Math 11 Advanced MAD11 Course Outline

Transcription

1 Math 11 Advanced MAD11 Course Outline 1. APPLIED TRIGONOMETRY (CHAPTER 6) 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) 2. SINUSOIDAL FUNCTIONS (CHAPTER 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 3. TRIGONOMETRIC EQUATIONS AND IDENTITIES (CHAPTER 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 4. SOLVING SYSTEMS OF EQUATIONS (CHAPTER 1) 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 5. STATISTICS (CHAPTER 5) 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

2 Math 11 Advanced MAD11 General Curriculum Outcomes Students in Mathematics 11 Advanced will explore the following subjects: 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

3 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 develop, analyse and apply procedures for matrix multiplication (new) A4 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 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

4 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 analyse and apply the graphs of the sine and cosine functions C1 model situations with sinusoidal functions C2 create and analyze scatter plots of periodic data C3 determine the equations of sinusoidal functions C9 analyze tables and graphs of various sine and cosine functions to find patterns, identify characteristics, and determine equations

5 C21 describe how various changes in the parameters of sinusoidal equations affect their graphs CHAPTER FOUR: TRIGONOMETRIC EQUATIONS 4.1 Trigonometric Equations A1 demonstrate an understanding of irrational numbers in applications B5 analyse and apply the graphs of the sine and cosine functions C1 model situations with sinusoidal functions C9 analyse tables and graphs of various sine and cosine functions to find patterns, identify characteristics, and determine equations C15 demonstrate an understanding of sine and cosine ratios and functions for nonacute angles C18 Interpolate and extrapolate to solve problems C27 apply function notation to trigonometric equations C28 analyse and solve trigonometric equations with and without technology 4.2 Trigonometric Identities A1 demonstrate an understanding of irrational numbers in applications B1 demonstrate an understanding of the relationship between operations on fractions and rational algebraic expressions C9 analyse tables and graphs of various sine and cosine functions to find patterns, identify characteristics, and determine equations C24 derive and apply the reciprocal and Pythagorean identities C25 prove trigonometric identities C28 analyse and solve trigonometric equations with and without technology 4.3 Radian Measure A1 demonstrate an understanding of irrational numbers in applications 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

6 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 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 data collection, interpretation, and presentation F4 demonstrate an understanding of the differences in the quality of sampling F7 draw inferences from graphs, tables, and reports F8 apply characteristics of normal distributions F11 determine, interpret, and apply confidence F15 design and conduct surveys and simulate data collection to explore sampling variability FY demonstrate an understanding of how the confidence levels affects the confidence interval FY2 demonstrate an understanding of the role of the central limit theorem in the development of confidence intervals FY3 distinguish between the calculation of confidence intervals for a known population mean versus an unknown population mean

7 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 B6 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 B6 derive and analyse the Law of Sines, the Law of Cosines, and the formula Area of triangle ABC = ½bc sin A

8 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