Review • MHR 95

In document IB grade 9 Math book-Chapter2 (Page 58-61)

Chapter 2 Review

2.1 Hypotheses and Sources of Data, pages 42⫺47

1. State a hypothesis about a relationship between each pair of variables. Then, state the opposite hypothesis.

a) the temperature in a town during the summer and the volume of water used by the town’s residents

b) a person’s height and marks in mathematics 2. State whether each data source is primary or secondary. Then, discuss whether the source is a good choice.

a) To determine the number of each size of school uniform to buy, a principal surveyed 200 of the school’s students by telephone.

b) To check trends in house prices across Canada, a real-estate agent found a database on the Internet.

c) To find data on the sizes of bears in British Columbia, a student used an encyclopedia.

d) To choose music for a school dance, the dance committee checked a list of the top-selling CDs in Canada in a music magazine.

2.2 Sampling Principles, pages 48⫺55

3. You want to survey students’ opinions about the extracurricular activities at your school.

a) Identify the population.

b) Describe how you could use a stratified random sample for your survey.

4. An airline wants to determine how its passengers feel about paying extra for in-flight meals.

a) Identify the population.

b) Describe how the airline could use a systematic random sample for its survey.

5. Identify the population in each situation and describe the sampling technique you would use.

a) A department store wishes to know how far away its customers live.

b) The Ontario government wants to find out the incomes of people who camp in provincial parks.

c) Your school librarian needs to find out how to improve lunchtime services for students.

2.3 Use Scatter Plots to Analyse Data, pages 56⫺67

6. This table shows the heights and shoe sizes of ten grade-9 boys.

a) Make a scatter plot of the data.

b) Describe the relationship between a student’s height and shoe size.

c) Identify any outliers. Should you discard the outliers? Explain.

Height (cm) Shoe Size

157 7

7. This table shows the length of ten ferries and the number of cars each one can carry.

a) Make a scatter plot of the data.

b) Describe the

relationship between the length of a ferry and its capacity.

c) Identify any outliers.

What could cause these outliers?

2.4 Trends, Interpolation, and Extrapolation, pages 68⫺76

8. This table shows the population of Canada from 1861 to 2001.

a) Make a scatter plot of the data.

b) Describe the trend in the population.

9. This table lists the winning heights in the high jump for men and women at the Olympics from 1928 to 2004.

a) Graph the data. Use one colour for the men’s data and another for the women’s data.

b) Compare the trends in the men’s and women’s results.

c) Identify any outliers.

d) Predict the winning heights in the men’s and women’s high jump at the 2012 Olympics. Explain your reasoning.

Year Men (m) Women (m)

Winning Heights in Olympic High Jump Length

Time (days) Height (cm) 2.5 Linear and Non-Linear Relations,

pages 77⫺87

10. Graph each set of points on a grid. Then, draw a line of best fit. Is a line of best fit a good model for each set of data? Explain.

a) b)

11. Two ships are travelling on parallel courses that are 10 km apart. This table shows the distance between the two ships over a 12-h period.

a) Make a scatter plot of the data.

b) Describe the

relationship and draw a line of best fit.

c) Identify any outliers.

d) Estimate when the ships will be closest to each other.

2.6 Distance-Time Graphs, pages 88⫺94 12. Describe a situation that corresponds to

each distance-time graph.

a)

b)

c)

13. Draw a distance-time graph to represent each situation.

a) A worker with a wheelbarrow filled with bricks starts at a point 50 m from the entrance to a construction site. The worker pushes the wheelbarrow away from the entrance at a speed of 1 m/s for 10 s, stops for 5 s to unload, and then moves back toward the entrance at a speed of 2 m/s for 20 s.

b) A stone dropped from a height of 10 m steadily increases in speed until it hits the ground after about 1.4 s.

d

Time

For questions 1 to 4, select the best answer.

1. Which of the following is a primary data source?

A finding a list of the year’s top-grossing films in the newspaper

B having 20 of your friends ask their family members for their favourite colour C getting information on the world’s

longest rivers from an atlas

D using the Internet to find the results of the latest Paralympic Games

2. Which of the following is not an example of random sampling?

A using a random-number generator to select 10% of the players in each division of a provincial soccer league B selecting every 10th person on a list,

beginning with the name corresponding to a randomly generated number between 1 and 10, inclusive

C standing on a street corner and asking every 10th person who goes by for their opinions

D writing names on slips of paper and picking 10% of the slips out of a box after shaking the box thoroughly 3. Estimating values beyond the known data

for a relation is A extrapolation B interpolation C a line of best fit D discarding outliers

4. The final step in an experiment is the A procedure

B conclusion C evaluation D hypothesis

Short Response

Show all steps to your solutions.

5. Write the opposite of each hypothesis.

a) Caffeine can affect your sleep.

b) The more you study, the worse you do on tests.

c) At least half of the students in your school have a part-time job.

d) Cell phone use has more than doubled in the past 2 years.

6. A school board wishes to survey a representative sample of its teachers.

a) Identify the population.

b) Describe a suitable stratified random sample for this survey.

c) Describe a suitable systematic random sample.

d) Give an example of a non-random sample.

e) Explain why the non-random sample might not be representative of the population.

7. Make a scatter plot of each set of data. Draw a line or curve of best fit. State whether each scatter plot shows a linear or non-linear relationship. Justify your answer.

a) b)

In document IB grade 9 Math book-Chapter2 (Page 58-61)

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