Revision questions Integrating concepts Pack 1 Gr11

Study & Master Support Pack 1 | Grade 11 CAPS Mathematical Literacy Revision questions: Integrating concepts This revision pack for Mathematical Literacy Grade 11 provides revision questions to help learners with exam preparation. Revising content will also help learners to work out problems in other sections of the Curriculum. You have permission to print or photocopy this document, and to distribute it electronically via email or WhatsApp. For more information on our Study & Master CAPS-approved textbooks and valuable resource material, visit www.cambridge.org Brighter Thinking | Better Learning

Revision questions: Integrating concepts The questions in this section test your knowledge from different topics. Use them to help you prepare for the examinations. Question 1: The Comrades Marathon The Comrades Marathon is not simply a road running event, but one of the toughest endurance events on earth. 1. The route of the Comrades Marathon is shown below with distances in kilometres and height above sea level in metres. 900 800 Height above sea level (m) 700 Highest Point:Camper- Polly Umlaas Road down 600 Murray Shortts Nagel Dam Inchanga Alverstone Road Botha’s Hill 500 Cato Ridge Bayat’s Imkondeni Hillcrest Kloof Store Half Way: 400 Pietermaritzburg Mphusheni Drummond Field’s Hill Cowies Hill 300 Pinetown 200 45th Cutting Tollgate 100 0 90 km 80 km 70 km 60 km 50 km 40 km 30 km 20 km 10 km Durban Distance (km) a) i) Calculate the gradient between Pietermaritzburg and Durban. Use the change in vertical measure formula, gradient = __________________ ​​    change in horizontal measure ​​. Show your calculations.    ii) Is the gradient positive or negative? b) i) Calculate the gradient between Polly Shorts and Pietermaritzburg. Show your calculations. ii) Is the gradient positive or negative? c) Which route do you think will be easier to run – from Durban to Pietermaritzburg or from Pietermaritzburg to Durban? Give a reason for your answer. 2. An athlete set up two world records in the 5-km and 10-km races with times of Using a fitness 12:37 minutes and 26:17 minutes, respectively. programmes such as a) Calculate the athlete’s average speed for the 5-km and 10-km races in running, swimming, kilometres per hour (km/h). cycling and fast b) If the athlete runs a 15-km race at an average of 30 km/h, calculate his time walking can improve for the race. your fitness level. c) Plot a graph of the athlete’s times against his distances for the 5-km, 10‑km Gradually your heart rate will be lowered. and 15-km races. In general, the lower your resting heart 3. Counting your pulse rate is a simple way to estimate how fast your heart is rate, the fitter you are beating. We measure our pulse by counting the beats in a period of time (at (unless you have a least 15 seconds to 20 seconds) and then calculating the number of beats per pacemaker or a heart minute. Table 1 shows the normal range of a resting heart (pulse rate after disease). resting 10 minutes) in beats per minute according to age. 1

Table 1 Resting heart rate Age/Fitness level Beats per minute Babies: 1 year of age 100–160 Children: 1–10 years of age 70–120 Children over 10 years of age and adults 60–100 Fit athletes 40–60 Table 2 shows the resting heart rate of the school’s first team rugby players and 15 learners from the chess club. Table 2 First team rugby players Chess club members Heart rate Number of Heart rate Number of players (  f  ) learners (  f  ) 70–60 3 100–90 4 60–50 7 90–80 3 50–40 4 80–70 5 40–30 1 70–60 2 60–50 1 Total 15 15 a) Which type of graph would be best to represent the data in Table 2? b) Use the information in Table 2 and represent the data for the rugby team and the chess club on a histogram on the same system of axes. c) Study the graphical representations and draw conclusions regarding the learners’ fitness levels. 4. The table gives the resting heart rate for five rugby players and five chess players. Rugby players Chess players Player A 55 Player F 63 Player B 43 Player G 60 Player C 47 Player H 95 Player D 59 Player I 88 Player E 60 Player J 69 a) For each team, calculate the following. i) the mean heart rate ii) the range of the heart rates b) Do you think the two sets of data are similar? Explain. 2

5. An athlete in training needs to consume 3 000 calories per day. a) Convert 3 000 calories to kilojoules. Kilojoules and calories are different ways of measuring the use of energy: 1 calorie = 4,186 kilojoules (kJ). b) The table gives the approximate calorie content of certain foods. Approximate calorie content of selected foods Food type Quantity Calories Carbohydrate-based White bread roll 1 120 Wholewheat bread 1 slice 70 Rye bread 1 slice 70 Cheese pizza 1 small 185 Apple pie 1 large piece 345 Chocolate cake with icing 1 slice 345 Proteins Steak 50 g 175 Hamburger patty 50 g 245 Frankfurter 1 155 Eggs, boiled 1 large 80 Sardines 50 g 175 Fats and oils Butter or margarine 1 portion 50 Peanut butter 1 tablespoon 100 Salad oil 1 tablespoon 125 Salad dressing 1 tablespoon 65 Dairy products Full cream milk 250 ml 160 Fat-free milk 250 ml 90 Low fat yoghurt 250 ml 120 Chocolate milkshake 340 ml 520 Cheese 30 g 105 Ice cream 125 ml 145 Fruit and vegetables Apple 1 medium 70 Banana 1 80 Fresh orange juice 125 ml 55 Green beans 125 ml 15 Peas 125 ml 50 Cabbage 125 ml 10 Lettuce 2 large leaves 10 3

Approximate calorie content of selected foods Food type Quantity Calories Beverages Carbonated drinks – cola 340 ml can 145 Carbonated drinks – fruit 340 ml can 170 Wine 1 glass 75 Beer 340 ml can 150 Snacks Hotdog with bread roll 1 average slice 245 i) Use the above table to calculate the calorie content of these three meals that were eaten by a training athlete in one day. Breakfast 2 boiled eggs 2 frankfurters 2 slices whole wheat rye bread 1 cup (250 ml) orange juice 1 apple Lunch 2 hot dogs 1 chocolate milk shake 1 banana 1 cup orange juice Supper 1 cheese pizza 1 can of beer apple pie and ice cream 1 can cola ii) Convert your answer in question 5ci to kilojoules. iii) Should the athlete who ate the three meals increase or decrease his kilojoule intake for the day? Give a reason for your answer. 6. Saneze runs a 42-km marathon. She runs the first part of her race at an average of 10 km/h and the second part of the race at an average of 15 km/h. Let x represent the time for the first part of the race and y represent the time for the second part of the race. If the total time Saneze takes to complete the marathon is 3,05 hours, the equation for the total time could be: x + y = 3,05 The total distance is described by the formula: 10x + 15y = 42 a) Explain how the second formula was derived. b) Solve the two equations simultaneously to work out the distance Saneze covered in the two parts of the race. Did you know that females tend to burn 7. The table on the next page shows the average number of calories athletes burn fewer calories than in one hour of exercise. (The results are not gender-specific.) males? 4

Number of calories an athlete burns in one hour Mass of athlete 60 kg 70 kg 87 kg Running 472 563 690 Walking 207 246 302 Cycling 472 563 690 Surfing 177 211 259 Swimming 472 563 690 Canoeing 413 493 604 Rock climbing 649 774 949 Tennis 413 493 604 a) Which statements are true and which are false? Show all your calculations. i) A person with a mass of 70 kg burns more calories rock climbing for half an hour than playing tennis for one hour. ii) Swimming and running burn the same number of calories per hour. iii) Cycling and swimming burn the same number of calories in half an hour. b) Calculate the percentage decrease in energy burnt for an athlete of 60 kg when he runs and when he walks. Use the formula, percentage decrease = _______________ difference of two values ​​       larger value ​​ × 100. c) Suggest a reason why someone who is surfing burns the smallest number of calories compared to the other activities given in the table. d) How many kilojoules will a person with a mass of 60 g burn when she canoes for two hours? Question 2: Wimbledon 1. During a men’s singles tennis match, the following data were collected. Player Suarez Yamamoto Number of official games played 54 37 Aces   6   2 Unforced errors 14 21 Forced errors 11 19 Double faults   5 10 Foot faults   0   1 Average speed of first serve (km/h) 136 128 Average speed of second serve (km/h) 96 97 a) Looking at the data, who do you think won the match? Explain. b) Draw a compound bar graph to help you compare Suarez’s and Yamamoto’s number of aces, unforced errors, forced errors, double faults and foot faults. (An ace is such a good tennis shot that an opponent cannot even try to return it.) c) Draw a pie graph that represents the number of official games both players have played. d) If Suarez served 240 times during the match, what is the probability that he will serve an ace for a match point? 5

2. Use the conversion factors in the table for the questions that follow. Length conversions 1 km 0,6214 miles 1m 3,2808 feet a) The length of a tennis court is 78 feet. How many kilometres is this? Round off your answer to three decimal places. b) How many seconds would it take for one of Yamamoto’s first serves to reach the service line on the other side of the court? (Assume that the speed of the tennis ball does not change and round off your answer to three decimal places). c) How many seconds would it take for one of Suarez’s second serves to reach the service line on the other side of the court? d) Which serve is faster, Yamamoto’s first serve or Suarez’s second serve? 3. The dimensions of a tennis court are given on the diagram. B Baseline Baseline Service line Net Singles 27 feet Doubles 36 feet 39 feet A distance a) Calculate the distance Yamamoto runs from A to B in feet. Round off your = speed × time answer to two decimal places. b) If Yamamoto gets to B in 2,5 seconds, at what average speed did he run? Give your answer in metres per second (m/s). c) The length of the court is 12,5 m and its width is 10,5 m. After the game, both players slowly jog around the court three times. How many miles do they jog? 4. Tennis balls are sold in two different cylindrical containers, a three-ball container and a four-ball container. The dimensions of the containers are: • three-ball container: height of 21 cm, diameter of 7,7 cm • four-ball container: height of 27,2 cm, diameter of 7,7 cm a) Calculate the volume of the two containers and round off your answer to the nearest cubic centimetre (cm3). Use the formula, volume of a cylinder = πr 2 × height. b) A standard tennis ball has a diameter of 63 cm. What is the volume of one tennis ball? Round off your answer to the nearest cubic centimetre (cm3). (Use the formula, volume of a sphere = _​​ 43 ​​ πr3.) 6

c) How much plastic is required to produce the lid of the tennis ball container? The lid has an overlap (overhang) of 6 mm. Round off your answer to the nearest square centimetre (cm2). (Use the formula, area of a circle = πr2.) d) How much metal is needed for the cylindrical part of one container? 5. A family of four plans to watch a few matches at Wimbledon. The return fare from Johannesburg to Heathrow costs R16 999 per person. Children under the age of 12 are given a discount of 25%. a) How much will a ticket cost from Johannesburg to Heathrow for a child under 12 years of age? b) How much will four tickets cost – for two adults, and two children under 12 years of age? c) If the family pays cash for the tickets, they qualify for a discount of 5%. How much will all four tickets cost if they pay cash? d) A number of people take out personal loans to pay for tickets for holidays. Calculate the interest on a personal loan of R50 000 at an interest rate of 7,2% compounded monthly, if the loan is taken over a period of three years. e) What will the monthly repayments be on the loan (question 5d)? f) Do you think it is advisable to take out a personal loan to pay for travel and holiday expenses? Give a reason for your answer. Question 3: Starting a small nursery Mr Ramlaul started a business to supplement his income as a pensioner. He built a small nursery in the back of his large garden. Mr Ramlaul specialises in groundcover because on average the plants take one month to grow to a size at which he can sell them. At the end of each month, Mr Ramlaul sells plants to nurseries. Setting-up costs are the expenses that Setting-up costs: are incurred when • 576 m of 1,5-m wide fencing at R65/m to keep his dogs away from the plants a business is being • 48 fencing poles (1, 5 m tall) at R48 each developed. They are • an irrigation system that costs R25 000 and R6 400 to install. generally once-off costs. Running costs: • watering plants daily for 15 minutes at R10,75 per minute Running costs refer to a business’s • small plastics bags at R80 for 100 bags for planting plants that are ready to expenses after it has be sold been set up. In this • topsoil at R360/m3 case, running costs • fine sifted bark compost at R450/m3. would include soil, water and plastic 1. Mr Ramlaul built his nursery in the shape of a square. To reach all the plants bags for the plants. easily, he used the floor plan on the next page. Note that the plan has not been drawn to scale. All measurements are given in metres. The shaded area represents flowerbeds and the white areas are pathways. 7

24 m 3m 0,5 3m 0,6 3m 0,5 0,6 3m 0,5 0,6 3m 24 m 0,5 24 m 0,6 3m 0,5 0,6 3m 3m 0,5 0,6 3m 11,70 m 11,70 m a) Determine the perimeter of the nursery. b) What is the total surface area of all the pathways? c) What is the total surface area available for planting groundcover plants? 2. The height of the plastic bags Mr Ramlaul uses for his plants is 25 cm and the diameter is 30 cm. a) Calculate the area (space) that is required for one plastic bag. 25 cm b) How many plastic bags would fit into Mr Ramlaul’s nursery? (Remember to exclude the pathways.) c) How much soil would fit into one plastic bag if it were filled to the top? d) Calculate the total volume of soil required to fill all the plastic bags that 30 cm can fit into the nursery. 3. Mr Ramlaul worked out his finances before starting the project. a) What did it cost him to set up his business? (Do not include his running costs.) b) What did Mr Ramlaul include in his running costs? c) Mr Ramlaul bought 144 m3 of soil to fill 7 200 plastic bags. Groundcover plants grow better in a specific soil mixture of two parts topsoil and three parts of fine sifted bark compost. How much topsoil and how much sifted bark compost did he buy? d) Calculate Mr Ramlaul’s running costs for his first month (which was 31 days). 4. After calculating his expenses, Mr Ramlaul applied for a bank loan to start his small business. The bank gave him a loan of R80 000 at an interest rate of 4% compounded annually, payable over six years. a) Calculate how much money Mr Ramlaul has to pay back to the bank, including the interest. Use the formula, A = P(1 + i)n = total amount of money at end of investment period, where P represents the initial amount borrowed, i represents the interest rate per annum as a percentage and n represents the number of years. 8

b) Providing the interest rate remains the same for the six-year period, what will Mr Ramlaul’s monthly instalments be if he pays the loan off over the full six years? 5. Mr Ramlaul sells each groundcover plant for R10. If he had sold all his plants in the first month, would he have covered his setting-up costs? 6. After running his business for 10 months, Mr Ramlaul realised that he had additional expenses that he did not consider in his initial calculations. Additional costs include transport costs to deliver plants to nurseries, pesticides to keep the plants healthy and additional water expenses during the very hot summer months. After 10 months, Mr Ramlaul drew graphs of this income and expenditure (including the loan that he was paying back) to see if he should continue with his business. e Inco Amount ((R) thousands) m y = 10x Expenditure 141 518,75 2 4 6 712 8 10 12 a) When was the income the same as the expenditure? b) What is the stage when income equals expenditure in a business called? c) Do you think Mr Ramlaul should continue with his business? Give a reason for your answer. 7. The table shows how many of Mr Ramlaul’s plants died each month. Month Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. Plants died 13 11 9 5 7 9 10 9 14 a) Draw a suitable graph to represent the information in the table. b) Find the following for the plants that died in the nine-month period. i) the range ii) the mean iii) the mode Question 4: Matric holiday A group of Grade 12 learners planned a matric holiday. They lived in Pretoria and decided to go to Jeffrey’s Bay for a few days. 1. The petrol price at the time of their trip was R12,86 per litre. The tank of the car they drove had a capacity of 45 ℓ. a) How much would it cost them to fill the tank? b) For every 100 km they drove, the car would need 7 ℓ of petrol. How far would they be able to drive on one full tank of petrol? Round off your answer to two decimal places. c) The group estimated that the distance to Jeffrey’s Bay was 1 260 km. How many times would they have to fill the car on their trip to Jeffrey’s Bay? d) How much would the trip to Jeffrey’s Bay cost (excluding toll fees)? 9

2. a) They would drive at an average speed of 110 km/h. How many hours would they be on the road if they did not make any stops? Convert your answer to hours and minutes. b) Only one person in the group had a driver’s license. The road safety regulations recommend that the driver take a break every two hours or every 200 km. The group decided to take a break for 20 minutes every two hours. How many breaks would they have to take? c) How long would the trip take, including the time for the stops? (Assume that all breaks would be exactly 20 minutes long.) 3. a) The group decided to save on costs and take food and coffee with them lid rather than buying these items on the road. There are no indications on the thermos flask they used of how many litres it could hold. What is the volume of the flask if the height of the cylinder is 21 cm and the diameter of the opening is 5,5 cm? b) They could use the lid of the flask as a cup. The lid can hold 125 ml. How flask many cups could they get from the flask? Would there be enough coffee for four people to each have one cup? (Remember, 1 cm3 = 1 ml) 4. On one of their stops, the group bought four small boxes of chocolate Smarties. To pass the time, they counted the number of chocolates in each box. The table shows what they found. Box 1 2 3 4 Number of chocolates 19 21 18 20 Green chocolates 2 5 3 0 Brown chocolates 5 3 3 6 Red chocolates 3 6 2 3 Purple chocolates 4 2 3 5 Yellow chocolates 1 3 3 2 Pink chocolates 4 2 4 4 a) What is the mean number of chocolates per box? b) What is the modal average of the yellow chocolates? c) What is the probability that the first chocolate someone took out of box 2 would be a pink chocolate? Give your answer as a fraction and a percentage. d) What is the probability that the second chocolate someone took out of box 2 would be yellow? Give your answer as a fraction and a percentage. 5. The group decided to go bungee jumping. 10

The graph represents one learner’s jump. Time (s) 2 4 6 8 10 12 14 16 20 40 Distance (m) 60 80 100 120 a) How many seconds did the initial fall last? b) How far did the learner fall? c) The initial fall is represented by the formula, y = − ​​ ___ 49 2 100 ​​  x . What type of graph does this formula represent? d) Approximately how far had the learner fallen after three seconds? Round off your answer to two decimal places. e) Approximately how long did it take the learner to fall 16 m? f) Explain what happened after seven seconds. g) What happened after 15 seconds? 6. Before someone is allowed to jump, they are weighed to determine the strength of the rope that is needed. There are four different categories according to mass. If someone’s mass is 45 kg, they are put into level 2 for safety reasons. Rope strength Mass (kg) Level 1 0–45 Level 2 45–60 Level 3 60–78 Level 4 78–105 The learners were divided into two groups of ten to make it easier for the instructors to ensure their safety. The tables show the body mass of the two groups. Group A Learner 1 2 3 4 5 6 7 8 9 10 Mass 78 64 59 62 43 102 71 65 54 52 Group B Learner 11 12 13 14 15 16 17 18 19 20 Mass 47 53 89 76 64 67 81 57 73 45 a) Represent the data collected for groups A and B on two bar graphs. (Use the mass classifications in the table.) b) Find the mean of each group. 11

Question 5: The Channel Tunnel The English Channel E N G LAN D joins the Atlantic Ocean to the North Amsterdam London Sea. It lies between N E T H E R LAN D S Great Britain Ashford and France. It is Calais approximately 563 km Fréthun long and it is 240 km Lille Brussels at its widest part. The BELGIUM Channel Tunnel that FRANCE connects England and France at the bottom Paris of the ocean is the 0 50 miles Eurostar longest tunnel in the Channel Tunnel 0 100 km world. The American Society of Civil Engineers declared it one of the Seven Wonders of the Modern World. The Channel Tunnel was officially opened by Queen Elizabeth II and French President François Mitterrand on 6 May 1994. The Channel Tunnel is commonly called the Chunnel. 1. The Channel Tunnel is 50 km long; 39 km of the tunnel is on the seabed. The average depth of the tunnel is 45 m under the sea’s surface. What portion of the tunnel is on the seabed? Give your answer as a fraction and as a percentage. 2. The Channel Tunnel consists of three parallel tunnels. There are two rail tunnels that are about 30 m from each other. Each tunnel is 7,6 m in diameter. Between the two tunnels is a service tunnel that is 4,8 m in diameter. The service tunnel is connected by cross-passages to the main tunnels at intervals of approximately 375 m. a) How many cross-passages are there along the entire Channel Tunnel? b) Approximately how many cubic metres of gravel (soil/chalk) had to be removed to build the Channel Tunnel (the two rail tunnels and the service tunnel)? Round off your answer to two decimal places. 3. The Channel Tunnel offers three main services: a shuttle service for vehicles, the Eurostar passenger train service that links London with Paris, Amsterdam and Brussels, and a freight service with trains that carry only goods. a) Calculate the average speed of the Eurostar passenger service that takes 20 minutes through the Channel Tunnel. b) Calculate the average speed of the shuttle train for vehicles that takes 35 minutes through the Channel Tunnel? c) The Eurostar can take you from London to Paris in 2,5 hours. The standard speed = ______ distance ​​  time ​​ cruising speed of the Eurostar is 300 km/h, but the speed inside the tunnel (50 km long) is 160 km/h. Assume that the Eurostar maintains these speeds and travels from Paris to London in 2,5 hours. How long will the Eurostar take to travel through the Channel Tunnel? Give your answer in minutes and seconds. d) Calculate the total approximate distance by rail between Paris and London. 12

4. Bianca took a gap year in the United Kingdom and then went to visit her aunt who lived in Paris. Study the table below. Eurostar Standard Class tickets: London to Paris Fare type One-way Round-trip Duration Pass holder $135 $270 2,5 hours Youth $117 $234 2,5 hours Leisure round-trip in same day $96 2,5 hours Bus/Ferry combo: London to Paris Fare type One-way Round-trip Duration All fares £37 £50 7–8 hours a) Which option should she choose for each trip? Use the exchange rates, R10,28 = $1 and R16,81 = £1. i) a quick trip from London to Paris ii) the cheapest trip from London to Paris in an amount in rand b) Bianca wanted to experience the Eurostar. How much more would a one- way ticket cost if she took the Eurostar rather than the bus/ferry combo? Give your answer in rand. Question 6: Free energy from the sun Because South Africa has a sunny climate, many South Africans enjoy swimming. A solar energy system uses energy from the sun to warm water for domestic and other uses. A solar system can be attached to a swimming pool filter system so that cool water is drawn from the pool and passes through sun-warmed panels before being recycled into the swimming pool. Once a favourable water temperature has been reached, the recycled water can be switched to bypass the heating panels. 1. A swimming pool company claims their solar heating system will increase the temperature of the water in a swimming pool by 34%. If the temperature of the pool water is 6 °C without a solar heating system, what will it be the system is being used? 2. Temperature of water in swimming pool of average size in high altitudes of Gauteng, KwaZulu-Natal and the Free State 40 solar heated pool with cover 35 solar heated pool 30 normal pool Temperature (°C) 25 20 15 10 5 0 Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun. normal swimming season swimming season of solar heated pool swimming season of solar heated, covered pool 13

a) How many months are seen as the normal swimming season in South Africa? b) How many months are seen as the swimming season in South Africa with the solar heating system, but without a swimming pool cover? c) The company claims that about 75% of heat loss is through evaporation, but that this can be prevented by using a pool cover. How many months are seen as the swimming season in South Africa with a solar system as well as a swimming pool cover? d) The average swimming season in the Cape Town area is approximately three months per year. How many months would the swimming season be in Cape Town if a solar system and a swimming pool cover were used? e) i) What would the water temperature be in a swimming pool in mid- January if a solar system and a swimming pool cover were used? ii) Do you think the temperature is a comfortable temperature for swimming on a hot summer’s day? Give a reason for your answer. f) i) What would the water temperature be of a swimming pool in mid- January if a solar heater and a swimming pool cover were not used? ii) Would this be a pleasant temperature for swimming on a hot day? 3. A solar heating system consists of smooth black panels, usually installed on the roof of a house and connected to a swimming pool pump. The dimensions of one solar panel are 2,8 m by 1 m. roof solar panel heated water to pool water from pool automatic control pool fliter pool pump swimming pool Formulae used to calculate the number of panels needed for a pool: Number of panels needed (without a swimming pool cover) swimming pool surface area __________________ = ​​       panel surface area ​​ × 0,75 Number of panels needed (with a swimming pool cover) swimming pool surface area __________________ = ​​       panel surface area ​​ × 0,5 Determine the number of solar panels needed to heat each swimming pool. a) 5 m × 10 m, without a swimming pool cover b) 5 m × 10 m, with a swimming pool cover c) 3 m × 3 m, without a swimming pool cover 14

Question 7: Tumi’s beads Tumi makes beaded Aids badges to supplement her income. She sells the badges to a craft shop, Crafters, which is close to where she works. The owner of Crafters gets 20% of Tumi’s sales, Tumi gets 75% and she donates 5% of her sales to an Aids charity organisation. 1. Tumi sews a small safety pin onto the back of each badge. Each badge is sold attached to a card that gives Tumi’s logo and her contact details. Each card measures 60 mm by 70 mm. Tumi buys large A3 sheets of cardboard and she makes her own cards. (The dimensions of an A3 sheet of paper or cardboard are 420 mm by 297 mm.) a) What is the area of one A3 sheet of cardboard? b) What is the area of one of Tumi’s cards? c) Use your answers to the above questions to work out how many cards Tumi can cut from one A3 sheet of cardboard. d) After cutting out the first cards, Tumi realised that she was making fewer cards than she had calculated from one A3 sheet. She decided to draw all the cards on the A3 sheet before cutting out cards. Which layout option will give Tumi more cards? Give a reason for your answer and show all your calculations. 297 mm 297 mm 70 60 60 70 420 mm 420 mm Option A Option B Note: Diagrams are not drawn to scale e) Calculate the amount of square millimetres (mm2) that is wasted for each option to find out which layout results in the least wastage. 2. Tumi kept accurate records of her income and expenses. The table that follows shows her income and expenditure at the end of her first month. Expenses Quantity Total Income Quantity Total A3 sheets 4 sheets (R17,95/sheet) 71,80 Badges sold 98 badges (R5,00/badge) R490,00 Red beads 100 g bulk pack 85,99 White beads 100 g bulk pack 85,99 Safety pins 150 bulk pack pins 35,00 Cotton 2 reels (R12,95/reel) 25,90 Needles 1 packet 19,25 Stamp* 425,00 Stamp pad 95,00 Total R843,93 R490,00 * Tumi’s name and logo 15

profit = income – a) Tumi did not indicate in her budget how much money the owner of Crafters expenditure and the Aids charity organisation receive. Calculate these two amounts and Tumi’s income. percentage mark-up b) Calculate Tumi’s profit for the first month. selling price – cost price c) Do you think Tumi’s business venture will be successful? Will she make a = _______________ ​​   ​​ cost price profit in the long run? Give a reason for your answer. × 100 d) Tumi calculated that the cost price for one badge is R2,50. If the selling price is R5,00 (inclusive of VAT), what is her percentage mark-up? e) During Aids Awareness Week, Tumi gave a discount of 12% on all the badges. Calculate the discounted price of an Aids badge. 3. Every three months, Tumi drew graphs to show her income and expenditure for the three months. The graph shows her income and expenditure for her first three months. Cost and sales of Aids badges 1 000 900 Third month 800 Second month 700 Cost (exp 600 enses) Amount (R) 500 First month 400 e) m 300 co in s( 200 le Sa 100 0 20 40 60 80 100 120 140 160 180 200 220 Number of Aids badges a) At what point did Tumi’s business break even? Give the coordinates of this point. b) How many Aids badges were sold by break-even point? c) What was Tumi’s income from sales at break-even point? d) How many badges did Tumi sell in the second and third month of her business? e) What was Tumi’s income from sales in her second and third months? f) Is Tumi’s business successful? If so, do you think it will remain successful? Give a reason for your answer. 4. The table gives Tumi’s sales for her first year. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. 67 143 155 177 98 160 180 165 177 163 177 77 a) Represent the data in the table on a broken-line graph. b) In which month were Tumi’s sales the lowest? Give a possible explanation for the low sales in these months. c) If Tumi wanted to calculate her average sales for the whole year, would she determine the mean, the mode or the median? d) Calculate the follow for Tumi’s data. i) the mean ii) the mode iii) the range 16

Question 8: The Ribbok Hiking Trail A group of seven Grade 11 learners and three teachers decided to tackle the Ribbok Hiking Trail in the April school holidays. This hiking trail is in the Golden Gate Highlands National Park in the Free State. Hikers are only allowed to sleep in the hiking huts that are provided by the park. Study the maps and answer the questions that follow. Ribbokkop Generaalskop Snow Hill Lesotho View Wodehouse Hill Swartkop Spitskop 2 400 m Glen 2 200 m Ribbok Hut Brandwag Reenen Glen Reneen 2 000 m 2 000 m 1 800 m 1 800 m Profile of trail To Glen Reenen hut To Ribbok hut 13,9 km; ±8,5 hours 14,2 km; ±7,5 hours Spitskop 2 376 Wodehouse Hill L it t l e C 2 438 al ed on R iv er The Golden L it t le C a le d o n R iv e Gate r Glen Reneen A Golden View Brandwag Resort Hotel Langtoon e Dam Driv ie w V B u f f e ls p e Gam B Ribbok Hut ru i Swartkop t 2 422 Hiking trail N W E 0 1 2 km Generaalskop 2 732 Scale - 1 : 50 000 (2 cm = 1 km) S Ribbokkop Lesotho View 2 829 17

1. a) Do you think the Ribbok Hiking Trail is a circular route? Give a reason for your answer. b) What is the total distance of the Ribbok Hiking Trail? c) i) How many days would a hiker need to complete the hiking trail? ii) What distance would a hiker cover each day? d) The direct distance (as the crow flies) between Ribbok Hut and Glen Reenen on the map is 8 cm. Use the scale on the map to determine this distance in real life. e) In which direction(s) would a hiker walk from Ribbok Hut towards Generaalskop? f) Generaalskop is the highest point along the route and so it is an ideal viewing point. Standing at this viewing point, in which direction would a hiker look to see each place? i) Langtoon dam ii) Lesotho iii) Golden View Resort iv) Ribbokkop 2. a) If the group wanted to cover the first 14,2 km in the recommended time of 7,5 hours, what average speed would they have to walk? b) If the group wanted to cover the second 13,9 km in the recommended time of 8,5 hours, what average speed would they have to walk? c) If the group wanted to take an hour lunch break each day, how fast would they have to walk to cover the distance in each recommended time? i) 14,2 km in 7,5 hours ii) 13,9 km in 8,5 hours d) Why do you think it is necessary to stay within the recommended time when hiking? e) i) The group packed enough food and water for the two-day hike. If five more learners wanted to join the group on the morning of their departure, would there be enough food and water for everyone for two days? ii) How long would their food and water last if they took five more hikers along? iii) Is the food supply and the number of hikers an example of direct proportion or inverse proportion? g) Do you think it would be a good idea to take additional people along if you do not have additional provisions? Give a reason for your answer. Question 9: Going on holiday As part of a school fundraiser, the Grade 11 classes was responsible for raffle tickets. The first prize was a luxury tent. Through a contact the Grade 11 classes could purchase the tent for R6 000. 1. a) If the raffle tickets were sold for R20,00 each, how many tickets would have to be sold to cover the cost of buying the tent? b) How many tickets would have to be sold to make a profit of R1 000? c) It cost the learners R1,50 per ticket to print the raffle tickets. They hoped to sell 350 tickets. How much profit would they make if they sold each ticket for R20? d) If the price of the raffle tickets increased to R25 each, calculate the percentage increase in the ticket price. e) How much more profit would they make if they sold 350 tickets? 18

2. a) If you bought two of the 350 raffle tickets, what would your chance be of winning the tent? Simplify your answer. b) Jacob bought 12 tickets. Calculate the chance that he would win the tent. Give your answer as a percentage rounded off to two decimal places. 3. Jacob was very lucky – he won the tent! For his next holiday his family wanted to go to Victoria Falls in Zimbabwe. Jacob had to plan the holiday. The exclusive camp site he had in mind is shown below. 30 m B 6,5 m blo Abl ck utio B 4m 21 n m2 8m C 25 m 35 m2 4m A 42 m2 Pool 75 m 6m X 76 m2 Y Lapa with kitchen 15 m Plan not drawn to scale 20 m a) Jacob chose campsite B, as it has the best view into the bush. Calculate the area of the campsite. b) Estimate the area the swimming pool covers. Show all your calculations. c) If the pool is on average 1,5 m deep, estimate the volume of the water needed to fill the swimming pool. d) Calculate the length of the fence XY. Round off your answer to one decimal place. e) Calculate the perimeter of the entire campsite. f) Estimate the area of lawn that is fenced in. Show all your calculations. 4. Jacob could also book accommodation at a lodge. A travel agency gave him the following information. The Victoria Falls Hotel Vic Falls Safari Lodge Bed and Breakfast Bed and Breakfast Special rates for families 4 days from R6 790 3 days from R6 490 5 days from R7 490 4 days from R6 890 Airport taxes for OR Tambo International Airport taxes for OR Tambo International Airport from R1 030 Airport from R1 030 a) If Jacob booked at the Vic Falls Safari Lodge, would he have a better deal if they stayed for three days or for four days? Substantiate your answer with a calculation. b) For which deal would Jacob pay the lowest amount per day? 19

5. Before Jacob went on vacation, he looked for equipment the family will need. Binoculars R559,00 Leatherman Scale: 1 : 7 a) A 5%-discount is given on all cash payments. How much would the Leatherman cost if he paid cash? b) The binoculars were marked down from R1 700 to R1 105. What was the percentage discount? c) The smaller pair of binoculars are 3 cm long in the diagram. Use the scale on the diagram to calculate the actual size of the small pair of binoculars. 6. The map below shows Jacob’s destination. Zam be z ZAMBIA Katima Mulilo i NAMIBIA Impalila Island Kasai Channel Kazangula Livingstone Kasane Victoria Falls be Ch o N W E B O T S WANA 0 25 30 km ZIMBABWE S a) Explain how to use the scale on the map. b) Calculate the distance between the Victoria Falls and Livingstone if the distance between these two places on a map is 6 mm. 7. A third option for accommodation was a camper. The dimensions of the camper are shown in the diagram. 1 355 mm 750 mm A Bed 1 2 000 mm B G B Bed 2 D C Cupboard 1 F 1 750 mm D Cupboard 2 1 165 mm H A E C E Stove/washbasin F Table 1 810 mm 2 010 mm G Shower I H Awning I Awning 4 000 mm 20

a) What is the length of the bed in room A in metres? b) By how many millimetres (mm) is bed B wider than bed A? c) Calculate the area of the kitchen (area H). Round off your answer to one decimal place. 8. The weather report predicted that Zimbabwe would be hit by a heat wave during Jacob’s trip and so he thought about other holiday destinations. A website gave the following average temperatures. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Cape Town 27 27 26 23 20 19 17 18 19 22 24 26 Durban 27 28 27 26 24 23 22 22 23 24 25 26 Johannesburg 26 26 24 22 19 16 16 20 23 25 25 26 Kimberley 33 31 28 25 21 19 19 22 25 28 39 32 Port Elizabeth 25 26 25 23 22 20 20 20 20 21 22 24 Skukuza 31 31 31 29 21 25 25 26 29 29 30 30 Mbabane 25 25 24 23 31 19 19 21 23 24 24 25 a) What is the mean temperature for Cape Town in an average year? b) What is the modal temperature for Port Elizabeth? c) Calculate the median for the temperature in Johannesburg. d) Calculate the temperature in the car in Fahrenheit if it was 32 °C? Remember, F = ​​ _5 ​​C + 32. 9 9. Jacob’s family decided to visit the Kruger National Park for their holiday. While in the park, they wanted to go on a game drive. The cost of a game drive is calculated using the formula: C = ____ 1 250 ​​  P ​​, where C represents the cost (R) per game drive and P represents the number of people. The maximum number of people allowed in the vehicle is 30. a) Complete a copy of the table below, using the above formula. Number of people (P) 0 1 5 10 25 Cost of the game drive (C) (R) b) Explain why calculators give an error message when you substitute 0 people into the formula. c) Represent the information in the table on a graph. d) Should you join the dots of your graph? Give a reason for your answer. e) Use your graph to estimate how much each person must pay for a game drive if there are 17 people on a game drive. Mark you answer with an X. f) Calculate how much each person must pay if 17 people go on a game drive. g) What is the maximum number to indicate on the horizontal axis (number of people) on your graph? Give a reason for your answer. 10. Colddrinks are on sale during the game drive. They are kept in a small fridge that is cooled from the power outlet of the vehicle. The dimensions of the fridge are 80 cm by 55 cm by 70 cm. a) Calculate the volume of the fridge. b) For practical purposes, only bottled drinks are sold on the drive. Why do you think this decision was taken? 21

c) The diameter of one bottle is 5,5 cm and its height is 12 cm. Calculate the volume of one bottle. Round off your answer to two decimal places. d) Using calculations only, how many bottles should be able to fit into the fridge? e) Is your answer realistic? Give a reason for your answer. Animals spotted during the day 11. At the camp. the following information is Monkey displayed about animals that have been spotted 11% Giraffe in the surrounding area on a particular day. Lion 23% 8% a) Explain why the chart is not a good way to represent the data. b) What would you change? Give reasons for Elephant 16% your answer. c) If visitors to the park saw two lions, how many elephants did they see? Zebra 42% d) If the total number of animals people spotted was 56, approximately how many of the animals were giraffe? e) Jacob kept at record of the animals they saw on the game drive. The table gives his results. Represent the information in the table in a bar graph. Type of animal Number of animals spotted Kudu 5 Hippo 2 Lion 1 Giraffe 4 Wild dog 0 Zebra 12 Rhino 5 Elephant 3 12. While on holiday, Jacob made friends who were from other schools. They compared the teacher to learner ratio for the their schools. a) As a decimal fraction correct to two decimal places, find the teacher to learner ratio for each school. School Teachers Learners 1 76 1 254 2 54 1 389 3 63 987 4 59 1 008 5 45 574 b) If a school has 70 teachers and the same teacher to learner ratio as school 3, how many learners would be at the school? c) If a school has 1 148 learners and the same teacher to learner ratio as school 5, how many teachers are at the school? d) Which school has the best teacher to learner ratio? Give a reason for your answer. e) Draw a compound bar graph to represent the information in the table. 22