Grade 12 Mathematical Literacy questions: Paper 1

Transcription

1 Mathematical Literacy/Grade 12/P1 1 Exemplar Grade 12 Mathematical Literacy questions: Paper 1 QUESTION 1 Children s birthday parties are big business. Many restaurants offer children s birthday party services. Parents give the restaurant a list of the children to be invited and the restaurant does the rest. From sending invitations to entertainment to meals, they can do it all. A typical birthday party has a number of different activities and each of these contribute to the cost of the party. The activities and costs involved in hosting a party at one restaurant are listed below. Meals Extras Meal (Option 1) R 50,00 Jumping castle R250,00 Meal (Option 2) R 80,00 Balloon bowl R200,00 Party pack (per 10) R250,00 Adults meal R 85,00 Face painting R50,00 Electronic invitations R50,00 Minimum of 10 children per party Theme game R50,00 T-shirts (per 10) R350, Calculate the total cost of each of two party packages listed below: Meals Extras Fabulous Party (10 children 2 adults) Super Duper Party (10 children 4 adults) Children Option 1 Option 2 Adults Jumping castle Balloon bowl Party pack (per 10) Face painting Electronic invitations Theme game T-shirts (per 10) (9) 1.2 It is also possible for families to put together their own packages. Two mothers each have a budget of R2 000 to host their children s party at the restaurant One mother decides that she will only pay for the electronic invitations and the jumping castle. The rest of her budget will be spent on Option 1 meals for children only. How many children will this mother be able to invite? (4)

2 Mathematical Literacy/Grade 12/P1 2 Exemplar The other mother wants to invite 10 children (Option 2 meals) and 6 adults and to have as many of the extras as she can. Determine a possible combination of extras that she can choose and still stay within her budget. (5) 1.3 One cost not covered by the restaurant is the transport to get the children to the restaurant. A family has settled on two alternatives: Taxi 1: basic charge R75 and R7 per km. Taxi 2: basic charge R120 and R6 per km Show that Taxi 1 will charge R215 for a round trip of 20 km. (3) Taxi 1 is the more economical taxi to use for shorter distances and Taxi 2 is the more economical for longer distances. For what distance will the two taxis cost the same amount? (6) [27]

3 Mathematical Literacy/Grade 12/P1 3 Exemplar QUESTION 2 The cost of sending a parcel by courier service is determined by a number of factors: the destination (distance), the speed with which the parcel must be delivered (overnight, next day, road) and the weight of the parcel. The table below summarises the cost that one courier company charges for parcels shipped from Cape Town to Johannesburg and Kimberley. Service Destination Overnight Next day Road freight Johannesburg R50 first 2kg + R19,50 per kg R50 first 5kg + R12,50 per kg R55 first 10kg + R2,20 per kg Kimberley ** R50 first 2kg + R21,00 per kg R50 first 5kg + R13,00 per kg R55 first 10kg + R2,90 per kg Additional charges: Fuel levy: 20% Document fee: R6,00 ** Regional surcharge R30 per 2; 5 and 10kg and R2,30 for each additional kg. Calculation of costs for a 25kg parcel sent Next day from Cape Town to Johannesburg: Charge mass 25kg Basic charge ,50 300,00 Fuel levy % 60,00 Document fee 6,00 Sub total 366,00 VAT (14%) 51,24 TOTAL R 417, Repeat the calculation for the same parcel sent by road freight from Cape Town to Johannesburg and show that the total cost will be R127,22. (6) 2.2 Calculate the percentage saved by sending the parcel by road freight instead of the next day service. (3) 2.3 Sending a parcel to Kimberley attracts a regional surcharge because the courier company does not have a depot in this town What is the regional surcharge for the first 5kg on a parcel sent by next day service to Kimberley? (2) What is the per kg surcharge for every additional 1kg sent by next day service to Kimberley? (2) Calculate the regional surcharge for a 25 kg parcel sent by next day service to Kimberly. (4) Hence or otherwise show that the total cost for a 25kg parcel sent by next day service to Kimberley will be R534,89. (6)

4 Mathematical Literacy/Grade 12/P1 4 Exemplar The charge mass referred to in the sample calculation is determined by comparing the actual mass (weight) and the volumetric mass of the parcel. The charge mass is the greater of the two. The formula for volumetric mass is: Volumetric mass (in kg) = length (in cm) width (in cm) height (in cm) Show that the volumetric mass of a parcel packed in a box with dimensions: 50cm 60cm 90cm is 45kg. (3) 2.5 A parcel with mass 3kg and has dimensions 30cm 20cm 50cm is to be shipped overnight from Cape Town to Johannesburg. What will be the charge mass for the parcel? (4) [30]

5 Mathematical Literacy/Grade 12/P1 5 Exemplar QUESTION 3 Two backpackers from Germany have decided to visit historical sights in Soweto. They have printed out the map above from maps.google.com and have also printed out some directions for walking from one point to another. 3.1 The back packers are staying at a B&B at 7221 Thabete Street (marked with a cross on the map). They have the directions below for walking to the Hector Pieterson Memorial. Draw the route described by the directions onto the map. 3.2 According to maps.google.com the total distance of the walk in 3.1 is approximately 600 m and the anticipated walking time is about 6 minutes. Calculate the walking pace (in km/h) assumed by maps.google.com in making the time estimate? (4) (4)

6 Mathematical Literacy/Grade 12/P1 6 Exemplar 3.3 The backpackers have drawn the route that they plan to walk as they go from the Hector Pieterson Memorial to the former house of Nelson Mandela at 8115 Vilakazi Street onto the map. Complete the missing words and symbols on the maps.google.com directions below for this walk. You need only write down the letters and the missing information. (a) (b) (c) (d) 3.4 Measure the distance referred to by instruction 3 (in the directions in 3.3) on the map using your ruler. Use your measurement and the knowledge that the distance is 130m on the ground to calculate a scale for the map in the form 1 : x (rounded to the nearest 100). (4) 3.5 Use your answers for 3.2 and 3.4 to estimate how long it will walk from the former house of Nelson Mandela to Nambitha restaurant on Vilakzi Street. Show all your working as clearly as possible. (6) (8) [26]

7 Mathematical Literacy/Grade 12/P1 7 Exemplar QUESTION 4 An article published in The Times on 7 May 2010 reported on a study of student spending conducted on university campuses in Gauteng, KwaZulu Natal and Western Cape. The table above (from the article) summarises some of the data from the study. 4.1 Answer the following questions based on the information in the table: What is the average total monthly spend of a Coloured student? (2) Show that the individual amounts in the table for a Black student add up to R1 938 and not R2801 as the table suggests. (3) Assume that the difference between the actual amounts given and the total average should have been included in a row called Other. How much did Indian students spend on Other? (4) Show that the R362 spent on rent by Indian students represents 13,2% of their monthly spend. (3) Calculate the percentage of their monthly spend that White students spend on rent. (3) Hence, or otherwise, answer the following questions with respect to the White and Indian students: (a) Who, in absolute terms, spends more on rent every month? (b) Who, in relative terms, spends more on rent every month? (2) 4.3 Use the blank pie chart supplied in Appendix A to draw a pie chart to represent the information for the Coloured students (you must include the category: Other). (8) [25]

8 Mathematical Literacy/Grade 12/P1 8 Exemplar QUESTION 5 Many people dream of starting their own business. One kind of business that is relatively easy to start in South Africa is a Prepaid airtime and electricity dispensing services. To start the business you need to buy an airtime and electricity dispenser these typically cost about R4 000 to purchase. Once you own a dispenser you sell airtime to clients printing their vouchers directly from your dispenser. To be able to sell airtime you need to maintain a positive balance in your account with the parent company through which you are working. Everytime you make a sale the cost of that sale is deducted from your account. The table below indicates the value of the vouchers that you sell and the cost of those vouchers to you. Product Voucher value Voucher cost MTN/Vodacom/Cell C R5,00 R4,77 MTN/Vodacom/Cell C R10,00 R9,50 MTN/Vodacom/Cell C R15,00 R14,25 MTN/Vodacom/Cell C R30,00 R28,50 MTN/Vodacom/Cell C R60,00 R56,70 MTN/Vodacom/Cell C R180,00 R167,40 Eskom electicity % margin = 1,5% 5.1 Answer the following questions based on the information in the table: What does a voucher which sells for R10,00 cost the vender? (2) What combinations of vouchers would the vendor sell to a client who wanted R100 worth of airtime? List at least two different options. (2) If the vendor sold a R150,00 Eskom electricity voucher to a client, how much money (in Rand) would they make? (2) Show that the vendor earns approximately 4,8% profit on the sale of a R5,00 voucher. (3) Calculate the profit, expressed as a percentage, which the vendor makes when selling a R180 airtime voucher. (3) On a particular morning a vendor sells the following vouchers: 1 R180,00 5 R60,00 2 R30,00 15 R5,00 (a) What was the total income generated? (b) What was the cost of the vouchers? (c) How much profit did the vendor make in Rand? (d) How much profit did the vendor make as a % of costs? (9)

9 Mathematical Literacy/Grade 12/P1 9 Exemplar 5.3 The vendor is typically paid in cash for the vouchers that he/she sells. To maintain a positive balance with the parent company, vendors deposit money into the account of the company. The bank typically charges R4,00 plus 1,245% of the deposit amount as a cash deposit fee If a vendor deposits R 500,00 into the account of the parent company and the parent company deducts the cash deposit fee from the deposit, show that the vendor s account have been credited with R489,77. (4) What % of the deposit does the fee represent? (2) 5.4 Assume that the vendor earns on average 5,8% of sales and loses 2% every time he/she makes a cash deposit into the parent company s account. Consider the case of a vendor who sells R1 000,00 worth of vouchers on a day Show that the vendor s balance with the parent company will have been reduced by R942? (3) Show that the vendor must deposit at least R961,22 into the parent company s account to cover the cost of sales. (4) What percentage of the R1 000 income is the vendor left with at the end of the day? This is the vendor s real profit. (2) If a vendor wants to make at least R2 000,00 in a month in order to look after his/her family, what should their monthly sales be? (3) 5.5 How realistic do you think it is to make a living selling prepaid airtime and electricity in this way? Substantiate your answer. (3) [42]

10 Mathematical Literacy/Grade 12/P1 10 Exemplar Appendix A Question 3.1 Question 4.3