Unit: Trigonometric & Polar Functions Chapter: Solving with Waves: Sinusoidal Models & Equations Reference: – Introduction, Periodic functions, Amplitude & Midline, Graph of Sinusoidal functions, Trigonometric Equations, Phase shift, Frequency & Angular Velocity, Trigonometric functions of Angles, Inverse Trigonometric equations, Modelling, Polar Functions. Identities, Graphical Functions After studying this chapter, you should be able to: […]
Unit: Trigonometric & Polar Functions Chapter: Core Trigonometric Functions: Sine, Cosine & Tangent Reference: – Definition of Core Trigonometric Functions, Graphical Representation of Sine, Cosine & Tangent, Domain and Range, Periodicity & Symmetry, Amplitude, Frequency, and Phase Shift, Special Angles and Exact Values, Pythagorean Identities, Reciprocal Relationships, Applications of Core Functions, Connection to Polar Representation […]
Unit: Exponential & Logarithmic Functions Chapter: Exploring Logarithms and Validating Models Reference: – Logarithmic functions, Basic properties, Analysing functions, Scattering, Residual plots, Data points, Logarithmic operations, Exponential functions, Graphical Analysis, Logarithmic rules, Intercepts, Transformation, Inequalities, Logarithmic differentiation After studying this chapter, you should be able to: Introduction to Logarithmic functions & Their Properties Residual plot, […]
Unit: Exponential & Logarithmic Functions Chapter: Building and Reversing Functions: Composition & Inverses Reference: – Introduction to Function Composition, Domain & Range in Composition, Properties of Composition, Exponential Functions in Composition, Logarithmic Functions in Composition, Inverse of a Function (Definition), Finding Inverses of Exponentials, Finding Inverses of Logarithms, Graphical Symmetry in Inverses, Applications of Composition […]
Unit: Exponential & Logarithmic Functions Chapter: Growth Patterns: Sequences and Exponential Models Reference: – Introduction to Sequences, Explicit and Recursive Formulas, Geometric Sequences in Depth, Exponential Growth Models, Exponential Decay Models, Compound Interest & Continuous Growth, Connection Between Geometric Sequences & Exponential Functions, Graphical Representation of Exponential Functions, Model Fitting with Data, Applications in Real-World […]
Unit: Polynomials & Rational Functions Chapter: Modeling, Transformation, and Representation of Functions Reference: – Function Transformations – Basics, Composite Transformations, Equivalent Representations of Polynomial & Rational Expressions, Piecewise and Absolute Value Transformations, Model Selection in Real-World Scenarios, Assumption Articulation in Modeling, Function Construction from Conditions, Inverse Functions and Their Representations, Graphical vs Algebraic Models, Applications […]
Unit: Polynomials & Rational Functions Chapter: Structure & Behaviour of Polynomial & Rational Functions Reference: – Polynomial Degree and Leading Coefficient, Zeros of Polynomial Functions, End Behavior of Polynomials, Graphical Behavior Near Zeros, Structure of Rational Functions, Zeros of Rational Functions, End Behavior of Rational Functions, Vertical Asymptotes, Holes in Rational Functions, Equivalent Algebraic Representations, […]
Unit: Polynomials & Rational Functions Chapter: Dynamics of Change in Functions Reference: – Understanding Change in Tandem, Average Rate of Change, Instantaneous Rate of Change (Intro), Rates of Change in Linear Functions, Rates of Change in Quadratic Functions, Comparing Linear vs. Quadratic Rates of Change, Rates of Change in Higher-Degree Polynomials, Graphical Interpretation of Rates […]
Unit: Polynomial & Rational Function Chapter: Change of Quantity & Behaviour of Functions Reference: – Degree coefficient, Leading coefficient, Polynomial function, Behavior of function, Positive infinity, Negative infinity, Zeros & Factors, Multiplicity of zeros, Turning points, Graphical Behavior, Rational functions, Vertical Asymptotes, Horizontal Asymptotes, Oblique Asymptotes After studying this chapter, you should be able […]
Unit: Infinite Sequence & Series Chapter: Taylor Series, Maclaurin Series Reference: – Divergence test, Geometric series, Integral test, Comparison test, Limit comparison test, Alternating series test, Absolute convergence, Conditional Convergence, Ratio test, Root test, Taylor series, Radius of convergence, Interval of convergence. After studying this chapter, you should be able to: Introduction to Taylor […]