Download MBF 3C1 Final Exam Review

Grade 11 College Math
Final Exam Review
Trig Summary
Rule Name
Pythagorean
Theorem
Formula
side12 + side22 = hyp2
sin  
SOHCAHTOA
Sine Law
opp
hyp
cos  
Alternate Form
side12 = hyp2 – side22
side22 = hyp2 – side12
opp
adj
a
b
c


sin A sin B sin C
a  b  c  2bc cos A
2
Cosine Law
2
2
b 2  a 2  c 2  2ac cos B
c 2  a 2  b 2  2ab cos C
tan  
opp
adj
sin A sin B sin C


a
b
c
a2  b2  c2
 2bc
2
b  a2  c2
cos B 
 2ac
2
c  a2  b2
cos C 
 2ab
cos A 
Given
2 sides of a right
angle triangle
2 sides of a rightangle triangle
Use to find
The remaining side
1 side and 1 angle of
a right angle triangle
A corresponding
side-angle pair and
one other side or
angle
SAS
Any other side
Any angle
The opposite angle given
a side; the opposite side
given an angle
The side opposite the
given angle
or
SSS
Any angle
Grade 11 College Math
Final Exam Review
Summary of Quadratic Forms
Expand & Simplify
Vertex Form
y = a(x – h)2 + k


Standard Form
y = ax2 + bx + c
(Complete the Square)
Factor


Factored Form
y = a(x – r)(x – s)
FOIL
a is vertical stretch/compression factor  direction of opening
Vertex Form
Standard Form
Vertex is (h, k)
y-intercept is c
Describing transformations
Sketching the graph
Read information from a graph
Examples
pp. 146 #1, 2, 4, 5, 6
Factored Form
Roots / x-intercepts are r and s
Grade 11 College Math
Final Exam Review
One-Variable Statistics
Graph types – which one is best to show a set of data and why?
Tally Chart / Frequency Table
Histogram
Pie Graph
Pictograph
Identify data as:
Numerical / Quantitative
Continuous (decimals)  Histogram
Discrete (whole numbers)  Bar Graph, Pictogram, Pie Graph
Categorical / Qualitative  Bar graph
Definitions:
Population, Census, Sample, Biased sample
Given a scenario, describe how to take a sample using:
Random Sampling Methods
Simple Random Sampling, Stratified Sampling, Cluster Sampling,
Systematic Sampling
Other Sampling Methods
Convenience Sampling, Judgement Sampling, Voluntary Sampling
Know how to calculate and interpret:
Measures of Central Tendency: Mean
Median
Mode
Measures of Spread
Range = max – min
Standard Deviation
Probability Review
Experimental
# of times the desired outcome occurred
total # of trials
probability
n( A)
where; n(A) represents the number of
n( S )
ways that event A can occur and n(S) represents the number
of total outcomes possible for the experiment.
Theoretical Probability
P(A) =
Tree diagrams
e.g. Draw a tree diagram for flipping a quarter, loonie and toonie. What is the
probability of getting less than 2 heads?
Grade 11 College Math
Final Exam Review
Exponential Functions Review
Standard Form of Equation y = a•bx where a = starting value, b = growth/decay
factor
Growth factor 1 + r
Decay factor 1 – r
Where r is % increase/decrease
Doubling time – the time it takes for a quantity to double
Half life - the time it takes for a quantity to be cut in half
Exponent Rules
Multiplication – keep the base, add the exponents
Division – keep the base, subtract the exponents
Power of a Power – keep the base, multiply the exponents
Zero a0 = 0, 00 = undefined or ∞
1
1
Negative Exponents 4-3 = 43 = 64
Linear
Quadratic
Exponential
1
𝑎5
= 𝑎−5
1st diff. are constant, 2nd diff. are 0.
1st diff. are not equal, 2nd diff are constant
1st and 2nd diff are not equal, ratio is constant (approximately)
Investing
Simple Interest
I = Prt
where I = Total interest
P = Original principal
r = annual interest rate
t = time in years
Compound Interest
𝑨 = 𝑷(𝟏 + 𝒊)𝒏
𝑨
𝑷 = (𝟏+𝒊)𝒏
where A = Total amount
P = original principal
i = interest rate per compounding period
n = number of compounding periods
Grade 11 College Math
Final Exam Review
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Grade 11 College Math – Final Exam Review
Topic
Questions
 Trigonometry
 Trigonometry
pp. 208 – 210 #1-4
pp. 388 – 390 #1-2
 Quadratics
 Quadratics
pp. 208 – 210 #9-17
pp. 388 – 390 #6-9
 One-Variable Statistics
 One-Variable Statistics
 Probability
p. 344
#1-6
pp. 388 – 390 #24
pp. 388 – 390 #26 – 29
 Exponential Functions
 Exponential Functions
 Personal Finance
pp. 208 – 210 #18, 19ab, 20, 22-24
pp. 388 – 390 #10-13
pp. 388 – 390 #14-18
 Geometry
pp. 208 – 210 #6ab, 8