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Circles, SM-Bank 013

What fraction of a circle is indicated in the diagram below?  (1 mark)

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\(\dfrac{1}{4}\)

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\(\text{Angle}\) \(=\dfrac{\theta}{360}\)
  \(=\dfrac{90}{360}\)
  \(=\dfrac{1}{4}\)

Circles, SM-Bank 012

What fraction of a circle is indicated in the diagram below?  (1 mark)

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\(\dfrac{3}{8}\)

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\(\text{Angle}\) \(=\dfrac{\theta}{360}\)
  \(=\dfrac{135}{360}\)
  \(=\dfrac{3}{8}\)

Circles, SM-Bank 011

What fraction of a circle is indicated in the diagram below?  (1 mark)

 

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\(\dfrac{1}{8}\)

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\(\text{Angle}\) \(=\dfrac{\theta}{360}\)
  \(=\dfrac{45}{360}\)
  \(=\dfrac{1}{8}\)

Circles, SM-Bank 010

What fraction of a circle is indicated in the diagram below?  (1 mark)

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\(\dfrac{1}{3}\)

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\(\text{Angle}\) \(=\dfrac{\theta}{360}\)
  \(=\dfrac{120}{360}\)
  \(=\dfrac{1}{3}\)

Circles, SM-Bank 009

What fraction of a circle is indicated in the diagram below?  (1 mark)

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\(\dfrac{1}{6}\)

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\(\text{Angle}\) \(=\dfrac{\theta}{360}\)
  \(=\dfrac{60}{360}\)
  \(=\dfrac{1}{6}\)

Circles, SM-Bank 008

If the diameter of a circle is 16.2 millimetres, what is the length of its radius?  (1 mark)

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\(8.1\ \text{mm}\)

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\(\text{Radius}\) \(=\dfrac{\text{diameter}}{2}\)
  \(=\dfrac{16.2}{2}\)
  \(=8.1 \text{mm}\)

Circles, SM-Bank 007

If the radius of a circle is 24 centimetres, what is the length of its diameter?  (1 mark)

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\(48\ \text{cm}\)

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\(\text{Diameter}\) \(=2\times\text{radius}\)
  \(=2\times 24\)
  \(=48\ \text{cm}\)

Circles, SM-Bank 006

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Secant}\)

b.    \(\text{Quadrant}\)

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a.    \(\text{Secant}\)

b.    \(\text{Quadrant}\)

Circles, SM-Bank 005

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Major segment}\)

b.    \(\text{Tangent}\)

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a.    \(\text{Major segment}\)

b.    \(\text{Tangent}\)

Circles, SM-Bank 004

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Centre}\)

b.    \(\text{Arc}\)

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a.    \(\text{Centre}\)

b.    \(\text{Arc}\)

Circles, SM-Bank 003

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Semicircle}\)

b.    \(\text{Minor segment}\)

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a.    \(\text{Semicircle}\)

b.    \(\text{Minor segment}\)

Circles, SM-Bank 002

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Radius}\)

b.    \(\text{Sector}\)

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a.    \(\text{Radius}\)

b.    \(\text{Sector}\)

Circles, SM-Bank 001

Name the circle parts indicated in the drawing below.  (2 marks)

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a.    \(\text{Diameter}\)

b.    \(\text{Chord}\)

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a.    \(\text{Diameter}\)

b.    \(\text{Chord}\)

Rectilinear Figures, SM-Bank 045

An isosceles triangle has a base of length 4 centimetres and a perimeter of 20 centimetres.

Find the length of the equal sides.  (2 marks)

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\(8\ \text{cm}\)

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\(\text{Let the length of the equal sides be}\ x\)

\(\text{Then,}\ \ 2\times x+4\) \(=20\)
\(2x\) \(=20-4\)
\(2x\) \(=16\)
\(x\) \(=8\)

\(\therefore\ \text{The equal sides are of length }8\ \text{cm}\)

Rectilinear Figures, SM-Bank 027

A farmer uses the river bordering his property and fencing to create a large grazing paddock for his horses, as shown in the diagram below.

The fencing has 4-strand wiring which is also shown below.

Given that fencing is not required on the river boundary, how many kilometres of wire will be required to fence the rest of the paddock?  (2 marks)

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\(5.6\ \text{km}\)

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\(\text{Wire needed}\)

\(=4\times(700+200+300+1100+200+200+1200)\)

\(=4\times 3900\)

\(=15\ 600\ \text{m}=15.6\ \text{km}\)

Rectilinear Figures, SM-Bank 026

Jill cut a piece of binding in half.

She then placed one half on top of the other half, as shown below.

What is the perimeter of the newly formed shape in millimetres?  (2 marks)

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\(1600\ \text{mm}\)

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\(\text{Calculating the perimeter clockwise from top right:}\)

\(\text{Perimeter}\)

\(=18+2\times 382 +18+2\times 400\)

\(=1600\ \text{mm}\)

Rectilinear Figures, SM-Bank 025

Martha cut a piece of material in half as shown below.

 

She then placed the one half on top of the other half, as shown below.

What is the perimeter of the newly formed shape in millimetres?  (2 marks)

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\(320\ \text{mm}\)

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\(\text{Calculating the perimeter from the top down:}\)

\(\text{Perimeter}\)

\(=30+2\times 50+2\times 25+2\times 30+80\)

\(=320\ \text{mm}\)

Rectilinear Figures, SM-Bank 024

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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\(9.5\ \text{cm}\)

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\(\text{Perimeter of Rectangle}\)

\(=2\times 12 +2\times 7\)

\(=38\ \text{cm}\)

\(\text{Side length of square}\)

\(=\dfrac{38}{4}\)

\(=9.5\ \text{cm}\)

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?

  1. \(76.5\ \text{mm}\)
  2. \(93.5\ \text{mm}\)
  3. \(153\ \text{mm}\)
  4. \(187\ \text{mm}\)
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\(D\)

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\(\text{Perimeter}\)

\(=\text{Number of sides}\times 8.5\)

\(=22\times 8.5\)

\(=187\ \text{mm}\)

\(\Rightarrow D\)

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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\(14.8\ \text{km}\)

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\(\text{Perimeter of paddock}\)

\(=2\times 1.4+2\times 2.3\)

\(=7.4\ \text{km}\)

\(\text{Total distance walked each day}\)

\(=2\times 7.4\)

\(=14.8\ \text{km}\)

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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\(96\ \text{cm}\)

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\(\text{Longer side}\) \(=\dfrac{5}{3}\times 18\)
  \(=30\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=2\times 18 +2\times 30\)
  \(=96\ \text{cm}\)

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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\(72\ \text{cm}\)

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\(\text{Longer side}\) \(=8\times 3.5\)
  \(=28\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=2\times 8 +2\times 28\)
  \(=72\ \text{cm}\)

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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\(30\ \text{m}\)

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\(\text{Let}\ \ d=\text{long side of parking lot}\)

\(2\times d + (2\times 10)\) \(=80\)
\(2d\) \(=80-20\)
\(2d\) \(=60\)
\(\therefore\ d\) \(=30\ \text{m}\)

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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\(5.7\ \text{km}\)

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\(\text{Fencing required}\)

\(=3\times (450 + 200 + 150 + 500 + 600)\)

\(=3\times 1900\)

\(=5700\ \text{m}=5.7\ \text{km}\)

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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\(\text{Height}=8\ \text{cm}\)

\(\text{Length}=12\ \text{cm}\)

Show Worked Solution
\(\text{Let}\ \ \ x\) \(=\text{height}\)
\(\dfrac{3}{2}x\) \(=\text{length}\)
\(2\times \Big(x +\dfrac{3}{2}x\Big)\) \(= 40\)
\(2\times \Big(\dfrac{5x}{2}\Big)\) \(= 40\)
\(5x\) \(= 40\)
\(x\) \(= 8\)
\(\therefore\ \text{Height}\) \(= 8\ \text{cm}\)
\(\therefore\ \text{Length}\) \(=\dfrac{3}{2}\times 8\)
  \(=12\ \text{cm}\)

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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\(64\ \text{cm}\)

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\(\text{Length of 1 side}\) \(=\dfrac{24}{6}\)
  \(=4\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=16\times 4\)
  \(=64\ \text{cm}\)

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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\(1.3\ \text{km}\)

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\(\text{Express as a perimeter equation:}\)

\(2\times 2.8 + 2x\) \(= 8.2\)
\(2x\) \(= 8.2-5.6\)
\(2x\) \(= 2.6\)
\(\therefore x\) \(=1.3\ \text{km}\)

\(\therefore\ \text{Side length is }1.3\ \text{km}\)

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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\(108\ \text{cm}\)

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\(\text{Length of 1 side}\) \(=\dfrac{27}{3}\)
  \(=9\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\)

\(= (10\times 9) + (4\times 4.5)\)

\(= 90 + 18\)

\(=108\ \text{cm}\)

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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\(48\ \text{cm}\)

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\(\text{Perimeter from the top left corner (clockwise)}\)

\(=12+4+4+4+4+8+4+8\)

\(=48\ \text{cm}\)

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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\(22.5\ \text{cm}\)

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\(\text{Perimeter of rectangle}\) \(= (2\times 25) + (2\times 20)\)
  \(=90\ \text{cm}\)

 

\(\therefore\ \text{Side length of square}\) \(=\dfrac{90}{4}\)
  \(=22.5\ \text{cm}\)

Rectilinear Figures, SM-Bank 009 MC

A regular hexagon is drawn below.

5 identical hexagons are connected as shown in the diagram below.

What is the perimeter of the larger shape?

  1. \(110\ \text{cm}\)
  2. \(121\ \text{cm}\)
  3. \(132\ \text{cm}\)
  4. \(165\ \text{cm}\)
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\(B\)

Show Worked Solution
\(\text{Perimeter}\) \(=\text{Number of sides}\times 5.5\)
  \(=22\times 5.5\)
  \(=121\ \text{cm}\)

\(\Rightarrow B\)

Rectilinear Figures, SM-Bank 006

A rectangular car park is shown below with a perimeter of 70 m.

 
 
What is the length of the short side \(\large x\)?  (2 marks)

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\(10\ \text{m}\)

Show Worked Solution
\(\text{Perimeter}\) \(=25 + 25 + x +x\)
\(70\) \(=50 + 2x\)
\(2x\) \(=70-50=20\)
\(\therefore x\) \(=10\ \text{m}\)

 

Rectilinear Figures, SM-Bank 004

Justin connects three of his restaurant tables together to make one long table.

The view from above the tables is shown below.
 

 Each table is 70 cm long and 50 cm wide.

What is the perimeter of the long table?  (2 marks)

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\(520\ \text{cm}\)

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\(\text{Perimeter}\) \(= 2\times (210 + 50)\)
  \(= 2\times 260\)
  \(= 520\ \text{cm}\)

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?

  1. Rectangle 1
  2. Rectangle 2
  3. Rectangle 3
  4. Rectangle 4
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\(A\)

Show Worked Solution

\(\text{Consider rectangle 1}\)

\(\text{Perimeter}\) \(= 2\times \text{length} + 2\times \text{width}\)
  \(= (2\times 9) + (2\times 5)\)
  \(=28\ \text{cm}\)

  
\(\therefore\ \text{Rectangle 1 has a perimeter of 28 cm.}\)

\(\Rightarrow A\)

Rectilinear Figures, SM-Bank 001 MC

What is the perimeter of the shape below given each square has a side length of 1 cm?
 

  1. \(8\ \text{cm}\)
  2. \(18\ \text{cm}\)
  3. \(20\ \text{cm}\)
  4. \(36\ \text{cm}\)
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\(C\)

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\(\text{Starting at the bottom right corner and}\)

\(\text{moving clockwise:}\)

\(\text{Perimeter}\) \(=5+3+1+2+1+2+1+2+2+1\)
  \(=20\ \text{cm}\)

\(\Rightarrow C\)

Linear Relationships, SM-Bank 062

Use the graph of  \(y=3x-10\) below to find the solution to the equation  \(3x-10=-1\).  (2 marks)

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\(x=3\)

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\(\text{To solve }3x-10=-1\ \text{graphically, find the point}\)

\(\text{of intersection of the lines }y=-1\ \text{and }y=3x-10\)

\(\text{i.e. }(3\ ,-1)\)

\(\therefore\ \text{The solution is }x=3\)

Linear Relationships, SM-Bank 061

Use the graph of  \(y=7-2x\) below to find the solution to the equation  \(7-2x=-3\).  (2 marks)

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\(x=5\)

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\(\text{To solve }7-2x=-3\ \text{graphically, find the point}\)

\(\text{of intersection of the lines }y=-3\ \text{and }y=7-2x\)

\(\text{i.e. }(5\ ,-3)\)

\(\therefore\ \text{The solution is }x=5\)

Linear Relationships, SM-Bank 060

Use the graph of \(y=2x+3\) below to find the solution to the equation \(2x+3=11\).  (2 marks)

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\(x=4\)

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\(\text{To solve }2x+3=11\ \text{graphically, find the point}\)

\(\text{of intersection of the lines }y=11\ \text{and }y=2x+3\)

\(\text{i.e. }(4\ ,\ 11)\)

\(\therefore\ \text{The solution is }x=4\)