Activity 1

Do the conversions.

1.  A tennis court is 23,78 m long. Convert to cm. (1)
2. Thabiso fills a bath with 23,7 ℓ of water. How much water is this in mℓ? (1)
3. The distance between Cape Town and Betty’s Bay is 90,25 km.How far is this in metres? (1)
4. The distance from Phumza’s house to the shop is 1 890 000 mm.How far is this in kilometres? (1)
5. A can of cola has a capacity of 330 mℓ. How many litres of cola is this? (1)
6. A boulder weighs 2,35 t. Convert the weight of the boulder into grams. (1)
7. A book weighs 0,85 kg. Convert the weight of the book into grams. (1)
8. Jack and Thembile live 6 473 m apart. Convert this distance to km. (1)
9. The dam on Cara’s farm contains 6,025 kℓ of water. How much is this in litres? (1)
10. A playground is 4,02 m wide. How wide is the playground in cm? (1)
11. A car weighs 1 250 000 g. What is the mass in tonnes? (1)
12. A long workbench is 295 cm long. How long is it in metres? (1) [12]

Activity 2

Jenny has started a decorating business and has a contract to provide decor at a wedding reception.

1. The tables used at this wedding are rectangular with a length of 3 m and a width of 1 m as shown The fabric she plans to use for the tablecloth costs R75 per metre (but can be bought in lengths smaller than a metre) and is sold in rolls that are 1,4 m wide. The bride and groom want the tablecloths to hang at least 20 cm over the edges of the tables. Calculate the cost of the cloth for each table.     (2)
2. If there are 15 tables at the wedding, calculate how much she is going to spend on tablecloths (1) [3]
   

Solutions

1.  3,4 × 1,4 × 75 = (3,4 × 75) ✓ in 1,4 m width = R255,00 ✓
2. R3 825,00 ✓

Activity 3

You should never carry more than 15% of your body weight. Elias weighs 66 kg and his backpack, with school books, weighs 12 kg. Elizabeth weighs 72 kg and her school bag, with school books, weighs 8 kg.

1. Determine 15% of Elias’s Is his bag too heavy for him? (1)
2. Determine 15% of Elizabeth’s Is her bag too heavy for her? (1)

Solution

1. 9,9 The bag is too heavy for him because it weighs more than 9,9 kg. ✓ (1)
2. 10,8 kg. The bag is not too heavy for her because it weighs less than 15% of her body ✓  (1) [2]

Activity 4 

A chef is preparing a meal that needs 3,75 kg of rice and 1,5 kg of beef. The recipe will feed 8 people.

1. Rice is sold in packets of 2 kg. How many packets will he need for the meal? (1)
2. If rice costs R 31,50 per 2 kg pack, calculate the total cost of the rice he will need.    (1)
3. If beef costs R 41,75 per kg, calculate the total cost of the beef needed for the (1)
4. Calculate the total cost of the rice and the (1) [4]

Solutions

1.  2 ✓
2. R63,00 ✓
3. R62,63 ✓
4. R125,63 ✓

Activity 5

Jonathan uses the following recipe to make chocolate muffins:

• 2 cup of baking cocoa
  3
• 2 large eggs
• 2 cups of flour
• 1 cup of sugar
  2
• 2 teaspoons of baking soda
• 1 1 cups of milk
     3
• 1 cup of sunflower oil
  3
• 1 teaspoon of vanilla essence
• 1 teaspoon of salt
  2

QUESTIONS

1. If 1 teaspoon = 5 mℓ, calculate how much baking soda Jonathan will use. Give your answer in mℓ.    (1)
2. Calculate the amount of vanilla essence Jonathan will use in this Give your answer in mℓ. (1)
3. Jonathan does not own measuring cups but he does own a measuring jug calibrated in mℓ. How many mℓ of flour does he need? (1 cup = 250 mℓ)      (1)
4. If Jonathan buys a 100 mℓ bottle of vanilla essence, how many times will he be able to use the same bottle, if he bakes the same amount of muffins each time?    (1)
5. The recipe above is used to make 30 muffins. Calculate how many cups of flour Jonathan will need to make 45 (1) [5]

Solutions

1. 10 mℓ ✓
2. 5 mℓ ✓
3. 500 mℓ ✓
4. 20 times ✓
5. He will need 3 cups of ✓

Activity 6

• Thandi is baking cupcakes and her recipe requires 1¹/₃ cup of milk
  1.1 Calculate how many mℓ of milk she will need if 1 cup = 250 mℓ.   (1)
  1.2 If the recipe is for 20 cupcakes, calculate the amount of milk required to bake 30 Give your answer in litres. (2)
  1.3 Milk is sold in bottles of 1 litre for R8,50 at the local store. Calculate the amount of money Thandi will need to spend on milk to make the 30 (1)
  

  Solutions
  1.1 333 mℓ of milk. ✓
  1.2 She will need 500 mℓ of milk, ✓ which is 0,5ℓ. ✓
  1.3 R8,50 (although she will only use half). ✓

• Thabiso decides to sell homemade He has made 5 litres of lemonade to sell at the local schools’ rugby tournament.
  2.1 Thabiso will be selling his lemonade in 250 mℓ plastic. Calculate the number of cups of lemonade he will be able to sell.    (1)
  2.2 If he sells the lemonade at R5 per cup, how much money will he make from the lemonade? (Assume that he sold all of his lemonade).    (1)
  2.3 If it cost Thabiso R120 to make the lemonade, how many cups would he need to sell (at R5 each) before he’s made back the money he spent? (1)
  Solutions
  2.1 20 cups ✓
  2.2 R100 ✓
  2.3 He would need to sell 24 cups just to cover his costs. ✓

Activity 7

Study the diagram alongside and answer the questions that follow.

1. Before Mr Dlamini builds his fish pond, he decides he wants to make the patio smaller. Using a ruler, measure the new perimeter of the patio on the diagram (in cm). (1)
2. Mrs Dlamini decides it might be better to build her vegetable garden on the right of the garden because that area gets more Using a ruler, measure the perimeter of the new triangular garden on the diagram (in mm). (1)
3. Mrs Dlamini also buys a new, circular table for the Using a piece of string and a ruler, estimate the circumference of the table (in cm).   (1)   [3]
   

NB : You will always be given the perimeter formulae in your assessments.

Solutions

1. approximately 10 cm ✓
2. approximately 82 mm ✓
3. approximately 2,5 ✓

Note: 

• The radius (r) of a circle is the length of the line from the centre of the circle to any point on its circumference.
• The diameter (d) of a circle is a straight line drawn from one edge of the circle to the other, that passes through the centre of the circle. diameter = 2 × radius.
• Pi (π) is a special symbol we use when calculating perimeter and area of circles. The value of π is 3,141 592 645…. For all of our calculations, we will use the approximate value of π = 3,142.

Worked example 13
Using the formulae given earlier, study the diagram alongside and answer the questions that follow.

1. Calculate the perimeter of the back yard, including the patio (i.e. the whole diagram) (in cm).
2. Calculate the perimeter of the patio (in mm).
3. Calculate the perimeter of Mrs Dlamini’s garden (in cm).
4. Calculate the perimeter of the table on the patio (in cm). Round your answer to 1 decimal place.
5. Is your answer to number d) different to the table circumference you estimated in the previous activity, using string and a ruler? If it is, discuss why this could be with a friend.

Solutions

Related Items

1. Perimeter of rectangular back yard
   = 2 × length + 2 × width
   = (2 × 6,2 cm) + (2 × 5,2 cm)
   = 12,4 cm + 10,4 cm
   = 22,8 cm
2. Perimeter of square patio
   = 4 × length
   = 4 × 2,5 cm
   = 10 cm
   10 cm × 10 = 100 mm
3. Perimeter of triangular garden
   = length 1 + length 2 + length 3
   = 2 cm + 2,9 cm + 3,5 cm
   = 8,4 cm
4. Circumference of table
   = π × diameter
   = π × 0,8 cm
   = 3,142 × 0,8 cm
   = 2,5136 cm
   = 2,5 cm
5.  Previously, we estimated the circumference of the table using a piece of string and a ruler. Using the formula to calculate the circumference of a circle is more accurate than using a piece of string.

Note:

• The shapes we have worked with so far have been simple. Sometimes we have to calculate the perimeter of a more complicated shape, which is made up of regular shapes that have been joined together, or in which the units are not all the same. We will look at how to do this in the next activity.

Activity  8

Mrs Dlamini buys a new lampshade for a lamp. She measures the radius of the inside circle in the lampshade to be 50 mm. The diameter of the outside (larger) circle is 40 cm. (Note, the diagram is not drawn to scale.)

1. Calculate the circumference of the smaller, inner circle (in cm). (3)
2. Calculate the circumference of the larger, outer circle (in cm). Round off your answer to one decimal place.  (3)
3. Calculate the perimeter of half of the larger, outer circle (in cm). (1)
4. Calculate the width of the area shown by the dotted line in the diagram (1)  [8]

Solutions

1. Inside circle perimeter/circumference
   = 2πr ✓
   = 2 × 3,142 × 5 cm ✓
   = 31,42 cm ✓   
2. Circumference/perimeter
   = 2πr ✓
   = 2 × 3,142 × 20 cm ✓
   = 125,7 cm ✓

3. Half perimeter
   = Perimeter = 125,7 = 62,85 cm ✓  
            2               2                      

4. Inner circle radius = 5 cm. Entire radius = 20 cm.
   Difference between radii = 20 cm – 5 cm = 15 cm ✓    (1)  [8]

Activity 9 

For your birthday, a friend gives you a rare, lucky coin that has a square cut out of the middle as shown in the photo and diagram.

1. You measure the diameter of the circle to be 3 cm, and the length of one side of the square to be 0,9 cm. Calculate the area of the coin in cm².
   Round off your answer to one decimal place.         (7)
   
2. If the coin is worth R3,58 per cm², calculate its value.   (2)  [9]

Solutions

1. To calculate the area of the coin, we need to calculate the area of the circle, and then subtract from this the area of the square cut-out.
   The formula for the area of a circle is π × radius². ✓
   We know the diameter is 3 cm, therefore the radius is 1,5 cm.
   Therefore the area of the circle is:
   π ×  (1,5 cm)²
   = 3,142 × 2,25 cm² ✓
   = 7,0695 cm². ✓
   (Remember, we shouldn’t round off while we are still busy with our calculations! We should only round off our final answer.)
   The formula for the area of a square is side × side = (side)². ✓
   Therefore the area of the square is:
   (0,9 cm)² = 0,81 cm². ✓
   We now subtract the area of the cut-out square from the area of the circle: 7,0695 cm² – 0,81 cm² = 6,2595 cm² ✓
   so the area of the coin is 6,2595 cm² ≈ 6,3 cm². ✓   (7)
2. 6,2595 cm² × R3,58 ✓ = R22,409 01 ≈ R22,41 ✓      (2)  [9]

Activity 10

Allison needs to bake cookies for her son’s crèche. She finds a recipe for cookies. She needs to calculate the volume of 1 cookie so that she knows what size container she can use. Each cookie is shaped like a flat cylinder. She measures a cookie and finds that it has these dimensions: diameter = 80 mm; height = 7 mm.

1. Calculate the volume of 1 biscuit, to one whole (3)
2. Calculate the volume of 50 (1)
3. Would a container with a volume of 700 cm3 hold the biscuits? (2) [6]

Solution

1. 35 190 mm³ ✓
   πr²h ✓
   = π(40)² (7) ✓
   = π(1600) (7)
2. 1 759 500 mm³ ✓
3. 1 759,5 cm³ (No 700 cm³ < 1 759,5 cm³) ✓✓

Activity 11

A school builds a swimming pool with the following dimensions: length = 15 m; depth = 1,3 m to the filling level, and width = 5 m.
(1 m³ = 1 000 ℓ and 1 000 ℓ = 1 kℓ)

1. Calculate the volume of the swimming pool up to the level it is filled.     (1)
2. Convert this volume
   (i) to litres
   (ii) and kilolitres.   (2)
3. When the school fills the pool, they use a pump which pumps water at a rate of 2 ℓ per second. How long would it take to fill up the pool? Give your answer in hours and minutes.   (1)
4. Water costs R8,64 per How much will it cost the school to fill up the pool? (1)  [5]

Solutions

1. 97,5 m³ ✓
2. (i) 97 500 ℓ
   (ii) 97,5 kℓ ✓✓
3. So the total time taken is 13 hr 32½ min ✓ 
4. R842,40 ✓ 

Activity 12

1. Unathi’s father goes to work at 8:00 m. He fetches her from school 7 hours and 30 minutes later. What time will he fetch her? Give your answer in the 24-hour format. (1)
2. Lauren finishes her music class at 15:30. It takes her 30 minutes to get home. She then does homework for 50 minutes. Lauren meets her friend 20 minutes after she finishes her What time do they meet? Give your answer in the 12-hour format. (1)
3. Heather starts baking biscuits at 6:15 p.m. The biscuits must come out of the oven at 6:35 m. and need to cool for another 20 minutes before they can be eaten.
   1. How long will the biscuits be in the oven? (1)
   2. What time will they be ready to eat? (Give your answer in the 12-hour format.)     (1)
4. Alison’s favourite TV show starts at 20:35. It is forty-five minutes long.
   1. What time will it finish? (1)
   2. If Alison watches the movie that follows her favourite show and it finishes at 10:50 p.m., how long was the movie (in hours and minutes)?  (1)
5. Vinayak is meeting his brother for lunch at 13:15. He also wants to go to the shops before It will take him 20 minutes to get from the shops to the restaurant where he’s meeting his brother. If he leaves home at 10:10 how much time does he have to do his shopping? Give your answer in hours and minutes.       (1) [7]

Solutions

1. 15:30 ✓  (1)
2. 5:10 p.m. ✓  (1)
3.                  
   1. 20 minutes✓  (1)
   2. 6:55 p.m. ✓  (1)
4.                        
   1. 21:20 ✓  (1)
   2. 1 hour, 30 minutes ✓  (1)
5. 2 hours, 45 minutes ✓  (1)

Activity 13

Sipho and Mpho are brothers. Their parents require them to do household chores every day. These chores need to fit into their school sports and homework timetables.
Using the information provided in the table below, construct a timetable for each brother for one day of the week.
The two brothers’ timetables need to be clearly laid out and easy to read.

Solution
For example:
Sipho:

Activity 14

Mr Odwa and his family live in the informal settlement in Langa Township. Mr Odwa has two school going kids Zonke and Andile who are attending the school at Philippi High. Mrs Odwa is a school teacher at Mandalay Secondary, while Mr Odwa works in a construction company in Woodstock.
Use the train table on the previous page to answer these questions.

1. If Zonke and Andile want to be at Philippi station at 07:31 what time must they catch a train in Langa station?  (1)
2. Which platform will that train depart from? (1)
3. Give the train number and platform number for the train that will stop at Heideveld at 08:23. (2)
4. If Mrs Odwa Pamela is at Mandalay at 09:12 what time did she depart from Langa station? (1)
5. Mr Odwa works night shift and he wants to meet his two kids at Langa station before they catch their train to What time should he take the train in Woodstock and at which platform is that train going to stop? (2) 
6. If the school starts at 08:00 and the kids miss the train mentioned in 1, what time will be the next train and what number and platform must they be on to catch the train?(3)
7. Is it possible for Mr Odwa to use the same time table to find the time for a train from Langa to Woodstock? Explain your answer. (2)  [12]

Solutions

1. 07:13 ✓ (1)
2. 16 ✓
3. Train number - 9513 ✓ (1)
   Platform - 16 ✓ (2)
4. 8:48 ✓ (1)
5. 6:33 (Platform 16 and Train 9507) ✓✓ (2)
6. 7:25 on Platform 20 (Arrive in Philippi at 07:44) ✓✓✓ (3)
7. No. The time table is one way from Cape Town to Chris Hani. ✓✓ (2) [12]