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# Mathematics - McGraw-Hill Ryerson Mathematics of Data Management...

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Mathematics - McGraw-Hill Ryerson Mathematics of Data Management Grade 12

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Tools for Data Management

Speciﬁc Expectations Section

Locate data to answer questions of signiﬁcance or personal interest, by

searching well-organized databases.

Use the Internet effectively as a source for databases.

Create database or spreadsheet templates that facilitate the manipulation

and retrieval of data from large bodies of information that have a variety

of characteristics.

Represent simple iterative processes, using diagrams that involve

branches and loops.

Represent complex tasks or issues, using diagrams.

Solve network problems, using introductory graph theory.

Represent numerical data, using matrices, and demonstrate an

understanding of terminology and notation related to matrices.

Demonstrate proﬁciency in matrix operations, including addition, scalar

multiplication, matrix multiplication, the calculation of row sums, and the

calculation of column sums, as necessary to solve problems, with and

without the aid of technology.

Solve problems drawn from a variety of applications, using matrix

methods.

C

H

A

P

T

E

R

1

C

H

A

P

T

E

R

1

1.3

1.3

1.2, 1.3, 1.4

1.1

1.1, 1.5

1.5

1.6, 1.7

1.6, 1.7

1.6, 1.7

VIA Rail Routes

When travelling by bus, train, or airplane,

you usually want to reach your destination

without any stops or transfers. However,

it is not always possible to reach your

destination by a non-stop route. The

following map shows the VIA Rail routes

for eight major cities. The arrows

represent routes on which you do not have

to change trains.

1. a) List several routes you have

travelled where you were able to

reach your destination directly.

b) List a route where you had to

change vehicles exactly once before

reaching your destination.

2. a) List all the possible routes from

Montréal to Toronto by VIA Rail.

b) Which route would you take to get

from Montréal to Toronto in the

least amount of time? Explain your

reasoning.

3. a) List all the possible routes from

Kingston to London.

b) Give a possible reason why VIA Rail

chooses not to have a direct train

from Kingston to London.

This chapter introduces graph theory,

matrices, and technology that you can use

to model networks like the one shown. You

will learn techniques for determining the

number of direct and indirect routes from

one city to another. The chapter also

discusses useful data-management tools

including iterative processes, databases,

software, and simulations.

Chapter Problem

Toronto

Montréal

Kingston

Ottawa

Sudbury

Niagara Falls

London

Windsor

4

MHR • Tools for Data Management

Review of Prerequisite Skills

If you need help with any of the skills listed in purple below, refer to Appendix A.

1. Order of operations Evaluate each

expression.

a) (−4)(5) + (2)(−3)

b) (−2)(3) + (5)(−3) + (8)(7)

c) (1)(0) + (1)(1) + (0)(0) + (0)(1)

d) (2)(4) +

1

3

2

− (3)

2

2. Substituting into equations Given

f (x) = 3x

2

− 5x + 2 and g(x) = 2x − 1,

evaluate each expression.

a) f (2)

b) g(2)

c) f (g(−1))

d) f ( g(1))

e) f ( f (2))

f) g( f (2))

3. Solving equations Solve for x.

a) 2x − 3 = 7

b) 5x + 2 =−8

c) − 5 = 5

d) 4x − 3 = 2x − 1

e) x

2

= 25

f) x

3

= 125

g) 3(x + 1) = 2(x − 1)

h) =

4. Graphing data In a sample of 1000

Canadians, 46% have type O blood, 43%

have type A, 8% have type B, and 3% have

type AB. Represent these data with a fully-

labelled circle graph.

5. Graphing data Organize the following set of

data using a fully-labelled double-bar graph.

6. Graphing data The following table lists the

average annual full-time earnings for males

and females. Illustrate these data using a

fully-labelled double-line graph.

3x − 1

4

2x − 5

2

x

2

City Snowfall (cm) Total Precipitation (cm)

St. John’s 322.1 148.2

Charlottetown 338.7 120.1

Halifax 261.4 147.4

Fredericton 294.5 113.1

Québec City 337.0 120.8

Montréal 214.2 94.0

Ottawa 221.5 91.1

Toronto 135.0 81.9

Winnipeg 114.8 50.4

Regina 107.4 36.4

Edmonton 129.6 46.1

Calgary 135.4 39.9

Vancouver 54.9 116.7

Victoria 46.9 85.8

Whitehorse 145.2 26.9

Yellowknife 143.9 26.7

Year Women ($) Men ($)

1989 28 219 42 767

1990 29 050 42 913

1991 29 654 42 575

1992 30 903 42 984

1993 30 466 42 161

1994 30 274 43 362

1995 30 959 42 338

1996 30 606 41 897

1997 30 484 43 804

1998 32 553 45 070

5

Review of Prerequisite Skills • MHR

7. Using spreadsheets Refer to the spreadsheet

section of Appendix B, if necessary.

a) Describe how to refer to a speciﬁc cell.

b) Describe how to refer to a range of cells

in the same row.

c) Describe how to copy data into another

cell.

d) Describe how to move data from one

column to another.

e) Describe how to expand the width of a

column.

f) Describe how to add another column.

g) What symbol must precede a

mathematical expression?

8. Similar triangles Determine which of the

following triangles are similar. Explain

your reasoning.

9. Number patterns Describe each of the

following patterns. Show the next three

terms.

a) 65, 62, 59, …

b) 100, 50, 25, …

c) 1, − , , − , …

d) a, b, aa, bb, aaa, bbbb, aaaa, bbbbbbbb, …

10. Ratios of areas Draw two squares on a sheet

of grid paper, making the dimensions of the

second square half those of the ﬁrst.

a) Use algebra to calculate the ratio of the

areas of the two squares.

b) Conﬁrm this ratio by counting the

number of grid units contained in each

square.

c) If you have access to The Geometer’s

Sketchpad or similar software, conﬁrm

the area ratio by drawing a square,

dilating it by a factor of 0.5, and

measuring the areas of the two squares.

Refer to the help menu in the software,

if necessary.

11. Simplifying expressions Expand and simplify

each expression.

a) (x – 1)

2

b) (2x + 1)(x – 4)

c) –5x(x – 2y)

d) 3x(x – y)

2

e) (x – y)(3x)

2

f) (a + b)(c – d)

12. Fractions, percents, decimals Express as a

decimal.

a)

2

5

0

b)

2

5

3

0

c)

2

3

d)

1

1

3

2

8

e)

6

7

f) 73%

13. Fractions, percents, decimals Express as a

percent.

a) 0.46 b)

4

5

c)

3

1

0

d) 2.25 e)

1

8

1

1

8

1

4

1

2

B

A

C

4

3

2

E

D

F

7

6

4

H

G

J

9

6

12

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