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? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ __________________________________________________________________________________ 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 __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________ (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. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ ________________________________________________________________________________ (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. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ ___________________________________________________________________________________ ______________________________________________________________________________________ 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