Advanced Mathematics – Year 11 – Future Aerospace Engineering

About Course

Course Overview: Deepen your mathematical knowledge with this comprehensive course. Explore advanced topics in algebra, calculus, geometry, and more, while developing problem-solving skills and analytical thinking.

Course Content

Lesson 1: Course Introduction and Objectives
o Welcome to the course and understand its structure.

Lesson 2: Polynomial and Rational Functions
o Study polynomial and rational functions, including end behavior. o Analyze the relationship between roots and factors.

Lesson 3: Exponential and Logarithmic Functions
o Explore exponential growth and decay models. o Understand logarithmic functions and solve related equations.

Lesson 4: Trigonometric Identities and Equations
o Dive into advanced trigonometric identities. o Solve complex trigonometric equations and prove identities.

Lesson 5: Complex Numbers and Polar Coordinates
o Introduce complex numbers and their operations. o Represent complex numbers in polar form and perform operations.

Lesson 6: Derivatives and Applications
o Understand the concept of a derivative and its applications. o Apply differentiation to optimize problems.

Lesson 7: Techniques of Differentiation
o Explore differentiation rules for various functions. o Differentiate exponential, logarithmic, and trigonometric functions.

Lesson 8: Integration and Antiderivatives
o Introduce integration and antiderivatives. o Explore the fundamental theorem of calculus.

Lesson 9: Applications of Integration
o Apply integration to calculate areas, volumes, and work. o Study the concept of definite and indefinite integrals.

Lesson 10: Euclidean Geometry and Proofs
o Explore axiomatic systems and Euclidean geometry. o Develop geometric proofs and theorems.

Lesson 11: Vectors and Vector Operations
o Introduce vectors, vector operations, and their properties. o Analyze applications of vectors in geometry and physics.

Lesson 12: Probability Distributions and Statistics
o Study probability distributions and statistical analysis. o Calculate measures of central tendency and dispersion.

Lesson 13: Probability and Discrete Random Variables
o Explore probability models, discrete random variables, and binomial distribution. o Analyze probability experiments and solve related problems.

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Advanced Mathematics – Year 11

About Course

What Will You Learn?

Course Content

Lesson 1: Course Introduction and Objectives o Welcome to the course and understand its structure.

Lesson 2: Polynomial and Rational Functions o Study polynomial and rational functions, including end behavior. o Analyze the relationship between roots and factors.

Lesson 3: Exponential and Logarithmic Functions o Explore exponential growth and decay models. o Understand logarithmic functions and solve related equations.

Lesson 4: Trigonometric Identities and Equations o Dive into advanced trigonometric identities. o Solve complex trigonometric equations and prove identities.

Lesson 5: Complex Numbers and Polar Coordinates o Introduce complex numbers and their operations. o Represent complex numbers in polar form and perform operations.

Lesson 6: Derivatives and Applications o Understand the concept of a derivative and its applications. o Apply differentiation to optimize problems.

Lesson 7: Techniques of Differentiation o Explore differentiation rules for various functions. o Differentiate exponential, logarithmic, and trigonometric functions.

Lesson 8: Integration and Antiderivatives o Introduce integration and antiderivatives. o Explore the fundamental theorem of calculus.

Lesson 9: Applications of Integration o Apply integration to calculate areas, volumes, and work. o Study the concept of definite and indefinite integrals.

Lesson 10: Euclidean Geometry and Proofs o Explore axiomatic systems and Euclidean geometry. o Develop geometric proofs and theorems.

Lesson 11: Vectors and Vector Operations o Introduce vectors, vector operations, and their properties. o Analyze applications of vectors in geometry and physics.

Lesson 12: Probability Distributions and Statistics o Study probability distributions and statistical analysis. o Calculate measures of central tendency and dispersion.

Lesson 13: Probability and Discrete Random Variables o Explore probability models, discrete random variables, and binomial distribution. o Analyze probability experiments and solve related problems.