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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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