
   • The cost of a box with no fudge in it must be $13.
   • There are 13 pieces of fudge in each box.
   • It would cost $13 to get started with the production.
   answer
   
    

7. A sketch of the graph y = -2x + 1 would look like:
    
   • 
     
   • 
     
   • 
     
   answer
   
    
8. This graph shows that the cost, C, of a holiday varies directly with the distance, d, from home.
    
   
   If the cost of travelling 630 km is $90 the equation of this graph would be:
   • C = 7d
   • C = 7/d
   • C = d/7
   answer
   
    
9. This graph shows that the cost, C, of a holiday varies directly with the distance, d, from home.
    
   
   For a cost of $840 you could travel:
   • 5880 km from home.
   • 120 km from home.
   • 1200 km from home.
   answer
   
    

10. This is a graph of the distance travelled by Priya on her way to school.
     
    
    The section AB represents:
    • Priya went back towards home (maybe she had dropped something).
    • Priya reached a down-hill section of the road.
    • Priya stopped for a short period of time.
    answer
    
     
11. A suburban car park has the following parking rates:
     
    

    Time	Cost
    Up to 1 hour	Free
    More than 1 hour and up to 2 hours	$5
    More than 2 hours and up to 3 hours	$9
    More than 3 hours	$12

    
    When using this table of data to graph Cost against Time, the type of graph produced is called:
    • A scatter or dot graph.
    • A step graph.
    • A pie or sector graph.
    answer
    
     
12. When representing some physical phenomena as a linear function(such as shoe size against age) there are often limitations to the model produced because:
     
    • The graph may be too big to fit on a page.
    • The graph may be a vertical line.
    • The graph may only be a straight line for a limited section.
    answer
    
     

13. This represents a little pocket graph that a group of year 12 students took with them to Bali after the HSC. It converts the currency in Bali (Rupiah) to Australian dollars.
     
    
    This graph uses the conversion rate of 5000 Rupiah to the dollar which is a reasonable approximation.
     
    The students are offered a great deal on an excursion to other islands for 425 000 Rupiah.
     
    What is this approximately equivalent to in Australian dollars?
    • $90
    • $85
    • $850
    answer
    
     
14. This is a travel graph representing two cars travelling between Taree and Maitland.
     
    
    The point where the two lines cross shows where:
     
    • The two cars collided.
    • Car A overtook Car B which was going slower.
    • Cars A and B pass each other travelling in opposite directions.
    answer
    
     
15. When using a pencil and ruler to sketch a line of best fit for the scatter plot below, you should just use your ruler to get the general trend of the gradient of the line and:
     
    
     
    • Draw a line that has about the same number of points on either side of it.
    • Find a straight line that goes through any four points.
    • Join the lowest and highest points.
    answer
    
     


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Answers

1. n, the number of students.
    
2. w = 2b
    
3. 
   

   n	0	1	2	3
   C	50	54.5	59	63.5

   
    
4. 4/3
    
5. The cost per box of fudge.
    
6. It would cost $13 to get started with the production.
    
7. 
   
    
8. C = d/7
    
9. 5880 km from home.
    
10. Priya went back towards home (maybe she had dropped something).
     
11. A step graph.
     
12. The graph may only be a straight line for a limited section.
     
13. $85
     
14. Cars A and B pass each other travelling in opposite directions.
     
15. Draw a line that has about the same number of points on either side of it.
     



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