Part A – Parts of a Circle
In this activity you will use GeoGebra to construct a circle and display all
the circle parts.
a) Click View Grid and click off the Axes. To construct a large circle,
use Circle with Center Through Point or Circle with Centre and
Radius (suggest radius of 4 units) or circle through three points.
b) Click Interval between Two pints and draw a radius and a chord in
your circle
c) Click Insert Text to label the chord and the radius.
Construct each of the circle parts below on your page and label each one
1. Centre
2. Diameter
3. Sector
4. Arc
5. Tangent
6. Segment
This is how your labelled
circle should look.
Part B - Measuring area and circumference of a circle
This is a measuring activity in which you will need a ruler, 4 round objects
such as cans, round cake, pipes, money, bottles and so on.
a) Measure to find the radius in millimeter of four different objects. Record
your results in the table.
b) Calculate the Area, using the formula. Round to two decimal places.
c) Calculate the Circumference, using the formula. Round to two decimal
places.
Object
Radius ( mm)
Area
( A = 𝝅 𝒙 𝒓𝟐 )
1.
2.
3.
4.
Circumference
( C = 𝟐𝒙 𝝅 𝒙 𝐫 )
Part C - Volume Investigation
a) Roll a die to determine the lengths for the height, width and depth
(cm) for Shape 1.
b) Fill in the table and work out the Volume of Shape 1.
c) Then, increase only the width by 1cm and write the new lengths in
the table. Keep the height and depth the same length for each shape.
d) Continue increasing the width by 1 repeatedly and each time work
out what the new volume will be.
1.
2.
3.
4.
5. Plot the Volumes you get for different widths. Make sure you extend
the line across the whole grid above.
6. Can you explain the pattern?
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Part D - Algebra_____________________________________________________________________
1. Write an algebraic expression for each line of this puzzle.
I am thinking of a number.
Let the pronumeral n represent this
Add eight
Double the answer
Take away the number I first thought of
Write this answer as simply as possible
Subtract five
Take away the number I first thought of
What is the final answer?
2. Does this puzzle always give the same answer? Explain why?
3. List four factors, other than one and itself, for the algebraic term
5𝑎2 𝑏
4. If an algebraic term has the factors 5, 7 and k, write four other
terms that must also be factors (other than 1)
Extension
(a) Explain in your own words how to find the volume of a solid
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(b) If you have two cylinders and one is twice as tall, but its radius is
only half as long, which cylinder has the greater volume? Explain or show
work.
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(c)
A rectangular prism has length ( l) , width ( w) and height (h). What
would happen to the volume if the length was doubled, but other
measurements stayed the same? Show working out.
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Marking rubric
Part A
8 marks – (1 – mark) for each part of the circle constructed and labelled.
1.
2.
3.
4.
5.
6.
7.
8.
Radius
Chord
Centre
Diameter
Sector
Arc
Tangent
Segment
1/2 mark for constructed however, not labelled.
Part B - 8 marks
Object
Radius ( mm)
Area
( A = 𝝅 𝒙 𝒓𝟐 )
Circumference
( C = 𝟐𝒙 𝝅 𝒙 𝐫 )
1.½ mark for round object
½ mark for radius
written
½ mark for correct
answer
½ mark for correct
answer
2..½ mark for round object
½ mark for radius
written
½ mark for correct
answer
½ mark for correct
answer
3.½ mark for round object
½ mark for radius
written
½ mark for correct
answer
½ mark for correct
answer
4.½ mark for round object
½ mark for radius
written
½ mark for correct
answer
½ mark for correct
answer
Part C
Question 1, 2 ,3 , 4
½ mark for a
number written
½ mark for a
number written
½ mark for a
number written
½ mark for
volume
calculated
correctly
½ mark for
width increased
by one
½ mark for
height kept the
same as above
½ mark for
depth kept the
same as above
½ mark for
volume
calculated
correctly
½ mark for
width increased
by one
½ mark for
height kept the
same as above
½ mark for
depth kept the
same as above
½ mark for
width increased
by one
½ mark for
height kept the
same as above
½ mark for
depth kept the
same as above
½ mark for
volume
calculated
correctly
½ mark for
volume
calculated
correctly
Part C
Question 5
4 marks – Each of the four volumes are plotted correctly and joined up to form a line
that is increasing
3 marks – 3 points are plotted correctly, however not plotted
2 marks – 2 points are plotted correctly, however not plotted
1 mark- 1 points are plotted correctly, however not plotted
Question 6
2 marks – The volume increases as the width increases
1 mark- The volume is increasing, or the line graph is increasing
 Something along these lines, teacher judgement is needed.
Part D
Question 1 ( 4 marks)
Let the pronumeral n represent this
number
½ mark for n
Add eight
½ mark for n +8
Double the answer
½ mark for 2 x ( n+8)
½ mark for 2 x ( n +8 ) - n
Take away the number I first thought of
Write this answer as simply as possible
½ mark for n +16
Subtract five
½ mark for n +11
Take away the number I first thought of
½ mark for n +11- n
What is the final answer?
½ mark for n +11- n = 11
PART D
Question 2 ( 2 marks)
 1mark for yes it always gives the same result
 1 mark for discussing the steps
(We doubled the number and subtracted 5 and took away n)
Question 3 ( 2 marks)
½ mark for any of 4 of these – 5, a, b, 𝑎2 , ab, 5a, 5b, 5ab, 𝑎2 b
Question 4 ( 2 marks)
½ mark for each of these – 35, 7k, 5k and 35k