Assignment 60 Marks 1 March, 2018

Transcription

1 Wynberg Boys High School Mathematical Literacy Grade 12 Assignment 60 Marks 1 March, 28 Instructions: Complete all the questions Do all steps necessary to get all the marks QUESTION 1 Below is a recipe for making macaroni with mushrooms and garlic. Use the recipe to answer the questions that follow. Macaroni with mushrooms and garlic Serves 4 This is a delicious supper dish that goes well with a moist main dish and makes an ideal vegetarian lunch. Best served with a mixed salad. Ingredients 8 oz macaroni salt and freshly ground black pepper 2 oz butter 2 tablespoons olive oil 3 cloves garlic, crushed 12 oz button mushrooms, sliced 2 tablespoons parsley, chopped 2 tablespoons chopped fresh basil or 1 tablespoon dried basil freshly grated Parmesan cheese to serve Wash and slice the mushrooms. Cook the macaroni in plenty of boiling salted water for about 15 minutes, or until tender but not soft. Drain thoroughly. While the pasta is cooking, place the butter and oil in a bowl with the garlic and cook for 1 minute in the microwave on full power. Toss in the mushrooms and mix well. Then cover the bowl with cling film, allowing a small gap for the steam to escape. Cook in the microwave for 5 minutes. As soon as the pasta is cooked, mix it with the mushroom mixture and the herbs. Add plenty of black pepper and a little salt. Then sprinkle with Parmesan cheese and serve.

2 Provided is the following conversion. Mass Ounces to grams 1 ounce (oz) 28 grams (g) Pounds to grams 1 pound (lb) 454 grams (g) Volume Pints to millilitres 1 pint 567 ml Tablespoons to millilitres 1 tablespoon 12,5 ml Teaspoons to millilitres 1 teaspoon 5 ml 1.1 You only have metric measuring utensils. Convert all the given measurements in the recipe to their equivalent metric measurements.(5) 1.2 If you want to make a meal for ten people, how much of each ingredient do you need to use? (Give the quantities using metric units.) (5) 1.3 If you only have access to 5 ml, 30 ml and 80 ml measuring utensils, explain briefly how you would measure the olive oil and dried basil.(2) 1.4 If a large pot of water takes about 10 minutes boil, estimate how many minutes you will need to prepare this meal for 4 people from start to finish. Explain your reasoning.(3) 1.5 To make it easier in future, when you have to convert measurements from ounces (oz) to grams (g), you decide to draw up a table of values, so that you can look up the quantities. Copy and complete this table. Ounces Grams (5) [20]

3 QUESTION 2 This graph shows the monthly number of immigrants (people coming into the country) to South Africa from January 20 to June 23. Total number of immigrants to South Africa per month, January 20 June Number of immigrants Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan 03 Mar 03 May 03 Months Source: graph drawn using data from Statistics South Africa Where do immigrants to South Africa come from? (20 23: total number: ) Americas 5% Europe 36% Asia 30% Australia and New Zealand 2% Africa 27% Source: graph drawn using data from Statistics South Africa

4 2.1 What was the number of immigrants to South Africa in: a) January 20 (1) b) January 20? (1) 2.2 What was the percentage change in the number of immigrants between January 20 and January 20? (2) 2.3 If the number of immigrants to South Africa for January 20 was 320, how many times more immigrants to South Africa were there in January 20 than in January 20? (2) 2.4 For which month was the number of immigrants approximately: a) two times as much as January 20 (1) b) half as much as January 20? (1) 2.5 Calculate the ratio of the number of immigrants to South Africa in January 23 to the number of immigrants to South Africa in January 20. (2)[10] QUESTION 3 Theo decides to set up a telephone centre in his area. Most of the people who live in the area do not have telephones. He plans to rent a container, install telephone lines and then charge people for using his telephones. Theo has worked out the following: The container will cost him R3 per month in rent. The telephone company will charge him R120 per month for each phone he rents. He decides he will rent ten phones. The telephone company will charge him 20c per unit for his telephone usage. (A later table explains exactly how long one unit allows a person to talk on the telephone for.) Electricity for the lights in the container will cost R103 per month. He will employ one worker at a cost of R2 0 each per month. 3.1 Calculate Theo s fixed costs, in other words, the costs that stay the same each month. (2) 3.2 Calculate Theo s total costs for the month if people using his phones use: a) 1 units in the month (1) b) 2 0 units in the month. (1)

5 3.3 Write an equation that gives Theo s total costs (c) in relation to the number of units (u) used in the month. (3) 3.4 Theo decides to charge the people who use his phones 50c per unit. Write an equation that gives Theo s total revenue (r) in relation to the number of units (u) used in the month. (3) 3.5 On the same set of axes, draw the graphs of Theo s costs and revenue. (2) 3.6 By solving simultaneous equations, find at what number of units these two graphs cross each other. (3) 3.7 Use your solution to question 7.6 to complete the following sentence: If Theo wants to make a profit he must sell units of telephone calls in a month. (2)

6 3.8 The telephone company provides a table that tells Theo how long a unit allows a person to talk for. This depends on whether the call is made to a cellphone or not and on whether it is local (a call to a phone in the same area) or long distance (a call to another city or town in South Africa) call. It also depends on whether the call is made during peak hours (daytime, weekday) or off-peak hours (after 7 p.m. and before 8 a.m., or on the weekend). Type of call Time of day that call is made For 1 unit you can talk for Local Long distance Peak Off-peak Peak Off-peak 30 seconds 1 minute 12 seconds 24 seconds Cellphone Any time 6 seconds Theo keeps records of the number of minutes customers spend on each type of call over the period of one week. These are summarised in the following table. Type of call Mon Tues Wed Thurs Fri Sat Sun Local (peak) 90 min 103 min 87 min 92 min 94 min 0 min 0 min Local (off-peak) 49 min 48 min 54 min 42 min 43 min 75 min 45 min Long distance (peak) 4 min 0 min 8 min 12 min 2 min 0 min 0 min Long distance (offpeak) 80 min 83 min 74 min 89 min 90 min 103 min 67 min Cellphone 10 min 20 min 4 min 7 min 9 min 25 min 12 min Based on the information given in these two tables, do you think Theo is likely to make a profit? Explain clearly why you say so. Show all your calculations. (3) [20]

7 QUESTION 4 On this map of South Africa, the lines of latitude and longitude have been drawn at 5 intervals. 4.1 The values for latitude get smaller as you go from the bottom to the top of the map of South Africa. Why is this? (1) 4.2 The values for longitude get smaller as you go from right to left on the map of South Africa. Why is this? (1) 4.3 Estimate the degrees of latitude and longitude for Upington. (2)

8 4.4 Thieves have stolen a truck, but they do not realise that it has a GPS tracking device. The GPS tracking device transmits the values for latitude and longitude of whichever place the truck is in, to a central tracking office. The central tracking office has received the reading S; E for the last 20 minutes. This indicates that the thieves have parked the truck. If they react quickly, in which town will the police find the truck? (2) 4.5 In approximately which direction do you travel if you are going directly from Nelspruit to Polokwane? (1) 4.6 Use the scale on the map of South Africa to estimate how many kilometres on the ground are represented by 1 of latitude. (3) [10] Total = 60 Marks