A rectangle has a length of 12 cm and a width of 7 cm.
A square has the same perimeter as this rectangle.
What is the side length of this square in centimetres? (2 marks)
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Rectilinear Figures, SM-Bank 023 MC
A hexagon with equal sides and an equilateral triangle are drawn below.
3 identical hexagons and 8 identical equilateral triangles are connected as shown in the diagram below.
What is the perimeter of the larger shape?
Rectilinear Figures, SM-Bank 022
Joyce is walking her dog around a paddock in the shape of a parallelogram.
If she walks the dog around the paddock in the morning and the afternoon, how many kilometres do they walk each day? (2 marks)
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Rectilinear Figures, SM-Bank 021 MC
The rhombus below has a side length
Which expression cannot be used for the perimeter?
Rectilinear Figures, SM-Bank 020
Tatiana is cutting a piece of material in the shape of a parallelogram for a sewing project.
The longer sides are one and two-thirds times the length of the shorter sides.
What is the perimeter of the piece of material? (2 marks)
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Rectilinear Figures, SM-Bank 019
Fumiko is laying pavers that are shaped like a parallelogram.
The longer sides are 3.5 times the length of the shorter sides.
What is the perimeter of one of the pavers? (2 marks)
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Rectilinear Figures, SM-Bank 018
What is the perimeter of the shape below given each square has a side length of 2 cm? (2 marks)
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Rectilinear Figures, SM-Bank 017
A rectangular parking lot has a perimeter of 80 metres.
Each short side has a length of 10 metres.
What is the length of the long side? (2 marks)
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Rectilinear Figures, SM-Bank 016
A farmer uses an existing stone wall and fencing to create a large grazing paddock for his sheep, as shown in the diagram below.
The fencing has 3-strand wiring which is also shown below.
How many kilometres of wire will be required? (2 marks)
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Rectilinear Figures, SM-Bank 015
The length of this rectangle is one and a half times its height.
The perimeter of the rectangle is 40 centimetres.
What are the dimensions of the rectangle? (2 marks)
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Rectilinear Figures, SM-Bank 014
Ronald places 5 identical hexagonal tiles side-by-side to make the pattern pictured below.
Each tile has a perimeter of 24 cm and is in the shape of a regular hexagon.
What is the perimeter of the large shape, in centimetres? (2 marks)
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Rectilinear Figures, SM-Bank 013
Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.
The length of the paddock is 2.8 kilometres.
How wide is the paddock?
Write your answer, in kilometres to one decimal place? (2 marks)
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Rectilinear Figures, SM-Bank 012
Penelope made a shape using 6 identical squares.
What is the perimeter of the shape? (2 marks)
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Rectilinear Figures, SM-Bank 011
This shape is made from eight equilateral triangles and one large parallelogram.
Each side of all the small triangles is 4 cm long.
What is the perimeter of the shape? (2 marks)
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Rectilinear Figures, SM-Bank 010
A rectangle has a length of 25 cm and a width of 20 cm.
A square has the same perimeter as this rectangle.
What is the side length of this square in centimetres? (2 marks)
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Rectilinear Figures, SM-Bank 009 MC
Rectilinear Figures, SM-Bank 008 MC
What is the perimeter of this shape?
Rectilinear Figures, SM-Bank 007 MC
Rectilinear Figures, SM-Bank 006
Rectilinear Figures, SM-Bank 004
Rectilinear Figures, SM-Bank 003 MC
The table shows the dimensions of four different rectangles in centimetres.
| Rectangle | Length (cm) | Width (cm) |
| 1 | 9 | 5 |
| 2 | 10 | 8 |
| 3 | 14 | 2 |
| 4 | 18 | 10 |
Which rectangle has a perimeter of 28 centimetres?
- Rectangle 1
- Rectangle 2
- Rectangle 3
- Rectangle 4
Rectilinear Figures, SM-Bank 002 MC
Which one of these shapes has the largest perimeter?
Show Worked Solution
Rectilinear Figures, SM-Bank 001 MC
Linear Relationships, SM-Bank 062
Use the graph of
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Show Worked Solution
Linear Relationships, SM-Bank 061
Use the graph of
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Show Worked Solution
Linear Relationships, SM-Bank 060
Use the graph of
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Show Worked Solution
Linear Relationships, SM-Bank 059
Verify that the points
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Linear Relationships, SM-Bank 058
Verify that the points
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Linear Relationships, SM-Bank 057
Verify that the points
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Linear Relationships, SM-Bank 056 MC
Which of the following points lies on the line
Linear Relationships, SM-Bank 055 MC
Which of the following points lies on the line
Linear Relationships, SM-Bank 054
Renee and Leisa are saving money so they can visit their grandmother on a holiday.
Renee has $100 and plans to save $30 each week.
Leisa has $200 and plans to save $10 each week.
- Write an equation to represent
(i) Renee's savings (1 mark)
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(ii) Leisa's savings (1 mark)
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- Complete the following tables of values for the equations above. (2 marks)
Renee's savings
Leisa's savings
- Using the tables of values, graph both equations on the number plane below. Be sure to extend your lines to the end of the grid. (2 marks)
- After how many weeks will Renee and Leisa have saved the same amount? (1 mark)
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a. (i)
(ii)
b.
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c.
d.
Show Worked Solution
a. (i)
(ii)
b.
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c.
d.
Linear Relationships, SM-Bank 053 MC
Linear Relationships, SM-Bank 052
Jeremy owns a paddle board hire company. He charges a $20 insurance fee with every hire and $35 for every hour of hire.
- Complete the table of values below, where
represents the number of hours of hire and represents his total earnings for each hour of hire. (2 marks)
- Write an equation to represent Jeremy's wages, using the variables
and . (1 mark)
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- Graph the equation of the line representing Jeremy's wages on the number plane below. Be sure to extend your line to the edge of the grid. (2 marks)
- For how many hours would Jeremy have to hire a paddle board to earn $230? (1 mark)
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a.
b.
c.
d.
Show Worked Solution
a.
b.
c.
d.
Linear Relationships, SM-Bank 051
Julie cleans carpets and upholstery. She charges a $40 call-out fee and $20 for every hour it takes to complete a job.
- Complete the table of values below, where
represents the number of hours Julie works and represents her total wage. (2 marks)
- Write an equation to represent Julie's wages, using the variables
and . (1 mark)
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- Graph the equation of the line representing Julie's wages on the number plane below. Be sure to extend your line to the edge of the grid. (2 marks)
- For how many hours would Julie have to clean to earn $150? (1 mark)
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a.
b.
c.
d.
Show Worked Solution
a.
b.
c.
d.
Linear Relationships, SM-Bank 050 MC
Which of the following is not true of the lines on the number plane below?
. . . .
Linear Relationships, SM-Bank 049 MC
What do the lines on the following number plane have in common?
. . . .
Linear Relationships, SM-Bank 048 MC
What do all the lines on the following number plane have in common?
. . . .
Linear Relationships, SM-Bank 047
- Complete the tables of values below for each given rule. (3 marks)
- On the number plane below, graph the equations from part (a). (2 marks)
- Using the graph, find the point of intersection of the two lines. (1 mark)
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a.
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b.
c.
Show Worked Solution
a.
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b.
c.
Linear Relationships, SM-Bank 046 MC
Monique has correctly drawn the graph of
She used the points
How many more different points could she have used to plot the line
Linear Relationships, SM Bank 045
- Complete the tables of values below for each given rule. (3 marks)
- On the number plane below, graph the equations from part (a). (2 marks)
- Using the graph, find the point of intersection of the two lines. (1 mark)
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a.
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b.
c.
Show Worked Solution
a.
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b.
c.
Linear Relationships, SM-Bank 044
- Complete the table of values using the graph of the straight line below. (2 marks)
- Using either the table or the graph, state the rule connecting
and . (1 mark)
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Linear Relationships, SM-Bank 043
- Complete the table of values using the graph of the straight line below. (2 marks)
- Using either the table or the graph, state the rule connecting
and . (1 mark)
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Linear Relationships, SM-Bank 042
- Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
- What do you notice about the points? (1 mark)
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- Using either the table or the graph, state the rule connecting
and . (1 mark)
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a.
b.
c.
Show Worked Solution
a.
b.
c.
Linear Relationships, SM-Bank 041
- Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
- What do you notice about the points? (1 mark)
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- Using either the table or the graph, state the rule connecting
and . (1 mark)
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a.
b.
c.
Show Worked Solution
a.
b.
c.
Linear Relationships, SM-Bank 040
- Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
- What do you notice about the points? (1 mark)
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- Using either the table or the graph, state the rule connecting
and . (1 mark)
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a.
b.
c.
Show Worked Solution
a.
b.
c.
Linear Relationships, SM-Bank 039 MC
Pepper uses matchsticks to make a pattern of shapes, as shown in the table below.
The equation used to show the relationship between
Linear Relationships, SM-Bank 038
- Complete the table of values below for the rule
. (2 marks)
- Use the table to list the coordinates of the points. (2 marks)
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Linear Relationships, SM-Bank 037
- Complete the table of values below for the rule
. (2 marks)
- Use the table to list the coordinates of the points. (2 marks)
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Linear Relationships, SM-Bank 036
Complete the table of values below for the given rule. (2 marks)
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Linear Relationships, SM-Bank 035
Complete the table of values below for the given rule. (2 marks)
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Linear Relationships, SM-Bank 034
Complete the table of values below for the given rule. (2 marks)
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Linear Relationships, SM-Bank 033
Complete the table of values below for the given rule. (2 marks)
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Linear Relationships, SM-Bank 032 MC
Which rule correctly describes the pattern below?
Linear Relationships, SM-Bank 031 MC
Which rule correctly describes the pattern below?
Linear Relationships, SM-Bank 030
Michael is making a geometric pattern using sticks to make pentagons.
The first 3 shapes in the pattern are shown below.
- Draw the next shape in the pattern. (1 mark)
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- Complete the table of values using the pattern. (2 marks)
Number of pentagons Number of sticks - Write the rule connecting the number of sticks
to the number of pentagons . (2 marks)
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- How many sticks will be needed to make
pentagons? (2 marks)
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a.
b.
c.
d.
Show Worked Solution
a.
b.
c.
d.
Linear Relationships, SM-Bank 029
Michael is making a geometric pattern using pins to form triangles.
The first 3 shapes in the pattern are shown below.
- Draw the next shape in the pattern. (1 mark)
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- Complete the table of values using the pattern. (2 marks)
Number of triangles Number of pins - Write the rule connecting the number of pins
to the number of triangles . (2 marks)
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- How many pins will be needed to make
triangles? (2 marks)
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a.
b.
c.
d.
Show Worked Solution
a.
b.
c.
d.
Linear Relationships, SM-Bank 028
A weekly gym membership can be purchased for different numbers of classes, as shown in the table below.
| Number of classes | 1 | 2 | 3 | 4 |
| Cost in dollars | 42 | 72 | 102 | 132 |
What is the rule connecting the number of classes purchased and the cost in dollars? (2 marks)
Linear Relationships, SM-Bank 027
A surfboard can be hired for different numbers of hours, as shown in the table below.
| Number of hours | 1 | 2 | 3 | 4 |
| Cost in dollars | 35 | 50 | 65 | 80 |
What is the rule connecting the number of hours of surfboard hire and the cost in dollars? (2 marks)
Linear Relationships, SM-Bank 026 MC
| Dress sizes | |||||
| Country A | 6 | 8 | 10 | 12 | 14 |
| Country B | 36 | 38 | 40 | 42 | 44 |
What is the rule connecting dress sizes in Country A and Country B?
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