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Extra Practice 1

|Lesson 7.1: Choosing an Appropriate Graph |

|1. Each graph below shows the instrument choice for the 2007 Grade 8 Kitsilano Band Program. |

| |

|[pic] [pic] |

|a) List 2 things you know from the bar graph. |

|b) List 2 things you know from the circle graph. |

|c) What are some advantages and disadvantages of the bar graph? |

|d) What are some advantages and disadvantages of the circle graph? |

|e) Could you use a line graph to display this data? Explain. |

|2. Here is the enrolment data for the Grade 8 Kitsilano Band Program for 2002–2007. |

|Band Program Enrolment |

| |

|Year |

|Number of Students |

| |

|2002 |

|56 |

| |

|2003 |

|60 |

| |

|2004 |

|61 |

| |

|2005 |

|72 |

| |

|2006 |

|80 |

| |

|2007 |

|96 |

| |

| |

|a) Graph these data. Justify your choice of graph. |

|b) What other types of graph could you use to display the data? |

|c) Could you use a circle graph to display the data? Why or why not? |

Extra Practice 2

|Lesson 7.2: Misrepresenting Data |

|1. These graphs show the cost of a 25-L bottle of water from two suppliers over the past 5 years. |

| |

|[pic] [pic] |

|a) How do the graphs misrepresent the data? |

|b) What features of the graphs make it seem that the cost of a bottle of water from |

|H2O water company is lower than for Mountain Clear water company? |

|c) What features of the graphs make it seem that the cost of a bottle of water from |

|Mountain Clear water company has risen more rapidly than for H2O water company? |

|d) Which company is more likely to have created these graphs? |

|2. Here are the numbers of first place finishes for last year’s sports day at Wewonnawin Elementary. Draw a graph to show how these data can be |

|displayed in each way. |

|First Place Finishes |

| |

|House |

|Number of Firsts |

| |

|Black |

|25 |

| |

|Red |

|20 |

| |

|Green |

|18 |

| |

|Yellow |

|15 |

| |

|a) The Black house wants to show they won by a lot. |

|b) The Yellow house wants to show that each house had about the same number |

|of first place finishes. |

|c) The Green house wants to make it look like they won. |

Extra Practice 3

|Lesson 7.3: Probability of Independent Events |

|1. What is the probability of tossing two coins and having them both show heads? |

|2. Every time Mr. Coleborn throws a ball of paper in the garbage can, the probability the ball goes in the can is [pic]. What is the probability he |

|misses 2 times in a row? |

|3. A spinner has 3 congruent sectors coloured red, blue, and yellow. The pointer is spun and a |

|4-sided die labelled 1, 2, 3, and 4 is rolled. |

|a) Find the probability of each event: |

|i) Landing on red and rolling a 4. |

|ii) Landing on blue and rolling an even number. |

|iii) Not landing on yellow and rolling an odd number. |

|b) Verify your answers to part a using a tree diagram. |

|4. An experiment consists of picking a card from a standard deck of playing cards and drawing a counter from a bag that contains 5 counters: 2 blue, |

|2 white, and 1 red. |

|Find the probability of each event: |

|a) Picking a spade and drawing a blue counter. |

|b) Picking a red card and drawing a red counter. |

|c) Picking a face card and not drawing a white counter. |

|d) Picking a diamond and drawing a green counter. |

Extra Practice 4

|Lesson 7.4: Solving Problems Involving Independent Events |

|1. A regular 6-sided die is rolled three times. Find the probability of each event: |

|a) Three 6s in a row |

|b) 5, 1, even |

|c) Odd, greater than 2, 5 |

|2. Each time Parker shoots a free throw in basketball, he has an 80% chance of making the shot. |

|Suppose he is given 3 free throws. Find the probability of each event. |

|a) Makes the basket, misses the basket, makes the basket |

|b) Makes all 3 shots |

|c) Misses all 3 shots |

|d) Misses the first two shots and makes the third |

|3. Gretchen knows the combination to a bank vault lock is two letters followed by two numbers. |

|a) What is the probability that Gretchen guesses the combination on her first attempt? |

|b) Suppose she knows the combination starts with the letter M. |

|What is the probability she guesses the combination on her first attempt? |

|4. Karen, Gavin, Nasra, and Ali each have a deck of playing cards. |

|Each student randomly draws a card from the deck. Find the probability of each event: |

|a) Each student draws a club. |

|b) Karen draws a red card, Gavin draws a king, Nasra draws a black card, and Ali draws the |

|2 of clubs. |

|c) Karen draws a heart, Gavin draws a heart, Nasra draws a face card, and Ali draws an ace. |

Extra Practice Sample Answers

Extra Practice 1 – Master 7.17

Lesson 7.1

1. a) Twenty students chose the trumpet; more students chose the saxophone than the clarinet.

b) 20% of students chose the trumpet; the clarinet was the least popular choice.

c) Advantages: The bar graph lets you compare the popularity of instruments by the heights of the bars; you can find the number of students who chose each instrument by reading the height of the bar.

Disadvantages: It might be hard to determine the number of students who chose each instrument when the bar does not end on a grid line; the bar graph does not show you the percent of students who chose each instrument.

d) Advantages: The circle graph displays the percent of students in the class who chose each instrument; you can compare the popularity of different choices using the size of the sectors.

Disadvantages: The circle graph does not display the number of students who chose each instrument or how many students are in the class.

e) Line graphs are good for graphing data that change over time. Because the categories represent instruments, not time, a line graph would not make sense.

2. a) The data change over time, so a line graph is best.

[pic]

b) You could also use a bar graph or a pictograph.

c) No. There is no obvious part-to-whole relationship.

Extra Practice 2 – Master 7.18

Lesson 7.2

1. a) The graphs give the impression that it costs more to buy water from H2O water company than from Mountain Clear water company. They also seem to show that the cost of the water from H2O water company is increasing more rapidly than for Mountain Clear water company. However, the cost of a 25-L bottle of water from H2O water company in 2003 was about $38, but only about $30 from the Mountain Clear water company. Also, from 2003 to 2007, the cost of a bottle of water increased by about $10 for H2O water company, and by about $7 for Mountain Clear water company.

b) The graph of Mountain Clear water company’s costs has a vertical scale of 1 square represents $25, and the scale continues far beyond the greatest data value so the cost each year appears at the bottom of the graph. The graph of H2O water company’s costs has a vertical scale of

1 square represents $2, and the scale ends just above the greatest data value, so the most of the data appears in the top half of the graph.

c) The graph of Mountain Clear water company’s costs has a vertical scale of 1 square represents $25, and the scale continues far beyond the greatest data value so the trend lines have a very small slope. The vertical scale on the graph of H2O water company’s costs starts at $25 and ends at $40, so the difference between the data values for each year is exaggerated and the trend lines have steeper slopes.

d) Mountain Clear water company most likely made the graphs since they seem to show that the Mountain Clear water is cheaper and its costs are rising less rapidly than for H2O water company.

2. a)

[pic]

Extra Practice Sample Answers continued

b)

[pic]

c)

[pic]

Extra Practice 3 – Master 7.19

Lesson 7.3

1. [pic] × [pic] = [pic]

2. [pic] × [pic] = [pic]

3. a) i) [pic] × [pic] = [pic]

ii) [pic] × [pic]= [pic] × [pic] = [pic]

iii) [pic] × [pic] = [pic] × [pic] = [pic] = [pic]

b)

[pic]

P(red and a 4) = [pic];

P(blue and even) = [pic] = [pic];

P(not yellow and odd) = [pic] = [pic]

4. a) [pic]× [pic] = [pic] = [pic]

b) [pic] × [pic] = [pic]

c) [pic] × [pic] = [pic] × [pic] = [pic]

d) 0

Extra Practice 4 – Master 7.20

Lesson 7.4

1. a) [pic] × [pic] × [pic] = [pic]

b) [pic] × [pic] × [pic] = [pic] × [pic] × [pic] = [pic]

c) [pic] × [pic] × [pic] = [pic] × [pic] × [pic] = [pic]

2. a) 0.8 × 0.2 × 0.8 = 0.128 or 12.8%

b) 0.8 × 0.8 × 0.8 = 0.512 or 51.2%

c) 0.2 × 0.2 × 0.2 = 0.008 or 0.8%

d) 0.2 × 0.2 × 0.8 = 0.032 or 3.2%

3. a) [pic] × [pic] × [pic] × [pic] = [pic]

b) [pic] × [pic] × [pic] = [pic]

4. a) [pic] × [pic] × [pic] × [pic] = [pic]

b) [pic] × [pic] × [pic] × [pic] = [pic]

c) [pic] × [pic] × [pic] × [pic] = [pic]

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Master 7.17

Master 7.18

Master 7.19

Master 7.20

Master 7.21a

Master 7.21b

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