Mathematics Examination 563-212 Secondary Cycle One Year One June 2008 Student Booklet 2 Competency 2 and Competency 3 Situations Calculator allowed Time : minutes Name : Group : June 2008
The following criteria will be used to evaluate your level of competency development in the different situations presented in this booklet. Evaluation Criteria Uses Mathematical Reasoning Cr3 - Proper application of mathematical reasoning suited to the situation Cr2 - Correct use of the concepts and processes appropriate to the situation Cr4 - Proper organization of the steps in an appropriate procedure Cr5 - Correct justification of the steps in an appropriate procedure Cr1 - Formulation of a conjecture appropriate to the situation Evaluation Criteria Communicates By Using Mathematical Language Cr1 - Correct interpretation of a message involving at least one type of mathematical representation suited to the situation Cr2 - Production of a message suited to the context, using appropriate mathematical terminology and following mathematical rules and conventions Instructions 1. Fill in all the required information in the spaces provided in this booklet. 2. There are 7 questions in this booklet. For each question, you must demonstrate your reasoning to justify your answer. The steps in your procedure must be organized and clearly presented. 3. You are permitted to use graph paper, a ruler, a compass, a set square, a protractor and a calculator. 4. You may refer to the memory aid you prepared on your own before the examination. The memory aid consists of one letter-sized sheet of paper (8½ 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid is forbidden. All other reference materials are forbidden. Note: Figures are not necessarily drawn to scale. Secondary Cycle One Year One 563-212 Booklet 2 Page 1
9. Burn It Off Jenna and Mario are concerned about nutrition and overall good heath. They wanted to know how many minutes it would take to burn off the calories from a Fair Trade chocolate bar. The chocolate bar has 282 calories. They set up a table to record their friends weight and favourite activity, as shown below. Friends Weight in pounds Favourite activity Minutes needed to burn off the calories in the Fair Trade bar Tanya 120 Hiking Mitch 175 Weight training Freddie 160 Running Gina 124 Basketball Peter 180 Watching TV Your job is to use the information in the chart below to calculate how many minutes it would take each of their friends to burn off the calories in the Fair Trade chocolate bar. You must show your calculations. Activity Number of calories burned per minute by approximate weight 120 pounds 140 pounds 160 pounds 180 pounds Aerobics 7.4 8.6 9.8 11.1 Basketball 7.5 8.8 10.0 11.3 Hiking 4.5 5.2 6.0 6.7 Jogging 9.3 10.8 12.4 13.9 Running 11.4 13.2 15.1 17.0 Watching TV 1.2 1.3 1.5 1.7 Walking 6.5 7.6 8.7 9.7 Weight Training 6.6 7.6 8.7 9.8 Chocolate has long been heralded for its value as an energy source. Think of it this way: a single chocolate chip provides sufficient food energy for an adult to walk 46 metres; hence, it would take about 22 chocolate chips to walk a km. Secondary Cycle One Year One 563-212 Booklet 2 Page 2
10. Chocolate Trivia One click of a mouse burns 0.0000024 kcals of energy, so if you eat a chocolate bar, you will need to click your mouse 765,551,000 times to burn it off. Written in scientific notation, this sentence would look like: a) One click of a mouse burns kcals of energy, so if you eat a chocolate bar, you will need to click your mouse times to burn it off. The amount of caffeine in chocolate is lower than most people think. You can see that there is approximately the same amount of caffeine in a regular milk chocolate bar as there is in a cup of decaffeinated coffee. Food Item Average amount of caffeine 30 g of milk chocolate (one regular bar) 6 mg 30 g of dark chocolate (one regular bar) 20 mg 250 ml (a cup) of regular coffee 110 mg 250 ml (a cup) of decaffeinated coffee 5 mg 500 ml can of Coca Cola 34 mg b) Write another comparison you can make from the table above. The Swiss consume more chocolate per capita than any other nation on Earth. That is 22.4 pounds each, compared to 11.6 pounds per person in the United States. The average person in Britain eats 8.6 kg of chocolate per year. One kg = 2.2 pounds Who eats more chocolate on average:! British people or! American people? c) Explain your answer using words or numbers. Secondary Cycle One Year One 563-212 Booklet 2 Page 3
11. Healthy Choices Colleen loves chocolate. She also wants to make healthy choices about the food she eats. Here is the Nutritional Information from the labels of a Kit Kat bar and a Fair Trade Camino bar: Serving Size: 43 g Amount per Serving % Daily Value Total Calories 210 From Fat 100 Total Fat 11g 17% Saturated Fat 7g 35% Cholesterol < 5 mg 1% Sodium 30 mg 1% Total Carbohydrate 28g 9% Dietary Fibre < 1g 3% Sugars 22g Protein 3g 6 % Iron 2% Vitamin C 0% Calcium 6% Serving Size: 40 g Amount per Serving % Daily Value Total Calories 220 From Fat 140 Total Fat 16g 25% Saturated Fat 8g 40% Cholesterol 0 mg 0% Sodium 4 mg 0% Total Carbohydrate 20g 7% Dietary Fibre 3g 12% Sugars 16g Protein 2g Iron 20% Vitamin A 0% Vitamin C 0% Calcium 2% Compare the 2 chocolate bars using the above information. Focus on nutritional facts about the chocolate bars, and make 3 comparisons. Based on your comparisons, which bar is the healthier choice, and why? The healthier choice is the! Kit Kat bar! Camino bar because: Secondary Cycle One Year One 563-212 Booklet 2 Page 4
12. Sacs of Cocoa In Ghana, Africa, cooperatives buy cocoa from farmers, and sell it to chocolate companies. When the cooperative sells the cocoa to Fair Trade companies, the farmer earns 52 per sac, instead of the 22 per sac if they are sold to a regular company. The extra income helps to feed families, to clothe and educate children, and to pay for farm expenses. On November 14, 2007, a farmer brought 5 sacs of cocoa to the cooperative. Note: The currency exchange rate on that day was 1 (1 British Pound) = $1.89 CDN (Canadian dollars). Compare the income the farmer would make on the cocoa, in Canadian dollars, if the cocoa were sold to a Fair Trade company instead of to a regular company. Show or explain how you found your answer. The farmer would make Secondary Cycle One Year One 563-212 Booklet 2 Page 5
13. Box It Up! CANADIAN CHOCOLATIERS CORPORATION recently held a design contest that resulted in their new logo The C Bar. The company also redesigned its packaging, choosing a triangular prism to box their Fair Trade chocolate in, and a rectangular prism to box its regular chocolate in. Diagrams of these boxes are shown below. The boxes cost $0.01 per 10 cm 2 to produce. Which box is more economical to make? Drawings are not to scale. 2 cm 6 cm 10 cm 5 cm 4 cm 8 cm Organize and show your work here. The! rectangular prism! triangular prism is more economical to make. Chocolate can be lethal to dogs. About two ounces of milk chocolate can be poisonous for a 10-lb (4.5 kg) puppy. Secondary Cycle One Year One 563-212 Booklet 2 Page 6
14. Ironwoman! The Ironman competition is held every fall in Hawaii. The race is composed of three endurance events of a 3.86 km ocean swim, followed by a 180 km bike ride across the Hawaiian lava desert and back, and ending with a 42 km marathon run along the coast of the island. The women s 2006 and 2007 Ironman World Champion is Montréal s Samantha McGlone. When Samantha won the 2007 Ironman, she burned 9163 calories in 7 hours! The average woman burns only 2100 calories per day! Canadian Chocolatiers Corporation is a proud sponsor of Samantha. To power her through the race, 35% of Samantha s calories were obtained by eating C Bars. The C Bars has 11 calories per 2 grams, and each bar weighs 49 grams. How many "C Bars" did Samantha eat while competing in the 2007 Hawaiian Ironman? Organize and show your work here. Samantha ate "C Bars" during the Ironman competition. Secondary Cycle One Year One 563-212 Booklet 2 Page 7
15. Chocolate at the Movies Over the last 20 years, there have been a few movies made that have chocolate as part of their title. Here are some of the movie titles, along with the amount of money the movies made at the box office in North America. Date Movie Title Box Office Gross January 2007 Blood and Chocolate $ 3 526 847 July 2005 Charlie and the Chocolate Factory $ 206 459 076 December 2000 Chocolat $ 71 509 363 February 1993 Like Water for Chocolate $ 21 665 468 Present the above information in a circle graph to compare the amount of money that the movies made at the box office. Be sure to label your graph. Show all of your work. Secondary Cycle One Year One 563-212 Booklet 2 Page 8