THE WYKEHAM COLLEGIATE MATHEMATICAL LITERACY

Transcription

1 1 Date: AUGUST 2010 THE WYKEHAM COLLEGIATE MATHEMATICAL LITERACY GRADE 11 Examiner: Mrs F Salisbury Time: 2 hours Moderator: Mrs D Briggs Marks: 120 Please read the following instructions carefully 1. This question paper consists of eight questions 2. Your question paper consists of 12 pages including a 3 page answer sheet. 3. Answer all appropriate questions on the answer sheet and hand it in with your examination script. 4. Unless convention dictates otherwise, round all answers to TWO decimal places. 5. An approved, non-programmable calculator may be used. 6. It is in your own interest to write legibly and to show working at all times.

2 2 Question One The Grade 11 s are planning the Grade 12 ball. They have decided to save money by making the dessert themselves, and Whitney has offered her grandmother s foolproof chocolate mousse recipe. The ingredients for one bowl of mousse are given below in imperial units. ½ pound chocolate 6 eggs 4 ounces butter ½ teaspoon vanilla essence Conversions 1 pound = 16 ounces 1 ounce = 28 grams 1 teaspoon = 15 ml 1.1 Calculate how much of each of the following ingredients would be needed to make one bowl of mousse Butter, in grams (2) Vanilla essence, in ml (2) Chocolate, in grams (3) 1.2 There are 75 Grade 12 s coming to the ball, and each is bringing a partner If one bowl of mousse is enough for 4 people, how many whole bowls will be needed for the ball? (2) How much chocolate (in grams) will the Grade 11s need to buy? (2) If chocolate costs R8,55 for a 200 gram slab, how much will the chocolate for the mousse for the ball cost? (2) Question Two [13] Compound Interest Formula: Where A = final amount P = principal n = number of compounding periods r = interest rate 2.1 The caterers tell the Grade 11 s that they want an R8 000 deposit three months before the ball. The financial manager says that the school will lend them this money but wants R8 250 back on the day of the ball. What monthly interest rate does this represent? (5) 2.2 If banks are charging an annual interest rate of 15%, compounded monthly, do you think the financial manager has offered the Grade 11 s a good rate of interest? Explain your answer. (3) [8]

3 3 Question Three The Grade 11 s have to decide whether to have the ball at Venue A or at Venue B. Their budget is quite tight, so they will choose the cheapest venue. 3.1 Venue A charges a flat rate of R300 for each person attending the function. This price includes the venue and food. The formula to calculate the cost is: C = 300 X n where C = cost (in rands) and n is the the number of people attending the function Fill in the following table for the cost of the venue and food for holding a function at Venue A: No. of people Cost R R R (3) 3.2 Venue B charges R7 000 for the venue plus R200 for each person for food. Write a formula for calculating the cost (C) from the number of people attending the function (n) (2) 3.3 Fill in the following table: No. of people _ 150 Cost R R R (4) 3.4 Draw a graph for each venue on the same set of axes, provided in the answer sheet, showing how the cost changes with the number of people attending the Grade 12 ball. (5) 3.5 Answer the following questions from your graphs For how many people would the cost of the two venues be the same? Show on your graph where you read off your answer. (2) If 75 girls attended with their partners (150 people) which venue would be more expensive? How do you know this by looking at the graphs? (2) What would the difference in cost between Venue A and Venue B be for 150 people to attend? Show on your graph how you could read off your answer. (3) If only 60 people came to the ball (30 girls and their partners), suggest which venue should be used and give a reason for your answer (2) [23]

4 4 Question Four The Grade 11 s draw up a budget for the ball and they represent the information they have calculated in a pie chart. Invitations Gifts Music Decorations Food Venue 4.1 Item of expenditure Cost Percentage of total cost Food R ,3 % Venue R ,7 % Decorations R ,1 % Music R _ Gifts R ,5 % Invitations ,8 % Total R What percentage of the total cost is for the music? (1) What is the cost of the invitations? (2) 4.2 The Grade 11 s raise R from organising a sponsored walk but they still need R to pay for the ball. They decide to ask their parents to pay the extra amount. They will divide it equally among all the Grade 11 s and put it on their accounts Calculate the amount charged to each Grade 11 if there are 70 girls in Grade Calculate the amount charged to each Grade 11 if there are 60 girls in Grade 11 (2) (2)

5 Cost Cost Cost What kind of relationship is there between the number of Grade 11 s and the amount of money each has to pay towards the ball? Give a reason for your answer. (2) 4.4 Which of the following pictures (A,B or C) would represent the shape of the graph of cost (on the vertical axis) against the number of grade 11 s (on the horizontal axis)? (1) A B C Number of people Number of people Number of people 4.5 Explain why you chose this picture (in 4.4). (2) Question Five [12] Formulae: The following formulae may be useful to answer the following questions Area of a rectangle or a square Area of a circle = Volume of a cube or rectangular prism = Volume of a cylinder = Surface area of a cylinder = Surface area of a rectangular prism = 2 ( ) + 2( ) + 2 ( ) The Grade 11 s decide to make their own table decorations. They do this by using a Perspex (transparent plastic) box that has no top and pasting a piece of Perspex tube inside the box. The top of the box is 30cm X 30cm, and the height is 20 cm. The corners of the decoration are filled with water to hold flowers, and a candle is placed inside the tube.

6 6 20 cm 30 cm Perspex pipe 30 cm Perspex box Table decoration Candle 30 cm Water String of beads 30 cm Top view 5.1 The Grade 11 s want to stick a string of beads around the top of the candle. How long will the string of beads need to be? (2) Calculate the volume of the candle that could fit exactly into the centre of the decoration. (3) Calculate the volume of water that will be needed to fill the corners of the decoration. (4) 5.3 The Grade 11 s want to spray paint the decoration with silver spray paint. Only the outside and inside of the decoration needs to be painted (not the bottom) Calculate the surface area of the outside of the decoration. (3) Calculate the surface area of the inside of the decoration. (3) Calculate the total surface area that needs to be painted. (1) 5.4 If one can of spray paint can paint 0,5m 2, calculate how many cans of paint will be needed to paint 20 of these decorations. (4) [20]

7 7 Question Six Study the map below N Five Acres complex Parking 6.1 Mr and Mrs Jones have come down from Kenya for the cocktail party and to help Gill get ready for the ball. They are staying at the Aarondale Bed and Breakfast (E on the map). Give detailed instructions, including compass directions and landmarks, how to get to the parking in front of the school from the B & B. (5) 6.2 Calculate the distance from the Bed and Breakfast to the parking as the crow flies, using the scale bar on the map. (3) 6.3 Why do you think Google Maps uses this way of indicating distances instead of giving the scale in the ratio form (e.g. 1:2 000)? (3) [11]

8 8 Question Seven Before starting to prepare for the ball, the Grade 11s had to decide on a venue for the ball. They surveyed all the Grade 11s and 12s to see which venue they should choose. Each girl voted for one venue. The table below shows the results of the survey. Venue Grade 11 votes Grade 12 votes St Ive s Thistle Hotel 6 2 Secret Garden Joe Cool s 8 26 Pecanwood Draw a compound bar graph to represent the data above. (4) 7.2 What was the most popular choice of venue for the Grade 11s? (1) 7.3 What was the most popular choice of venue for the Grade 12s? (1) 7.4 What is this measure of central tendency called? (used in questions 6.2 and 6.3) (1) 7.5 Could you use the mean to measure the middle of this data? Explain your answer. (3) Question Eight [10] In order to raise funds for the ball, the grade 11s decide to do a sponsored walk. The following figures are the amounts raised by the 25 girls in one class. Pupil No. Amount (R) Pupil No. Amount (R) Pupil No. Amount (R) Pupil No. Amount (R) Pupil No. Amount (R) Calculate the following for the data in the table above: Mean (2) Median (2) Range (2) 8.2 Using the table provided in your answer sheet, draw up a cumulative frequency table for the different amounts raised by the Grade 11s. (5) 8.3 Using your table from (8.2), draw a cumulative frequency graph for this data (4)

9 9 8.4 On your graph, mark the following: Median (1) First quartile (2) Third quartile (2) 8.5 If Ayesha, as pupil number 31, collected R350 for the walk, which measure of central tendency would now be the most suitable one to use to find the middle of the data? Give a reason for your answer. (3) [23] Total Marks 120

10 Cost in rands 10 Name: Answer Sheet Question 3.4 Graphs showing the relationship between cost and the number of people attending a function y x Number of people

11 Number of pupils 11 Question 7.1 Double bar graph showing the number of Grade 11s and Grade 12s voting for different venues y x Venue chosen

12 Cumulative frequency 12 Question 8.2 Question 8.3 Fund raising of Grade 11 girls Amount raised 46 to 50 Frequency Cumulative Frequency Cumulative frequency graph of number of girls and amounts raised 51 to to to to to to to to to to to to to to to to to to to to to to to to to 110 Amounts raised