MAP4C1 College/Apprenticeship Mathematics Course Outline
Trigonometry
Lesson
Number
1
Lesson Title & Topics
Trigonometric Ratios with Acute angles
-missing side/angle
-angles of dep. and elev.
Textbook
Section
2.1
Homework
p. 80-81
#1-7, 9
2
Trig Ratios with Obtuse Angles
-Cartesian plane
-sin
-ASTC
-cosine/tangent ratios of obtuse angles
are negative (sine is pos).
2.2
p. 93-95 # 1, 3, 4, 6
3
Sine Law
2.3
p. 101-103 #1-11, 14
4
5
Cosine Law
Applications of Trig
REVIEW
2.4
2.5
p. 110-111 #1-9, 11
p. 126-128 # 1, 3-7, 9-11, 13
Problem Solving with Measurement and Geometry in Design
Lesson
Number
1
2
Lesson Title & Topics
Area
Volume
Textbook
Section
1.1
Homework
p. 11-13 #1, 2, 5-9
1.2
p. 23-24 # 1,2, 4-8, 9
-prisms
-cylinders
-spheres
3
Surface Area
1.3
p. 32-34 #1-9, *12
4
Optimize Perimeter and Area
1.4
p. 43-44 #5- 12
Analyze Optimum Volume and Surface
Area
p. 68, 69
Assignment
Graphical Models
Lesson
Number
Lesson Title & Topics
Linear Models
Textbook
Section
5.1
Homework
5.2
p. 289-293 #1, 3, 4, 6, 7, 8
5.3
p. 301-305 #4, 5, 7abe, 8abe, 9abc,
10ab
p. 276-279 #3-11
-rate of change/slope
-scatter plot/line of best fit
Quadratic Models
-finite differences
-looking at trends to determine the
graphical model (look at rates of
change near the vertex)
Exponential Models
-ratios
-growth/decay graphs
Analyse Graphical Models
p. 316-319 #3, 5-8, 10
-comparing models
-exponential rate of change effect by
initial value
How to determine the model?
p. 326-330 #5-10
-first differences close=linear
-second differences close=quadratic
-ratios close=exponential
-use r2 (close to 1)
-regressions
Test Day
REG ANALYSIS:
*make sure DIAGNOSTIC ON is activated (under CATALOG)
Enter values: STAT  EDIT enter into L1 and L2
Regression: STATCALC  4: LinReg  2nd 1  , 2nd , VARS Y-VARS 1:FUNC
5: QuadReg
0: ExpReg
Should have LinReg (ax+b) L1, L2, Y1
Algebraic Models
Lesson
Number
Lesson Title & Topics
Exponent Laws
Textbook
Section
Homework
p. 349-351 # 1, 2, 4, 5, 7, 9, 12, 13
Product, Quotient, Power, Fraction,
Power of Product, Zero Exp and Neg
Exp.
Rational Exponents
p. 359-361 # 1-9, 11, 13
-radical form
-word problems
Represent Exponential Expressions
p. 365-367 #1, 2, 4-11
-changing base
-using log
Tools and Strategies to Solve Equations
Involving Exponents
-variable as base = take nth root
-variable as exponent = trial/error or
logarithm method
p. 138 #1-4, 6-10, 12, 14
Annuities and Mortgages
Lesson
Number
Lesson Title & Topics
Annuity:
-ordinary (payments at end) VS. Annuity due (at beginning)
Textbook
Section
Homework
p. 409-411 #1-7, 9,
10, 12, 13, 16
-future value: sum of future values for each payment
*FV of first payment: n =number of payments in TOTAL (minus
1 if ordinary annuity)
-payment for an annuity: using TVM
*for regular payments N=number of payments made
-present value: sum of present values for each payment
P=A(1+i)-n where n is the number of payments made (i.e. first
payment
n =1)
Conditions of Annuity:
p. 417-419 #1-11
-you may be able to decide frequency of payments or the period
*the longer the period and/or the less frequent the payments,
the HIGHER the interest
Mortgages and Amortizations
p. 425-429 #1-5, 7-9
-mortgage (loan based on value of property), fixed/variable
rate, amortization (gradual elimination of debt), amortization
period (time for which calculation of mortgage payment is
determined), mortgage term (length of mortgage agreement,
usually 5 years), amortization table (breakdown of principal,
payments, interest paid, unpaid balance over certain timeframe)
-pay mortgage: monthly payments (C/Y is always 2 for
Canadian mortgages), ∑Prn, ∑Int
-appreciation rate
-reading amortization table
-other costs associated with buying/owning home:
Property taxes, land transfer tax, insurance, lawyer’s fees,
gas/water/electrical, telephone/tv/internet
-getting a mortgage (what determines what you can get?
APPRAISALS issue)
Conditions of a Mortgage
Semi-monthly: monthly/2 (24 times/year)
Bi-weekly: (monthly)24/52 (26 times/year)
Accelerated bi-weekly: monthly/2
(26 times/year)
Weekly: (monthly)12/52 (52 times/year)
Acc. Weekly: monthly/4 (52 times/year)
p. 434-436 #1-6, 1012
Personal Finance/Budgeting
Lesson
Number
Lesson Title & Topics
Savings Plans:
Textbook
Section
8.1
Homework
8.2
p. 458-461 #1, 2, 5-8, 10, 11
p. 451-453 #1-8, 10-12
-net earnings (take home pay)=pay
minus taxes, union fees, etc.
-saving % of earnings
-saving fixed amount (with future goal
in mind)
(i.e. how much do you need to save
each month to have $3000 after one
year?)
Cost of Renting Home:
(3, 4, 9 on spreadsheet)
-fixed expenses, utilities, lease, variable
expenses, tenant, landlord, deposits
-apartment with fixed expenses
(utilities included)
-apartment with variable expenses
-deposits (on apartment/utilities)
Cost of owning a Home:
8.3
p. 465-467 #1-8, 10, 11
8.4
p. 472-477 #1-4, 6, 7, 10, 11
-property taxes, utilities, luxuries
(cable, internet, etc), mortgage
payments, land transfer tax, incidental
costs (repairs, maintenance, etc)
-home VS. Condo (condo fees)
Living Expenses:
-budgeting
Case studies:
-group work for first two case studies,
third handed in TYPED for bonus marks
Assignment: create your own monthly
budget
(see p. 437 ex. 3)
8.5
LAB TIME
Two Variable Statistics
Lesson
Number
Lesson Title & Topics
Textbook Section
Homework
Two Variable Data Sets:
3.1
p. 146-151 #1-10
3.2
p. 156-159 #1-11,
*13 (marked)
3.3
p. 165-167 #1-7, *12
(group assignment)
-one variable VS. two variable (one attribute is known VS.
two)
-categorical variables
-relationships between variables
-drawing graphs: bar, scatter plots (for two variables)
Effective Surveys:
-principles of proper surveying: ethics, design for honest
responses, eliminate bias
* ways a survey can be biased: unrepresentative, wording,
interpretation/presentation of results
-types of questions: dichotomous, multiple choices, rating
scales, completion, open-ended
Collection and Organize Data:
-primary VS. secondary data
Stats Canada
questions (9,10) LAB?
*why is it better to use primary data?
-outlier (can be removed)
-keeping data accurate and fair: plan and set up in advance,
record results with recording sheet, random sampling, do
everything the same each time
The Line of Best Fit (Linear Regression):
3.4
p. 175-179 # 1-11
3.5
p. 186-189 #1-6, *8,
*9
-correlation coefficient (r): closer +1/-1 (sign tells us
whether it is pos/neg correlation)
If r = 0 (horizontal line, no relationship exists)
r between 0 and 0.5 = weak correlation
r = 0.5 moderate correlation
r between 0.5 and 1 =strong correlation
*does NOT tell us whether a relationship exists between
two variables
-extrapolation using model
-finding model using technology or algebra
Analysis + Conclusions
-cause and effect relationship VS. Correlation (two variables
may be related somehow but we cannot say which is cause
and which is effect or whether some hidden variable is
responsible)
-influential point (same trend, increases slope but doesn’t
reduce r2) and outlier (far away from main data but not
necessarily same trend)
-analysis errors: not enough data, linear regression for nonlinear relation, reversing the cause and effect relationship,
extrapolations, not considering effects of outliers or
influential points)
Apply Data Management
Lesson
Number
Lesson Title & Topics
Textbook Section
Homework
Statistical Measures:
4.1
p. 205-211 #1-9,
11
4.2
p. 219-225 #2-9,
11
4.3
p. 231-235 #1-10
4.4
p. 239-245 #1-13
4.5
p. 251-255 #1-4. 613
-per capita (used to make comparisons)
-percentage change (change in value over time) =
𝑁𝑒𝑤 𝑣𝑎𝑙𝑢𝑒 − 𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒
× 100
𝑜𝑙𝑑 𝑣𝑎𝑙𝑢𝑒
-percentile rank (percent of values less than or equal to a
particular value)
𝑝=(
𝐿+0.5𝐸
𝑛
) × 100
L=# of scores LESS than the score
E=# of scores EQUAL to the score
n=total number of scores
*finding score given percentile rank: use nxp, if it is a whole
number, take mean of nxp and (nxp)+1, if it is a decimal,
round UP.
-weighted mean =
𝑠𝑢𝑚 𝑜𝑓 (𝑣𝑎𝑙𝑢𝑒)(𝑤𝑒𝑖𝑔ℎ𝑡 𝑓𝑎𝑐𝑡𝑜𝑟)
𝑠𝑢𝑚 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑓𝑎𝑐𝑡𝑜𝑟𝑠
-net worth=
total assets(wealth) - total liabilities (debt)
Statistical Indices:
-weighted mean used to show change over time
-quantify trends
-consumer prices, human development, etc.
Interpret Statistics in Media:
-how does media manipulate stats
-media doesn’t explain data in graphs =what happened in
economy, population size, etc
-percentage points = 4.5% 19 times out of 20
Statistical Bias:
-external influences that may affect accuracy of stats
-types of bias: sampling, non-response, measurement
(measurement technique has errors), response
Critical Analysis:
-descriptive statistics
-inferential statistics
-when analysing study, look at sample, author, source,
relevance, bias
Assignment: analyze advertisement/study