Parking charges

Parking charges

Pencil and paper
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Marking Student Responses
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Further Resources
This task is about expanding, simplifying, and changing the subject of the equation.

carpark building

A parking building charges $3 for parking up to 2 hours and an additional $2 for every hour (or part of an hour) after that.
 
a)
 What is the cost of parking
 
i)       for 30 minutes?      $ __________
 
ii)      for 1 3/4 hours?      $ __________
 
iii)     for 4 hours?            $ __________
 
iv)     for 5 1/2 hours?       $ __________
 
For cars parked longer than 2 hours, the cost of parking is given by the equation:

c = 3 + 2 (t - 2)

Where:   c is the cost in dollars

              t is the time parked (in whole hours)
 

b)

Expand and simplify c = 3 + 2 (t - 2)

 

 

 

 
 

c)

Make t the subject of the equation: c = 2 ( t - 2) + 3

 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Copyright: 
Image: david creacion, iStock
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
substitution, changing subject, linear equations, expand, simplify
Description of task: 
Students use substitution to evaluate a linear equation for parking charges. Students expand, simplify, and change the subject of the equation.
Answers/responses: 

 

   

Y10 (10/2010)

1 mark
1 mark
1 mark
1 mark

a)

i)
ii)
iii)
iv)

3
3
7
11

moderate
moderate
moderate
difficult

2 marks
(for b) ii) correct)
or
1 mark
(if b) i) is correct but b) ii) is wrong)
or
(1 error in b) i) which is then correctly simplified)

 b)

i)
ii)

c = 3 + 2t - 4
c = 2t - 1

 

2 marks – very difficult

1 mark – very difficult
1 mark c)   t = (c + 1) or t =  very difficult
Diagnostic and formative information: 
   Common error Likely calculation Likely reason

a) i)
    iv)

 0.75
10

3 / 4
3 + 3.5 * 2 

 Ignores that parts of an hour must be paid for if they are not used.

a) iii)
    iv)

6
9

2 * 3
3 * 3 

 Assumes $3 for every 2 hour period or part thereof.
a) iii) 5 3 + 2 Assumes an extra $2 for second 2 hours.
b)  3 + 2t - 2    Wrong expansion.