11C Maths – Semester 1

REAL AND COMPLEX NUMBERS

INTRODUCTION TO GROUPS

MATRICES AND APPLICATIONS

VECTORS AND APPLICATIONS

STRUCTURES AND PATTERNS

1 / UNIT LEARNING GOALS:
  • Understand the structure of the real number system including:
rational numbers
irrational numbers
  • Simple manipulation of surds
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Understand and Apply the concepts of:
  • closure
  • associativity
  • identity
  • inverse
  • definition of a group
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  • definition of a matrix as data storage and as a mathematical tool
  • understand dimension of a matrix
  • apply matrix operations
addition
transpose
inverse
multiplication by a scalar
multiplication by a matrix
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For vectors as a one-dimensional 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
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  • sum to infinity of a geometric progression
  • purely mathematical and life-related applications of arithmetic and geometric progressions
  • sequences and series other than arithmetic and geometric
  • permutations and combinations and their use in purely mathematical and life-related situations
/ Assessment
  • Exam
Success Criteria:
  • Accurate and successful completion of problems from the textbook.
  • Reached set Target.
Key Verbs
Understand
Manipulation
Calculate
This semester has a large amount of DECLARATIVE KNOWLEDGE. Students are exposed to very new mathematical concepts and ideas.
Resources
Q MATHS 11C

11C Maths – SEMESTER 2

MATRICES AND APPLICATIONS II

REAL AND COMPLEX NUMBERS II

LINEAR PROGRAMMING

REAL AND COMPLEX NUMBERS III

VECTORS AND APPLICATIONS

DYNAMICS

1 / UNIT LEARNING GOALS:
  • definition and properties of the identity matrix
  • group properties of 2 x 2 matrices
  • determinant of a matrix
  • singular and non-singular matrices
  • solution of systems of homogeneous and non-homogeneous linear equations using matrices
  • Inverse of a matrix
  • Solution of simple matrix equations
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  • definition of complex numbers including standard and trigonometric (modulus-argument) form
  • algebraic representation of complex numbers in Cartesian, trigonometric and polar form
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  • recognition of the problem to be optimised (maximised or minimised)
  • identification of variables parameters and constraints
  • constructions of the linear objective function and constraints with associated parameters
graphing linear functions associated with the constraints and identification of the regions defined by the constraints
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  • geometric representation of complex numbers—Argand diagrams
  • operations with complex numbers including addition, subtraction, scalar multiplication, multiplication of complex numbers, conjugation
  • roots of complex numbers
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For vectors describing situations involving magnitude and direction
  • definition of a vector, including standard unit vectorsi, j and k.
  • relationship between vectors and matrices
  • two and three dimensional vectors and their algebraic and geometric representation
  • operations on vectors including: addition multiplication by a scalar
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  • Calculate derivatives of vectors
  • Apply Newton's laws of motion in vector form applied to objects of constant mass
/ Assessment
  • Exam
Success Criteria:
  • Accurate and successful completion of problems from the textbook.
  • Reached set Target
Key Verbs
Define
Apply
Recognise
Calculate
Represent
Resources
Q Maths 11C