Mathematics Examination — 563-212

Secondary Cycle One Year OneJune 2008

Student Booklet 2

Competency 2 and Competency 3 SituationsCalculator allowed

Name : Group :

June 2008

Time : __ minutes

The following criteria will be used to evaluate your level of competency

development in the different situations presented in this booklet.

Evaluation CriteriaUses 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 CriteriaCommunicates 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.

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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 Weightin 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

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 11.1Basketball 7.5 8.8 10.0 11.3Hiking 4.5 5.2 6.0 6.7Jogging 9.3 10.8 12.4 13.9Running 11.4 13.2 15.1 17.0Watching TV 1.2 1.3 1.5 1.7Walking 6.5 7.6 8.7 9.7Weight Training 6.6 7.6 8.7 9.8

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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.

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 amountof caffeine

30 g of milk chocolate (one regular bar) 6 mg30 g of dark chocolate (one regular bar) 20 mg250 ml (a cup) of regular coffee 110 mg250 ml (a cup) of decaffeinated coffee 5 mg500 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.

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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:

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:

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

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Serving Size: 43 gAmount per Serving % Daily Value

Total Calories 210From Fat 100Total Fat 11g 17%

Saturated Fat 7g 35%Cholesterol 5 mg 1%

Sodium 30 mg 1%Total Carbohydrate 28g 9%

Dietary Fibre 1g 3%Sugars 22gProtein 3g 6 %

Iron 2%

Vitamin C 0%Calcium 6%

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).

Show or explain how you found your answer.

The farmer would make

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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 cm2 to produce.

Which box is more economical to make?Drawings are not to scale.

Organize and show your work here.

The rectangular prism triangular prism is more economical to make.

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Chocolate can be lethal to dogs. About two ounces of milk chocolate can be poisonous for a 10-lb (4.5 kg) puppy.

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.

Organize and show your work here.

Samantha ate _________________ "C Bars" during the Ironman competition.

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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 GrossJanuary 2007 Blood and Chocolate $ 3 526 847July 2005 Charlie and the Chocolate Factory $ 206 459 076December 2000 Chocolat $ 71 509 363February 1993 Like Water for Chocolate $ 21 665 468

Show all of your work.

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