Canton - Mathematics of Data Management v.2 [intro] (McGraw, 2002).pdf

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Tools for Data Management
Specific Expectations
Section
1.3
Locate data to answer questions of significance or personal interest, by
searching well-organized databases.
1.3
Use the Internet effectively as a source for databases.
1.2, 1.3, 1.4
Create database or spreadsheet templates that facilitate the manipulation
and retrieval of data from large bodies of information that have a variety
of characteristics.
1.1
Represent simple iterative processes, using diagrams that involve
branches and loops.
1.1, 1.5
Represent complex tasks or issues, using diagrams.
1.5
Solve network problems, using introductory graph theory.
1.6, 1.7
Represent numerical data, using matrices, and demonstrate an
understanding of terminology and notation related to matrices.
1.6, 1.7
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.
1.6, 1.7
Solve problems drawn from a variety of applications, using matrix
methods.
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Chapter Problem
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.
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.
Montréal
Sudbury
Ottawa
Kingston
Toronto
London
Niagara Falls
Windsor
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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) (
5. Graphing data Organize the following set of
data using a fully-labelled double-bar graph.
4)(5)
(2)(
3)
City
Snowfall (cm) Total Precipitation (cm)
St. John’s
322.1
148.2
b) (
2)(3)
(5)(
3)
(8)(7)
Charlottetown
338.7
120.1
c) (1)(0)
(1)(1)
(0)(0)
(0)(1)
Halifax
261.4
147.4
1
3
2
−
d) (2)(4)
+
(3) 2
Fredericton
294.5
113.1
Québec City
337.0
120.8
Montréal
214.2
94.0
2. Substituting into equations Given
f ( x )
Ottawa
221.5
91.1
3 x 2
5 x
2 and g ( x )
2 x
1,
Toronto
135.0
81.9
evaluate each expression.
a) f (2)
b) g (2)
c) f ( g (
Winnipeg
114.8
50.4
Regina
107.4
36.4
Edmonton
129.6
46.1
1))
d) f ( g (1))
e) f ( f (2))
f) g ( f (2))
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
3. Solving equations Solve for x .
a) 2 x
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.
3
7
b) 5 x
2
= −
8
x
2
5
5
c)
Year
Women ($)
Men ($)
d) 4 x
3
2 x
1
1989
28 219
42 767
e) x 2
25
1990
29 050
42 913
f) x 3
125
1991
29 654
42 575
g) 3( x
1)
2( x
1)
1992
30 903
42 984
5
2
2 x
1
4
3 x
1993
30 466
42 161
h)
1994
30 274
43 362
1995
30 959
42 338
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.
1996
30 606
41 897
1997
30 484
43 804
1998
32 553
45 070
4
MHR • Tools for Data Management
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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?
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.
8. Similar triangles Determine which of the
following triangles are similar. Explain
your reasoning.
11. Simplifying expressions Expand and simplify
each expression.
a) ( x – 1) 2
b) (2 x
D
1)( x – 4)
c) –5 x ( x – 2 y )
d) 3 x ( x – y ) 2
e) ( x – y )(3 x ) 2
f) ( a
3
B
A
7
2
4
4
C
E
F
6
G
b )( c – d )
12
6
12. Fractions, percents, decimals Express as a
decimal.
J
9
H
5
0
2
5
3
0
2
3
2
a)
b)
c)
9. Number patterns Describe each of the
following patterns. Show the next three
terms.
a) 65, 62, 59, …
b) 100, 50, 25, …
1
1
3
2
8
6
7
f) 73%
d)
e)
13. Fractions, percents, decimals Express as a
percent.
4
5
1
0
1
2
1
4
1
8
a) 0.46
3
c) 1,
,
,
, …
b)
c)
1
8
1
d) a, b, aa, bb, aaa, bbbb, aaaa, bbbbbbbb, …
d) 2.25
e)
5
Review of Prerequisite Skills • MHR
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