A SWIMMING RACE. Barbara. Ann. Carol. Who was the winner? How long did the winner take to swim the 50 meter race?

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Vincent Blaze Green
5 years ago
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1 A SWIMMING RACE This problem gives you the chance to: describe a race, given a distance - time graph Ann, Barbara and Carol decide to have a race in the swimming pool. This graph shows what happened during the 50 meter race. The lines Ann, Barbara, and Carol show the distances from the starting point of the thre e swimmers at different times during the race. Distance in metres 50 Carol Ann Barbara Time in seconds (a) Who was the winner? (b) How long did the winner take to swim the 50 meter race? MARS 1999 page 1 A Swimming Race: Grade 9

2 Imagine you are the race commentator. Describe what is happening to each of the competitors during each stage of the race. (c) Stage One: 0-15 seconds (d) Stage Two: seconds (e) Stage Three: seconds MARS 1999 page 2 A Swimming Race: Grade 9

3 CALENDAR PATTERNS This problem gives you the chance to: investigate number patterns on a calendar check and prove rules M A Y Sun Mon Tue Wed Thu Fri Sat After Bill had investigated the number patterns in this calendar, he wrote the following summary of his findings. If you take any block of four numbers, like: 4 5 or I think the following rules work Rule 1 If you add the pairs of numbers in the opposite corners of a block, you get the same answer = 16 and = = = 40 Rule 2 If you add all four numbers, the answer is always a multiple of = 32 and = = 4 x 8 80 = 10 x 8 Rule 3 If you multiply the pairs of numbers in the opposite corners of a block, the two answers differ by 7. 4 x 12 = 48 and 16 x 24 = x 11 = x 23 = is 7 more than is 7 more than 384 MARS 1999 page 3 A Swimming Race: Grade 9

4 In the space below, test each rule separately. Is each rule always true? If it is always true, how can you prove it? Use words and algebra in your explanations. Rule 1 Rule 2 Rule 3 MARS 1999 page 4 A Swimming Race: Grade 9

FUN SIZE CAN This problem gives you the chance to: design cylindrical cans to hold a given amount find the dimensions which give the least surface area r FUN SIZE DRINK h

The drink will be sold in a `Fun Size cylindrical can which holds 200 cm 3. Here are two suggestions for the radius of the cylindrical can.

5 FUN SIZE CAN This problem gives you the chance to: design cylindrical cans to hold a given amount find the dimensions which give the least surface area r FUN SIZE DRINK h The volume of a cylinder is V = pr 2 h The surface area of a cylinder is S = 2pr 2 + 2prh The Fresha Drink Company is marketing a new soft drink. The drink will be sold in a `Fun Size cylindrical can which holds 200 cm 3. Here are two suggestions for the radius of the cylindrical can. I'm designing a can with radius 2 cm. My can has a radius of 5 cm. (a) Each of these cans holds 200 cm 3. Find the heights of these two cans. Are their dimensions suitable? Explain why. MARS 1999 page 5 A Swimming Race: Grade 9

6 (b) Find the surface area of the two cans. In order to keep costs low, the Company wants to sell the drink in cylindrical cans whic h use the smallest amount of aluminum. Find the radius and height of a can which holds 200 cm 3 and uses the smallest amount of aluminum. Show clearly how you figured it out. Make your dimensions correct to the nearest 0.1 centimeter. MARS 1999 page 6 A Swimming Race: Grade 9

7 HOMEWORK, TV and SLEEP The aim of this assessment is to provide the opportunity for you to: analyze data on a scattergraph; investigate positive, negative, and zero correlation. Annie asked a group of teenagers to say how much time they spent doing homework o ne evening and how much time they spent watching TV. Here is a scattergraph to show the results: 3 Number of hours spent doing homework A D B C Number of hours spent watching TV MARS 1999 page 7 A Swimming Race: Grade 9

1. Which of the four points A, B, C or D represents each of the statemen ts shown

I watched a lot of TV last night and I also did a lot of homework.

I went out last night. I didn't do much homework or watch much TV.

8 1. Which of the four points A, B, C or D represents each of the statemen ts shown below? Write one letter next to each statement. I watched a lot of TV last night and I also did a lot of homework. I spent most of my evening doing homework. I only watched one program on TV. I went out last night. I didn't do much homework or watch much TV. This is represented by point... This is represented by point... This is represented by point Make up a statement which matches the fourth point. 3. What does the graph tell you about the relationship between time spent watching TV and time spent doing homework? MARS 1999 page 8 A Swimming Race: Grade 9

9 4. Annie also drew scattergraphs which showed that : Older students tend to spend more time doing homework than younger students. There is no relationship between the time students spend watching TV and the time stu dents spend sleeping. On the axes below, show what Annie's scattergraphs may have looked like Hours spent doing homework Hours spent sleeping Age of student (years) Hours spent watching TV MARS 1999 page 9 A Swimming Race: Grade 9

10 HOUSE OF CARDS John builds a house of cards. It is three storeys high. These diagrams show how he builds a house of cards with different heights. height 1 height 2 height 3 height 4 John begins to make a table to show how many cards he needs to make a house of card s with different heights. height number of cards needed Count the number of cards needed for a house of cards with height 4. Write this number in John's table MARS 1999 page 10 A Swimming Race: Grade 9

11 2. Draw a house of cards with height 5. Count the number of cards needed and write this number in John's table. 3. Comment about how the number of cards needed increases. 4. Without drawing, how many cards do you think are needed to make a house of card s with height 6? Explain your reasons. 5. Try to write down a rule or a formula that will help you to find the number of cards n eeded to make a house of cards with any height. MARS 1999 page 11 A Swimming Race: Grade 9

TEST 6. 12, 7, 15, 4, 1, 10, Circle all the odd numbers.

TEST 6. 12, 7, 15, 4, 1, 10, Circle all the odd numbers. TEST 6. Complete the picture so that it has 7 dots. 2. What is the number shown? 0 5 0. Fill in the missing numbers. 2 + = 4 = (c) + 4 = (d) 4 + = 9 (e) 8 = (f) + 7 = 7 4. Write these numbers in order