Re: Announcement from BOSTES - significant change to calculus courses
The draft writing briefs are up now a few days early:
General 1 and 2:
http://www.boardofstudies.nsw.edu.a...oc/maths-gen-st6-draft-writing-brief-2015.pdf
2u/ext1/ext2:
http://www.boardofstudies.nsw.edu.a...oc/maths-ext-st6-draft-writing-brief-2015.pdf
Here is the proposed content:
General 1 and 2:
Option 1:
- there would be minor revision only of the current Preliminary Mathematics General, HSC Mathematics General 2 and HSC Mathematics General 1 courses
- a greater level of revision would be considered, if required, to align with agreed changes to the Mathematics (‘2 Unit’) course.
Option 2:
- there would be moderate revision of the current Preliminary Mathematics General course (to become Preliminary Mathematics General 2), and the HSC Mathematics General 2 and HSC Mathematics General 1 courses. The new Preliminary Mathematics General 2 and HSC Mathematics General 2 courses will have significant overlap with the Mathematics course to assist student movement and to obtain appropriate course relativity in ATAR scaling. This overlap would include rates of change (without getting to the stage of formally calculating derivatives) and could include aspects of such topic areas as financial mathematics, statistics, probability, algebra and modelling, and trigonometry
- there would be a new Preliminary course (Preliminary Mathematics General 1) that, together with the revised HSC Mathematics General 1 course, will build on student knowledge and skills from Stage 5.1.
Advanced (2 unit)
- Real numbers and algebraic techniques (surds and indices, algebraic expressions, equations and inequalities, logarithms)
- Real functions and their graphs (simple graphs, function notation, properties of functions and graphs, regions and inequalities, applications involving real functions: direct and inverse variation, constructing and using functions)
- Trigonometry (exact ratios, sine rule, cosine rule, area rule, angles of any magnitude, identities, equations, graphs, trigonometric functions, derivatives of trigonometric functions, applications of the calculus of trigonometric functions)
- Differential calculus (estimating change, the derivative function, differentiation, Euler’s number and natural logarithms, stationary points, the second derivative, curve sketching, maximising and minimising)
- Integral calculus (the primitive function, the definite integral, approximating definite integrals, applications of integration)
- Sequences and series (applications of series to finance: present and future value, annuities)
- Descriptive statistics (univariate and bivariate data, the normal distribution, lines of best fit)
- Probability (systematic counting of events, successive outcomes, tree diagrams, applications involving probability and finance: counting techniques and probability, investment, reducing-balance loans)
- Exponential and logarithmic functions (calculus of exponential and logarithmic functions, applications to the natural environment: rates of change of physical quantities, exponential growth and decay).
Extension 1
- Circle geometry
- Further algebra (general theory of quadratic equations, quadratic and cubic expressions and equations)
- Polynomials (polynomial functions and their graphs, the remainder and factor theorems)
- Transformations of graphs
- Further trigonometry (sums and differences, trigonometry in three dimensions, solution and applications of trigonometric equations, further calculus of trigonometric functions)
- Series, elementary difference equations (limiting sum of a geometric series, methods of solution of first-order linear difference equations)
- Descriptive statistics (discrete random variables, continuous random variables, types of distributions)
- Mathematical induction
- The binomial theorem (binomial expansions and identities, binomial probabilities)
- Methods and applications of integration (including substitution, solids of revolution)
- Inverse functions (including inverse trigonometric functions)
- Further applications of calculus involving mathematical modelling (including further exponential growth and decay, related rates, projectile motion, iterative methods for estimating roots of equations).
Extension 2
- The nature of proof (including proofs involving inequalities)
- Complex numbers and polynomials over the complex field (arithmetic of complex numbers, geometric representation, powers and roots, curves and regions, fundamental theorem of algebra and factorising polynomials)
- Graphs (graphing techniques, general approach to curve sketching)
- Integration techniques (including integration by parts, recurrence relations)
- Volumes (by slicing, by the method of cylindrical shells)
- Modelling with functions and derivatives (solving differential equations by integration, first-order linear differential equations)
- Mechanics (simple harmonic motion, Newton’s laws, resisted motion along a horizontal line, resisted motion under gravity)
- Difference equations (solving second-order difference equations, the logistic growth equation, equilibrium, periodic and chaotic solutions)
- Statisical inference (sample means, confidence intervals for means).