Maths (general advanced-extension)

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Maths (general advanced-extension)

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Maths (general advanced-extension)

  1. 1. GeneralMathematics
  2. 2. General MathematicsBoard Endorsed Course This is a NON ATAR 2 Unit coursePrerequisites:The course is constructed on the assumption that students have achieved theoutcomes of Advanced Mathematics, OR demonstrated a high level of competence inIntermediate Mathematics.Course Description:General Mathematics focuses on mathematical skills and techniques, which havedirect application to everyday activity. The course content is written in five areas ofstudy, with an emphasis on application of specific skills and on tasks that involveintegrating mathematical skills and techniques across a range of familiar andunfamiliar situations. These tasks may draw from more than one area of study, andencourage transfer of knowledge across the entire course, as well as linking with studyin other Stage 6 subjects. The course is fully prescribed, and is designed to supportTAFE and other vocational courses.
  3. 3. General Mathematics Financial Mathematics Preliminary Course HSC Course You will learn about... You will learn about...• Earning Money • Annuities and Loan• Investing Money Repayments• Taxation • Credit and Borrowing • Depreciation
  4. 4. General Mathematics Data Analysis Preliminary Course HSC Course You will learn about... You will learn about...• Statistics and Society • Interpreting Sets of Data• Data Collection and Sampling • The Normal Distribution• Displaying Single Data Sets • Correlation
  5. 5. General Mathematics Measurement Preliminary Course HSC Course You will learn about... You will learn about...• Units of Measurement and • Further Applications of Area Applications and Volume• Applications of Area and • Applications of Trigonometry Volume • Spherical Geometry• Similarity of 2D Figures• Right Angled Triangles
  6. 6. General Mathematics Probability Preliminary Course HSC Course You will learn about... You will learn about...• The Language of Chance • Multi Stage Events• Relative Frequency and • Applications of Probability Probability
  7. 7. General Mathematics Algebra and Modelling Preliminary Course HSC Course You will learn about... You will learn about...• Basic Algebraic Skills • Further Algebraic Skills and• Modelling Linear Relationships Techniques • Modelling Linear and Non Linear Relationships
  8. 8. Mathematics
  9. 9. MathematicsBoard Endorsed Course This is a NON ATAR 2 Unit coursePrerequisites:The School Certificate in MathematicsCourse Description:The course is constructed on the assumption that the students have achieved theoutcomes, and, demonstrated a high level of competence in Stage 5.3 Mathematics.This course further develops the understanding and competence in the aspects ofMathematics that follow.
  10. 10. Mathematics Preliminary Course Basic Arithmetic and Algebra You will learn about…• Rationals and Surds• Absolute Value• Algebraic Expressions• Linear Equations and Inequalities
  11. 11. Mathematics Preliminary Course Real Functions You will learn about…• Real Functions• Graphs• Algebraic Representations• Regions
  12. 12. Mathematics Preliminary Course Trigonometry You will learn about…• Trigonometric Ratios• Trigonometric Identities• Applied Trigonometry
  13. 13. Mathematics Preliminary Course Linear Functions You will learn about…• The Linear Function• The Gradient of a Line• Interval Formulae
  14. 14. Mathematics Preliminary Course The Quadratic Polynomial and The Parabola You will learn about…• The Quadratic Function• The Quadratic Equation• Other Quadratics• The Parabola as a Locus
  15. 15. Mathematics Preliminary Course Plane Geometry You will learn about…• Notations and Symbols• Definition, Recognition, and Properties• Congruence and Similarity• Intercept Theorems• Measurement
  16. 16. Mathematics Preliminary Course Tangent to a Curve and Derivative of a Function You will learn about…• Continuity and Limits• Secants and Tangents• Differential Rules• Equation of the Tangent
  17. 17. Mathematics HSC Course Geometrical Applications of Differentiation You will learn about…• Sign of the Derivative• The Second Derivative• Applications to Problem Solving• Primitive Functions
  18. 18. Mathematics HSC Course Integration You will learn about…• The Definite Integral• Area and Volume• Approximate Methods
  19. 19. Mathematics HSC Course Trigonometric Functions You will learn about…• Circular Measurement• Graphs• Limits• Differentiation• Integration
  20. 20. Mathematics HSC Course Logarithmic and Exponential Functions You will learn about…• The Log Function• The Exponential Function• Graphs• Differentiation• Integration
  21. 21. Mathematics HSC Course Applications of Calculus to the Physical World You will learn about…• Simple Rates of Change• Motion of a Particle with Respect to Time
  22. 22. Mathematics HSC Course Probability You will learn about…• Random and Complementary Events• Tree Diagrams• Mutually and Non Mutually Exclusive Outcomes• Multi Stage Events
  23. 23. Mathematics HSC Course Series and Series Applications You will learn about…• General Series• Arithmetic Series• Geometric Series
  24. 24. Extension 1Mathematics
  25. 25. Extension 1 MathematicsBoard Endorsed Course This is an ATAR 1 Unit course1 Unit additional to 2 Unit Mathematics in each of Preliminary and HSCPrerequisites:Before selecting this course, students need to have demonstrated a significantaptitude for Mathematics at Stage 5.3 level. Students must also pass an entrance examand obtain written approval from the Head Teacher of MathematicsCourse Description:The course runs concurrently with the Stage 6 Mathematics Course.It is constructed on the assumption that students are highly proficient in all Stage 5outcomes, and, have demonstrated a mastery of the skills in Stage 5.3 Mathematics. Itfurther develops the understanding and competence in the aspects of Mathematics.
  26. 26. Extension 1 Mathematics Preliminary Course Other Inequalities You will learn about…• Unknown in the Denominator
  27. 27. Extension 1 Mathematics Preliminary Course Further Plane Geometry You will learn about…• Theoretical Problems with more than One Step of Reasoning
  28. 28. Extension 1 Mathematics Preliminary Course Circle Geometry You will learn about…• Chord Properties• Angle Properties• Tangent Properties• Theoretical Problems with more than One Step of Reasoning
  29. 29. Extension 1 Mathematics Preliminary Course Further Trigonometry You will learn about…• Sums and Differences• Half Angles• Double Angles• T-Substitutions• Solution Methods• 3D Applied Trigonometry Problems
  30. 30. Extension 1 Mathematics Preliminary Course Permutations and Combinations You will learn about…• Counting Techniques• Factorial Notation
  31. 31. Extension 1 Mathematics Preliminary Course Polynomials You will learn about…• Operations• Remainder Theorem• Factor Theorem• Graphs
  32. 32. Extension 1 Mathematics Preliminary Course Angle Between Two Lines & Internal and External Division of Lines into Given Ratios You will learn about…• Applications of the Formula
  33. 33. Extension 1 Mathematics HSC Course Methods of Integration You will learn about…• Substitution Methods• Trig Substitution• Primitives of sin²x and cos²x
  34. 34. Extension 1 Mathematics HSC Course Further Exponential/Log Functions You will learn about…• Integration involving Partial Fractions• Newton’s Law of Cooling
  35. 35. Extension 1 Mathematics HSC Course Applications of Calculus to the Physical World You will learn about…• Related Rages of Change• Velocity and Acceleration as Functions of the Displacement• Projectile Motion• Simple Harmonic Motion
  36. 36. Extension 1 Mathematics HSC Course Inverse Functions and Inverse Trigonometric Functions You will learn about…• Graphs• Differentiation and Integration
  37. 37. Extension 1 Mathematics HSC Course Binomial Theorem You will learn about…• Pascal’s Triangle• General Binomial Theorem• Further Probability
  38. 38. Extension 1 Mathematics HSC Course Iterative Method for Estimation of Roots You will learn about…• Halving the Interval Theorem• Newton’s Method
  39. 39. Extension 1 Mathematics HSC Course Mathematical Induction You will learn about…• Summation Style• Divisibility Test• Inequalities• Other Contexts
  40. 40. Extension 2Mathematics
  41. 41. Extension 2 MathematicsBoard Endorsed Course This is a NON ATAR 2 Unit course1 Unit additional to the Mathematics Extension 1 course, for the HSCPrerequisites:Before selecting this course, students need to have demonstrated a significantaptitude for Mathematics at Extension 1 level. Students must also obtain writtenapproval from the Head Teacher of MathematicsCourse Description:This course is run concurrently with Stage 6 Mathematics and Extension 1.It is constructed on the assumption that students are highly proficient in allPreliminary outcomes, and, have demonstrated a mastery of the skills in Extension 1Mathematics. It further develops the understanding and competence in aspects ofMathematics.
  42. 42. Extension 2 Mathematics HSC Course only You will learn about…Please refer to the Board of Studies Website for Topics and DetailedSyllabus Noteshttp://www.boardofstudies.nsw.edu.au/syllabus_hsc/mathematics-advanced.html

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