Mathematics B (Authority Subject)

Transcription

1 Mathematics B (Authority Subject) Prerequisites A minimum of Year 10 Mathematics at a Satisfactory (C) Level of Achievement is recommended to study Mathematics B. Achievement Mathematics B is designed to develop in students the mathematical skills needed to make informed, intelligent judgments on economic, social, political and technological issues that may affect their lives. Mathematics B also provides the basis for further studies in fields as diverse as the Physical and Social Sciences, Engineering, Accounting, Geography, Art and Design, and Management. QCE credit Successful completion (Sound Achievement or higher) of all 4 semesters of Mathematics B attracts 4 QCE credit points. Assessment Criteria An overall level of achievement in this subject is determined by the teacher s on-balance judgment of the evidence presented in students summative assessment across the following: Knowledge and Procedure Modelling and Problem Solving Communication and Justification Delivery (mode, time requirements, lessons) Students have access to a one hour scheduled lesson and a one hour tutorial each week. Lessons are delivered via Collaborate and teleconferencing. Students are also expected to undertake independent study to complete tasks and assessment in accordance with the Work Rate Calendar. Course materials can be accessed in Blackboard. Student Requirements Access to a computer and internet, headset with microphone. Various stationery items, including A4 graph paper Graphics Calculator* Casio fx-cg20 Resources Maths Quest Maths B Year 11 for Queensland, ISBN (Returnable resource) Maths Quest Maths B Year 12 for Queensland, ISBN (Returnable resource) *Calculators - Not included in Textbook Hire Scheme Subject Fee $30.00

2 Year 11 Mathematics B (Semester 1) Unit 1: Introduction to Functions (1) Ordered pairs, tables, graphs and equations as representations of relations; graphs as a representation of the points whose coordinates satisfy an equation; solutions to simultaneous equations in two variables. Unit 2: Introduction to Functions (2) Concepts of function, domain and range; distinction between functions and relations; concept of the inverse of a function. Term 1 Unit 3: Periodic Functions and Applications (1) Trigonometry, including the definition and practical applications of the sine, cosine and tangent ratios; simple practical applications of the sine and cosine rules. Unit 4: Periodic Functions and Applications (1) Pythagorean identity; solution of trigonometric equations within a specified domain. Term 1 Exam Semester 1 Unit 5: Applied Statistical Analysis (1) Semester 1 Interim Reporting to Parents Use of summary statistics including mean, median, standard deviation and interquartile; distance as appropriate descriptors of features of data in context; use of graphical displays and summary statistics in describing key features of data, particularly in comparing datasets and exploring possible relationships. Term 2 Unit 6: Applied Statistical Analysis (2) Identification of variables and types of variables and data (continuous and discrete); practical aspects of collection and entry of data; select and use in context appropriate graphical and tabular displays for different types of data including pie charts, bar charts, tables, histograms, and stem-and-leaf and box plots. Unit 7: Exponential and Logarithmic Functions and Applications (1) Index laws and definitions; definitions of a x and loga x, for a > 1; logarithmic laws and definitions; definition of the exponential function e x ; graphs and the relationships ;solution of equations involving indices; use of logarithms to solve equations involving indices. Due: Week 5 Term 2 Exam Semester 1 Reporting to parents

3 Year 11 Mathematics B (Semester 2) Unit 8: Exponential and Logarithmic Functions and Applications (2) Applications of geometric progressions to compound interest including past, present and future values. Unit 9: Introduction to Functions (3) General shapes of functions, including polynomials up to degree 4, reciprocal and absolute value functions; relationships between the graph of f(x) and the graphs of f(x) + 1, f(x + a), af(x), f(ax) for both positive and negative values of the constant a; practical applications: polynomials up to degree 2, reciprocal functions, absolute value functions; composition of two functions. Term 3 Unit 10: Periodic Functions and Applications (3) Definition of a radian and its relationship with degrees; definition of a periodic function, the period and amplitude; definition of the trigonometric functions sin, cos and tan of any angle in degrees and in radians; graphs of y = sin x, y = cos x and y = tan x for any angle in degrees; applications of periodic functions. Unit 11: Introduction to Functions (4); Rates of Change (1) Practical applications of linear functions and polynomials up to degree 2 concept of rate of change; calculation of average rates of change in both practical and purely mathematical situations; interpretation of the average rate of change as the gradient of the secant; practical applications of instantaneous rates of change; gradient of the secant; practical applications of instantaneous rates of change. Semester 2 Term 3 Exam Semester 2 Interim Reporting to Parents Unit 12: Applied Statistical Analysis (3) Use of relative frequencies to estimate probabilities; the notion of probabilities of individual values for discrete variables and intervals for continuous variables. Term 4 Unit 13: Rates of Change (2) Understanding of a limit in simple situations; definition of the derivative of a function at a point; derivative of simple algebraic functions from first principles; evaluation of the derivative of a function at a point; interpretation of instantaneous rate of change at a point as the gradient of a tangent and as the derivative at that point; rules for differentiation; interpretation of the derivative as the gradient function; positive and negative values of the derivative as an indication of the points at which the function is increasing or decreasing zero values of the derivative as an indication of stationary points concept of relative maxima and minima and greatest values; methods of determining the nature of stationary points. Term 4 Due: Week 4 Term 4 Exam Due: Week 7 Semester 2 Reporting to parents

4 Year 12 Mathematics B (Semester 3) Unit 14: Introduction to Functions (5); Rates of Change (3); Optimisation (2) General shapes of functions, including polynomials up to degree 4, reciprocal and; absolute value functions; composition of two functions; concept of the inverse of a function; evaluation of the derivative of a function at a point; rules for differentiation; interpretation of the derivative as the gradient function; positive and negative values of the derivative as an indication of the points at which the function is increasing or decreasing. Unit 15: Rates of Change (4); Optimisation (3) Concept of rate of change; calculation of average rates of change in both practical and purely mathematical situations; practical applications of instantaneous rates of change positive and negative values of the derivative as an indication of the points at which the function is increasing or decreasing; zero values of the derivative as an indication of stationary points; concept of relative maxima and minima and greatest and least value of functions; methods of determining the nature of stationary points; greatest and least values of a function in a given interval; recognition of the problem to be optimised (maximised or minimised); identification of variables and construction of the function to be optimised; interpretation of mathematical solutions and their communication in a form appropriate to the given problem. Term 1 Unit 16: Exponential and Logarithmic Functions (3) Index laws and definitions; definitions of a x and loga x, for a > 1; logarithmic laws and definitions; definition of the exponential function e x ; graphs of, and the relationships between; solution of equations involving indices; use of logarithms to solve equations involving indices; development of algebraic models from appropriate datasets using logarithms and/or exponents. Semester 3 Unit 17: Exponential and Logarithmic Functions and Applications (4) Rates of Change (5) Derivatives of exponential and logarithmic functions for base e ; applications of exponential and logarithmic functions, and the derivative of exponential functions; derivative of simple algebraic functions from first principles evaluation of the derivative of a function at a point. Term 1 Exam Unit 18: Periodic Functions and Applications (4) Semester 1 Interim Reporting to Parents Definition of a radian and its relationship with degrees; definition of the trigonometric functions sin, cos and tan of any angle in degrees and in radians; applications of periodic functions; solution of trigonometric equations within a specified domain. Term 2 Unit 19: Introduction to Integration (1) Definition of the indefinite integral; rules for integration; indefinite integrals of simple polynomial and exponential functions; trapezoidal rule for the approximation of a value. Due: Week 4 Term 2 Exam Due: Week 9 Semester 1 Reporting to parents

5 Year 12 Mathematics B (Semester 4) Unit 20: Periodic Functions and Applications (5); Rates of Change (6); Optimisation (4) Derivatives of functions; applications of the derivatives; evaluation of the derivative of a function at a point; interpretation of the derivative as the gradient function; applications of the derivative to optimisation in life-related situations using a variety of function types. Unit 21: Applied Statistical Analysis (4) Probability distribution and expected value for a discrete variable; identification of the binomial situation and use of tables or technology for binomial probabilities; concept of a probability distribution for a continuous random variable; notion of expected value and median for a continuous variable. Term 3 Unit 22: Applied Statistical Analysis (5) The normal model and use of standard normal tables or technology. Semester 4 Term 3 Exam Due: Week 6 Semester 2 Interim Reporting to Parents Unit 23: Exponential and Logarithmic Functions and Applications (5) Applications of geometric progressions to annuities and amortising a loan. Term 4 Unit 24: Introduction to Integration (2) Definition of the definite integral and its relation to the area under a curve; the value of the limit of a sum as a definite integral; use of integration to find area; practical applications of the integral. Term 4 Exam Due: Week 5 Semester 2 Reporting to parents NB. Year 12 students do not receive a Semester 2 report.