Download Math 11 Advanced

Math 11 Advanced – MAD11
Course Outline
APPLIED TRIGONOMETRY (CHAPTER 6)
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Right angle triangles and their applications (trig ratios sin, cos, tan and
Pythagorean theorem)
Area and perimeter of a triangle
Azimuths
Law of Sines and law of Cosines (including the ambiguous case)
SINUSOIDAL FUNCTIONS (CHAPTER 3)
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3.
Periodic vs. Sinusoidal functions
Transformations on Sine curves (horizontal and vertical translation, horizontal
and vertical stretch)
Graphing and analyzing Sine curves (sinusoidal axis, amplitude, period)
Finding equations from sine graphs
TRIGONOMETRIC EQUATIONS AND IDENTITIES (CHAPTER 4)
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4.
Quadrants, positive and negative rotations, co-terminal angles
Special angles, 0˚, 30˚, 34˚, 60˚, 90˚ and their multiples in other quadrants
Trig Identities
Radian measure
SOLVING SYSTEMS OF EQUATIONS (CHAPTER 1)
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5.
Solving systems of [3x3] equations using substitution, elimination, Gaussian
elimination (row operations) and inverse matrices [2x2 only]
Matrix operations, addition, subtraction, multiplication
Applications using systems of equations
3D graphing and drawing
STATISTICS (CHAPTER 5)
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Different types of sampling
Drawing inferences and conclusions from data
Abuses of statistics
Binomial experiments, yes/no surveys
Populations and samples
90% and 95% box plots with applications
Normal distributions
Using confidence intervals
Math 11 Advanced – MAD11
General Curriculum Outcomes
Students in Mathematics 11 Advanced will explore the following subjects:
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Visualize planes in three dimensions: finding equations in 3-spaces
Solving systems of equations: relating the algebra and geometry: system
applications
Exploring and deriving properties of matrices: Using matrices to solve system
Research, present and learn mathematics independently
Periodic behavior: transformations and sinusoidal functions
Circular trigonometric identities: radian measure
Area of triangle: development and application of law of sines and cosines
Sampling and sampling variability: binomial experiments and yes/no surveys
Binomial distributions: 90% box plots and sampling distributions
Confidence intervals: hypothesis testing and the Chi-square test
Math 11 Advanced – MAD11
Course Units and Outcomes
CHAPTER ONE: INVESTIGATING EQUATIONS IN 3-SPACE
1.1 Solving Systems of Equations Involving Two Variables
B15 solve systems of “m” equations in “n” variables with and without technology
C12 interpret geometrically the relationships between equations in systems
C19 solve problems involving systems of equations
1.2 Visualization in Three Dimensions
C8 demonstrate an understanding of real-world relationships by translating between
graphs, tables, and written descriptions
C12 interpret geometrically the relationships between equations in systems
C13 demonstrate an understanding that an equation in three variables describes a
plane
E1 demonstrate an understanding of the position of axes in 3-space
E2 locate and identify points and planes in 3-space
1.3 Solving Systems of Equations Involving two or Three Variables
B15 solve systems of “m” equations in “n” variables with and without technology
C14 demonstrate an understanding of the relationships between equivalent systems of
equations
C19 solve problems involving systems of equations
1.4 Solving Systems of Equations Using Matrices
Bx
A4
develop, analyse and apply procedures for matrix multiplication (new)
demonstrate an understanding of the conditions under which matrices have
identities and inverses
A5 demonstrate an understanding of properties of matrices and apply them
B2 demonstrate an understanding of the relationship between operations on algebraic
and matrix equations
B4 use the calculator correctly and efficiently
B11 develop and apply the procedure to obtain the inverse of a matrix
B12 Adv derive and apply the procedure to obtain the inverse of a matrix
B13 solve systems of equations using inverse matrices
B15 solve systems of “m” equations in “n” variables with and without technology
C19 solve problems involving systems of equations
1.5 Using Equations for Predicting
B4
use the calculator correctly and efficiently
B14 Adv determine the equation of a plane given three points on the plane
B15 solve systems of “m” equations in “n” variables with and without technology
C5 determine quadratic functions using systems of equations
C8 demonstrate an understanding of real-world relationships by translating between
graphs, tables, and written descriptions
C19 solve problems involving systems of equations
CHAPTER TWO: MATHEMATICS—CHECK IT OUT!
2.1 The Investigative Process
I1
I2
I3
demonstrate an understanding of a mathematical topic through independent
research
communicate the result of the independent research
demonstrate an understanding of the mathematical topics presented by other
students
2.2 Choosing a Topic and Planning the Process
I1
demonstrate an understanding of a mathematical topic through independent
research
2.3 The Final Product and Presentation
I2
I3
communicate the results of the independent research
demonstrate an understanding of the mathematical topics presented by other
students
CHAPTER THREE: SINUSOIDAL FUNCTIONS
3.1 Periodic Behaviour
C8 demonstrate an understanding of real-world relationships by translating between
graphs, tables, and written descriptions
C23 identify periodic relations and describe their characteristics
3.2 Transformations and Sinusoidal Functions
B5
C1
C2
C3
C9
analyse and apply the graphs of the sine and cosine functions
model situations with sinusoidal functions
create and analyze scatter plots of periodic data
determine the equations of sinusoidal functions
analyze tables and graphs of various sine and cosine functions to find patterns,
identify characteristics, and determine equations
C21 describe how various changes in the parameters of sinusoidal equations affect
their graphs
CHAPTER FOUR: TRIGONOMETRIC EQUATIONS
4.1 Trigonometric Equations
A1
B4
B5
C1
C9
C15
C18
C27
C28
demonstrate an understanding of irrational numbers in applications
use the calculator correctly and efficiently
analyse and apply the graphs of the sine and cosine functions
model situations with sinusoidal functions
analyse tables and graphs of various sine and cosine functions to find patterns,
identify characteristics, and determine equations
demonstrate an understanding of sine and cosine ratios and functions for nonacute angles
Interpolate and extrapolate to solve problems
apply function notation to trigonometric equations
analyse and solve trigonometric equations with and without technology
4.2 Trigonometric Identities
A1
B1
B4
C9
C24
C25
C28
demonstrate an understanding of irrational numbers in applications
demonstrate an understanding of the relationship between operations on fractions
and rational algebraic expressions
use the calculator correctly and efficiently
analyse tables and graphs of various sine and cosine functions to find patterns,
identify characteristics, and determine equations
derive and apply the reciprocal and Pythagorean identities
prove trigonometric identities
analyse and solve trigonometric equations with and without technology
4.3 Radian Measure
A1
B4
demonstrate an understanding of irrational numbers in applications
use the calculator correctly and efficiently
C4 Adv determine the equations of sinusoidal functions expressed in radians
C10 Adv analyse tables and graphs of various sine and cosine functions to find
patterns, identify characteristics, and determine equations using radians
C16 Adv demonstrate an understanding of sine and cosine ratios and functions for nonacute angles expressed in radians
C17 Adv solve problems by determining the equation for the curve of best fit using
sinusoidal regression
C22 Adv describe how various changes in the parameters of sinusoidal equations,
expressed in radians, affect their graphs
C29 Adv analyse and solve trigonometric equations with and without technology,
expressing the solution in radians
D1 derive, analyse, and apply angle and arc length relationships
D2 demonstrate an understanding of the connection between degree and radian
measure and apply them
CHAPTER FIVE: STATISTIC
5.1 Descriptive Statistics
A3
demonstrate an understanding of the application of random numbers to statistical
sampling
F8 apply characteristics of normal distributions
F9 demonstrate an understanding of the difference between sample standard
population deviation and population standard deviation
F10 interpret and apply histograms
F15 design and conduct surveys and/or simulate data collection to explore sampling
variability
5.2 Inferential Statistics
F2 identify bias in data collection, interpretation, and presentation
FX distinguish between descriptive and inferential statistics
FX2 demonstrate an understanding of the differences in the quality of sampling
methods
5.3 Inferential Statistics and Normal Distribution
A3
F1
F2
F4
F7
F8
F11
F15
FY
FY2
FY3
demonstrate an understanding of the application of random numbers to statistical
sampling
draw inferences about a population from a sample
Identify bias in data collection, interpretation, and presentation
demonstrate an understanding of the differences in the quality of sampling
draw inferences from graphs, tables, and reports
apply characteristics of normal distributions
determine, interpret, and apply confidence
design and conduct surveys and simulate data collection to explore sampling
variability
demonstrate an understanding of how the confidence levels affects the confidence
interval
demonstrate an understanding of the role of the central limit theorem in the
development of confidence intervals
distinguish between the calculation of confidence intervals for a known population
mean versus an unknown population mean
G3 graph and interpret sample distributions of the sample mean and sample
distributions of the sample proportion
5.4 Inferential Statistics and Binomial Experiments
A3
demonstrate an understanding of the application of random numbers to statistical
sampling
F1 draw inferences about a population from a sample
F2 Identify bias in a collection, interpretation, and presentation
F4 demonstrate an understanding of how the size of a sample affects the variation in
sample results
F7 draw inferences from graphs, tables
F8 apply characteristics of normal distributions
F11 determine, interpret, and apply confidence intervals
F15 design and conduct surveys and simulate data collection to explore sampling
variability
F16 demonstrate an understanding of the difference between situations involving
binomial experiments and those which do not
FY Adv demonstrate an understanding of how confidence levels affects the confidence
interval
FY4 Adv distinguish between the calculation of confidence intervals for a known
population proportion versus an unknown population proportion
FY5 Adv identify the characteristics of a binomial experiment
G3 graph and interpret sample distributions of the sample mean and sample
distributions of the
CHAPTER SIX: TRIGONOMETRY AND ITS APPLICATIONS
6.1 Area of a Triangle
B4
B6
use the calculator correctly and efficiently
derive and analyse the Law of Sines, the Law of Cosines, and the formula Area of
triangle
ABC = ½bc sin A
D3 apply sine and cosine ratios and functions to situations involving non-acute angles
D5 apply the Law of Sines, the Law of Cosines, and the formula Area of triangle ABC
= ½bc sin A to solve problems
6.2 Law of Sines and Law of Cosines
B4
B6
use the calculator correctly and efficiently
derive and analyse the Law of Sines, the Law of Cosines, and the formula Area of
triangle ABC = ½bc sin A
C15 demonstrate an understanding of sine and cosine ratios and functions for nonacute angles
D3 apply sine and cosine ratios and functions to situations involving non-acute angles
D5 apply the Law of Sines, the Law of Cosines, and the formula Area of triangle
ABC = ½bc sin A to solve problems