Mathematics C (Authority Subject)

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1 Mathematics C (Authority Subject) Prerequisites At least High Achievement in Year 10 Mathematics and have completed Mathematics B or be studying it concurrently. Achievement Mathematics C 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 C 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 C 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 Computer with and internet access, headset with microphone. Resources Maths Quest 11, 12 Maths C for Queensland, N. Simpson, C Smith, P Posetti, S Campbell, John Wiley and Sons (provided by Cairns SDE???) Graphics Calculator Casio fx cg 20 or TI-84 *Calculators - Not included in Textbook Hire Scheme If parents are purchasing a new calculator CASIO fx cg 20 or later model is recommended. Subject Fee $30.00

2 Year 11 Mathematics C (Semester 1) Real and Complex Number Systems (1) Structure of the real number system including rational numbers, irrational numbers; simple manipulation of surds. Term 1 Matrices and Applications (1) Definition of a matrix as data storage and as a mathematical tool; dimension of a matrix; matrix operations - addition and subtraction, transpose; multiplication by a scalar; multiplication by a matrix; inverse of a matrix; singular and non-singular matrices; definition and properties of the identity matrix; solution of simple matrix equations; application of matrices in both life-related and purely mathematical situations. Introduction to Groups Concepts of closure, associativity, identity, inverse; definition of a group. Due: Week 9 Semester 1 Vectors and Applications (1) For vectors as a single column or single row array; definition of a vector; relationship between vectors and matrices; operations on vectors including addition; multiplication by a scalar; scalar product of two vectors; simple life-related applications of vectors. Structures and Patterns (1) Sum to infinity of a geometric progression; purely mathematical and life-related applications of arithmetic and geometric progressions and series; sequences and series other than arithmetic and geometric. Term 2 Vectors and Applications (2) For vectors describing situations involving magnitude and direction; definition of a vector, including standard unit vectors i, j and k; relationship between vectors and matrices; operations on vectors including addition, multiplication by a scalar; two and three-dimensional vectors and their algebraic and geometric representation; unit vectors; scalar product of two vectors; vector product of two vectors; resolution of vectors into components acting at right angles to each other; calculation of the angle between two vectors; applications of vectors in both life-related and purely mathematical situations. Due: Week 6 Due: Week 10 Semester 1 Reporting to parents

3 Year 11 Mathematics C (Semester 2) Real and Complex Number Systems (2) Definition of complex numbers including standard and trigonometrical (modulus-argument) form; algebraic representation of complex numbers in Cartesian, trigonometric and polar form; geometric representation of complex numbers - Argand diagrams; operations with complex numbers including addition, subtraction, scalar multiplication, multiplication of complex numbers, conjugation. Term 3 Matrices and Applications (2) Inverse of a matrix; determinant of a matrix; solution of systems of homogeneous and non-homogeneous linear equations using matrices; relationship between matrices and vectors; solution of simple matrix equations; applications of matrices in both life-related and purely mathematical situations. Due: Week 10 Semester 2 Matrices and Applications (3) Group properties of 2 x 2 matrices; application of matrices in both life-related and purely mathematical situations. Structures and Patterns (2) Permutations and combinations and their use in purely mathematical and life-related situations. Term 4 Vectors and Applications (3) Two and three-dimensional vectors and their algebraic and geometric representation; resolution of vectors into components acting at right angles to each other; applications of vectors in both life-related and purely mathematical situations. Due: Week 4 Criteria: Knowledge and Procedure, Modelling and Problem Solving, Communication and Justification Due: Week 10 Semester 2 Reporting to parents

4 Year 12 Mathematics C (Semester 3) Real and Complex Number Systems (3) Definition of complex numbers including standard and trigonometrical (modulus-argument form); algebraic representation of complex numbers in Cartesian, trigonometric and polar form; roots of complex numbers; use of complex numbers in proving trigonometric identities; powers of complex numbers, including de Moivre s Theorem; simple, purely mathematical applications of complex numbers. Term 1 Matrices and Applications (4) Applications of matrices in both life-related and purely mathematical situations. Calculus (1) Integrals of the form; simple integration by parts; development and use of Simpson s Rule; approximating of small changes in functions using derivatives. Semester 3 Criteria: Knowledge and Procedure, Modelling and Problem Solving, Communication and Justification Due: Week 9 Dynamics (1) Newton s laws of motion in vector form applied to objects of constant mass; application of the above to: - straight line motion in a horizontal plane with variable force - vertical motion under gravity with and without air resistance projectile motion without air resistance. Term 2 Conics (1) Definitions of circles, ellipses, parabolas and hyperbolas in terms of cones, and their use in the development of conic equations; concept of a locus, directrix and focal point; definition of eccentricity e; circle as a locus in - Cartesian form - complex number form; ellipse as a locus - in Cartesian form - complex number form; hyperbola as a locus - in Cartesian form, - complex number form; parabola as a locus in - Cartesian form - simple applications of conics. Due: Week 6 Due: Week 10 Semester 1 Reporting to parents

5 Year 12 Mathematics C (Semester 4) Vectors and Applications (3) Scalar product of two vectors; vector product of two vectors; applications of vectors in both life-related and purely mathematical situations. Structures and Patterns (3) Recognition of patterns in well-known structures including Pascal s Triangle and Fibonacci sequence; application of patterns; use of the method of finite differences; proof by induction, use mathematical induction to prove de Moivre s Theorem. Term 3 Calculus (2) Life-related applications of simple, linear, first-order differential equations with constant coefficients; solution of simple, linear, first-order differential equations with constant coefficients. Semester 4 Due: Week 4 Due: Week 9 Dynamics (2) Derivatives and integrals of vectors; Newton s laws of motion in vector form applied to objects of constant mass; application of the above to - straight line motion in a horizontal plane with variable force - vertical motion under gravity with and without air resistance - projectile motion without air resistance - simple harmonic motion (derivation of the solutions to differential solutions is not required); circular motion with uniform angular velocity. Term 4 Conics (2) Definitions of circles, ellipses, parabolas and hyperbolas in terms of cones, and their use in the development of conic equations; definition of eccentricity e; circle as a locus in - parametric form; ellipse as a locus in - parametric form - polar form; hyperbola as a locus in - parametric form - polar form; parabolas as a locus in - parametric form - polar form; simple applications of conics. Due: Week 6

6 Semester 2 Reporting to parents NB. Year 12 students do not receive a Semester 2 report.