Year 12 Mathematics: Specialist Course Outline

Transcription

1 MATHEMATICS LEARNING AREA Year 12 Mathematics: Specialist Course Outline Time Content area Topic Text Ref. Assessment SADLER Week 1 Preliminary U1 Prelim 1-2 Complex Numbers Factorising Polynomials Ch Polar Form Ch 2 Investigation Functions Functions, sketching Ch 3 Test Vectors Vector Equation of Line 2D Ch 4 Week 9 RETREAT D Vectors Ch 5 Investigation 2 Week 13 Linear Equations Systems of Equations Ch 6 Test Vector Calculus Differentiation/Integration Ch 7 Week 16 REVISION Exams Semester 1 Examination Week Rates of Change Differentiation: Techniques & Ch 8 Investigation 3 Applications Integration Techniques & Applications Ch 9 Test Differential Equations Ch 10 Week 26 Modelling Motion Simple Harmonic Motion Ch Statistical Inference Sample Means Ch 12 Week 29 Confidence Intervals Test 4 Week 30 REVISION Semester 2 Examination Programme Students will be provided with opportunities to: plan and carry through tasks: choose and use mathematical models and methods choose methods of processing written, with a calculator. interpret solutions: check answers fit specifications link solutions to contexts generalise results. argue to support or contest mathematical conclusions communicate methods, reasoning and results.

2 Unit 3 Week 1 Preliminary Complex numbers: A reminder; Algebraic fractions Sadler Chapter The remainder theorem The factor theorem Polar form of a complex number Polar form of a complex number The abbreviated form for cosθ + isinθ Multiplying and dividing complex numbers expressed in polar form Geometric interpretation Regions in the complex plane The cube roots of 1 The nth roots of a non zero complex number De Moivre's theorem Sadler Chapter Functions One-to-one and many-to-one Combining functions Using the output of one function as the input of another Domain and range of functions of the form f o g (x) Inverse functions Graphical relationship between a function and its inverse Condition for the inverse to exist The absolute value function Sadler Chapter 3 Investigation 1 The absolute value function The graph of 7-8 The graph of for and polynomials Vector equation of a line in the x-y plane Interception/ collision Vector equation of a straight line in the x-y plane Point of intersection of two straight lines Scalar product form of the equation of a straight line in the x-y plane Vector equations of curves in the x-y plane Vector equations of circles in the x-y plane Closest approach Distance from a point to a line Sadler Chapter 4 Test 1: Complex Numbers, Functions Week 9 Week 10 RETREAT Revision

3 Vectors in three dimensions Sadler Chapter 5 Week 12: Three dimensional vectors Investigation 2 The angle between two lines Vector product Vector equation of a line Vector equation of a plane Given three points Interception and collision Vector equation of a sphere Distance from a point to a line revisited Week 13 Systems of linear equations Systems of linear equations A systematic approach for solving systems of linear equations using a matrix form of presentation (and otherwise) Calculators and row echelon form Systems of linear equations having no solution Systems of equations having infinitely many solutions Sadler Chapter Vector calculus Differentiating vector functions Integrating vector functions Some particular types of motion Sadler Chapter 7 Week 14 - Test 2: Vectors; Systems of Equations Week Unit REVISION EXAMS Differentiation techniques and applications Explicitly defined and implicitly defined functions Differentiation of implicitly defined functions Differentiation of parametrically defined functions Related rates Semester 1 Exam Sadler Chapter 8 Week 20: Investigation 3 Small changes Marginal rates of change Logarithmic differentiation Integration techniques and applications Integration by substitution Definite integrals and the change of variable method Use of trigonometric identities to assist integration Sadler Chapter 9 Integration to give logarithmic functions More about partial fractions Volumes of revolution Numerical integration Week 24: Test 3 Differentiation, Integration

4 Differential equations Sadler Chapter Differential equations Differential equations of the form or The logistic model for growth Week 26 Can we get some idea of what the relationship between x and y will look like from the differential equation directly, without integrating? Slope fields Euler's method Simple harmonic motion Revision of rectilinear motion A particular type of rectilinear motion: simple harmonic motion Solving the differential equation Sadler Chapter Week 29 Week Sample means Sampling Distribution of sample means Increasing the number of samples Increasing the sample size The central limit theorem Sample size Samples with means that are unusually high or unusually low Inferring population parameters from sample statistics Confidence Intervals So do most 95% confidence intervals really contain the population mean? Let's check Choosing the sample size Revision Revision and Exams Sadler Chapter 12 Week 29: Test 4 Differential Equations, Harmonic Motion, Statistical Inference Semester 2 Exam

5 2017 Assessment Record Course 12 Specialist Units 3 and 4 Date My Raw YEAR Assessment Content Administered mark (%) Weighting Test 1 (Unit 3) Week 6 Term 1 Remainder & Factor Theorems; Complex Numbers; Functions 8% Test 2 (Unit 3) Week 4 Term 2 2D & 3D Vectors; Systems of Equations 8% Test 3 (Unit 4) Week 4 Term 3 Differentiation & Integration: Techniques and Applications 12% Test 4 (Unit 4) Week 9 Term 3 Differential Equations; Harmonic Motion; Statistical Inference 12% Investigation 1 Week 4 Term 1 Complex Numbers % YEAR Value (Raw mark x weighting) Total Weighting Assessment Type Investigation 2 Week 2 Term 2 Limits Investigation 3 Week 10 Term 2 Numerical Techniques Semester 1 EXAM Week 7 Term 2 Unit 3 Semester 2 EXAM Week 1 Term 4 Unit 3 & % % 3 15% 25% Assessment and Late Work Policy for Mathematics Classes Please refer to page 19B of the College Diary.