John Curtin 2018 AO.docx
MATHEMATICS DEPARTMENT 2018
Year: 11 SPECIALIST MATHEMATICS Course: AEMAS (Unit 1 and Unit 2)
Textbook: Maths Specialist Unit 1 & 2 (Sadler) Revision Series: Maths Specialist Unit 1 & 2 (O.T. Lee)
SEMESTER 1 (Unit 1)
Term 1 2018
| Term1 | Weekcommencing | Syll ref | Topic | Chapter/Topic | Assess- ments |
| Topic 1.1: Combinatorics (and parts of Topic 1.3 Geometry) | |||||
| The nature of proof & The pigeon-hole Principle | |||||
| 1 | 29 Jan | 1.1.61.3.11.3.21.3.31.3.41.3.5 | solve problems and prove results using the pigeon-hole principleuse implication, converse, equivalence, negation, inverse, contrapositiveuse proof by contradictionuse the symbols for implication (⇒), equivalence (⇔)use the quantifiers ‘for all’ ∀ and ‘there exists’ ∃use examples and counter-examples | Chapter 1OTL 4 | |
| Permutations (ordered arrangements) | |||||
| 2 | 5 Feb | 1.1.11.1.21.1.31.1.4 | solve problems involving permutations use the multiplication and addition principleuse factorial notation and solve problems involving permutations involving restrictions with or without repeated objects | Chapter 2OTL 1, 2, 3 | |
| The inclusion-exclusion principle for the union of two & three sets | |||||
| 3 | 12 Feb | 1.1.5 | determine and use the formulas for finding the number of elements in the union of two and three sets | Chapter 2OTL 1, 2, 3 | |
| Combinations (unordered selections) | |||||
| 4 | 19 Feb | 1.1.71.1.81.1.9 | solve problems involving combinationsuse the notation nr or nCrderive and use associated simple identities associated with Pascal’s triangle | Chapter 2OTL 1, 2, 3 | Test 1 (5%) |
| Topic 1.2: Vectors in the plane | |||||
| Representing vectors in the plane by directed line segments | |||||
| 5 | 26 Feb | 1.2.11.2.2 | examine examples of vectors, including displacement and velocitydefine and use the magnitude and direction of a vector | Chapter 3OTL 5, 6, 7, 8 | |
| 6 | 5 MarchMonday Labour Day | 1.2.31.2.4 | represent a scalar multiple of a vectoruse the triangle and parallelogram rules to find the sum and difference of two vectors | Chapter 3OTL 5, 6, 7, 8 | Inv 1 (6%) |
| Term1 | Weekcommencing | Syll ref | Topic | Chapter/Topic | Assess- ments |
| Algebra of vectors in the plane & Circle properties, including proof and use | |||||
| 7 | 12 March | 1.2.51.2.61.2.71.2.81.2.9 | use ordered pair notation and column vector notation to represent a vectordefine unit vectors and the perpendicular unit vectors i and jexpress a vector in component form using the unit vectors i and jexamine and use addition and subtraction of vectors in component formdefine and use multiplication of a vector by a scalar in component form | Chapter 4OTL 5, 6, 7, 8 | |
| Topic 1.3: Geometry (and parts of Topic 1.2: Vectors in the plane) | |||||
| 8 | 19 March | 1.3.61.3.71.3.81.3.91.3.101.3.111.3.12 | an angle in a semicircle is a right anglethe size of the angle at the centre subtended by an arc of a circle is twice the size of the angle at the circumference subtended by the same arcangles at the circumference of a circle subtended by the same arc are equalthe opposite angles of a cyclic quadrilateral are supplementarychords of equal length subtend equal angles at the centre, and conversely, chords subtending equal angles at the centre of a circle have the same lengththe angle in the alternate segment theoremwhen two chords of a circle intersect, the product of the lengths of the intervals on one chord equals the product of the lengths of the intervals on the other chord | Chapter 5OTL 16 | |
| 9 | 26 MarchFridayGood Friday | 1.3.131.3.141.3.15 | when a secant (meeting the circle at A and B) and a tangent (meeting the circle at T) are drawn to a circle from an external point M, the square of length of the tangent equals the product of the lengths to the circle on the secant(AM × BM = TM2)suitable converses of some of the above resultssolve problems determining unknown angles and lengths and prove further results using the results listed above | Chapter 5OTL 16 | Test 2 (7%) |
| 10 | 2 AprilMondayEaster Mon | 1.2.14 | solve problems involving displacement, force and velocity involving the above concepts | Chapter 6OTL 9,10,11 | |
| Geometric vectors in the plane including proof and use | |||||
| 11 | 9 April | 1.3.161.3.171.3.18 | the diagonals of a parallelogram intersect at right angles if, and only if, it is a rhombus,the midpoints of the sides of a quadrilateral join to form a parallelogram, the sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides | Chapter 7OTL 15 | Inv 2(7%) |
| END OF TERM 1 |
Term 2 2018
| Term2 | Weekcommencing | Topic | Reference:Chapter/Topic | Assess-ment | |
| Algebra of vectors in the plane | |||||
| 1 | 30 April | 1.2.101.2.11 | define and use scalar (dot) productapply the scalar product to vectors expressed in component form | Chapter 8OTL 12, 13, 14 | |
| 2 | 7 May | 1.2.121.2.13 | examine properties of parallel and perpendicular vectors and determine if two vectors are parallel or perpendiculardefine and use projection of vectors | Chapter 8OTL 12, 13, 14 | |
| 3 | 14 May | Revision | Test 3 (7%) | ||
| 4 | 21 May | Revision | |||
| 5 | 28 May | SEMESTER ONE EXAMINATION | |||
| 6 | 4 June |
| SEMESTER 2 (Unit 2) | |||||
| Topic 2.1: Trigonometry | |||||
| MODULE 1: Compound angles & Compound angles & The basic trigonometric functions | |||||
| 7 | 11 June | 2.1.52.1.3 | prove and apply the Pythagorean identitiesprove and apply the angle sum, difference, and double angle | Chapter 9OTL 17-24 | Mon West Australia Day |
| MODULE 2: Trigonometric identities & The reciprocal functions, secant, cosecant and cotangent | |||||
| 8 | 18 June | 2.1.72.1.42.1.62.1.8 | convert sums a cos x +b sin x to R cos(x±α) or R sin(x±α) and apply these to sketch graphs; solve equations of the form a cos x +b sin x=cdefine the reciprocal trigonometric functions; sketch their graphs and graph simple transformations of themprove and apply the identities for products of sines and cosines expressed as sums and differencesprove and apply other trigonometric identities | Chapter 9OTL 17-24 | |
| The basic trigonometric functions & Applications of trigonometric functions to model periodic phenomena | |||||
| 9 | 25 June | 2.1.12.1.22.1.9 | determine all solutions of f(a(x−b))=c where f is one of sine, cosine or tangentgraph functions with rules of the form y=f(a(x−b))+c where f is one of sine, cosine, or tangentmodel periodic motion using sine and cosine functions and understand the relevance of the period and amplitude of these functions in the model | Chapter 9OTL 17-24 | Inv 3(7%) |
Term 3 2018
| Term 3 | Weekcommencing | Topic | Reference:Chapter/Topic | Assess-ment | |
| Topic 2.2: Matrices | |||||
| Matrix arithmetic | |||||
| 1 | 16 July | 2.2.12.2.22.2.3 | apply matrix definition and notation define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity, and inversecalculate the determinant and inverse of 2 × 2 matrices and solve matrix equations of the form AX = B, where A is a 2 × 2 matrix and X and B are column vectors | Chapter 10OTL 25 | Test 4 (7%) |
| Systems of linear equations | |||||
| 2 | 23 July | 2.2.11 | interpret the matrix form of a system of linear equations in two variables and use matrix algebra to solve a system of linear equations | Chapter 10OTL 26, 27 | |
| Transformations in the plane | |||||
| 3 | 30 July | 2.2.42.2.52.2.62.2.7 | examine translations and their representation as column vectors define and use basic linear transformations: dilations of the form (x,y) ->(λ 1 x, λ 2 y), rotations about the origin and reflection in a line that passes through the origin and the representations of these transformations by 2 × 2 matrices apply these transformations to points in the plane and geometric objects define and use composition of linear transformations and the corresponding matrix products | Chapter 11OTL 28 | |
| 4 | 6 Aug | 2.2.82.2.92.2.10 | define and use inverses of linear transformations and the relationship with the matrix inverse examine the relationship between the determinant and the effect of a linear transformation on area establish geometric results by matrix multiplications; for example: show that the combined effect of 2 reflections is a rotation | Chapter 11OTL 28 | |
| Topic 2.3: Real and complex numbers | |||||
| Proofs involving numbers & Rational and irrational numbers | |||||
| 5 | 13 Aug | 2.3.12.3.22.3.3 | prove simple results involving numbersexpress rational numbers as terminating or eventually recurring decimals and vice versaprove irrationality by contradiction for numbers such as | Chapter 12OTL 30 | Test 5 (7%) |
| An introduction to proof by mathematical induction | |||||
| 6 | 20 Aug | 2.3.42.3.52.3.6 | develop the nature of inductive proof, including the ‘initial statement’ and inductive step prove results for sums, such as for any positive integer nprove divisibility results, such as is divisible by 5 for any positive integer n | Chapter 12OTL 30 | |
| Complex numbers | |||||
| 7 | 27 Aug | 2.3.72.3.82.3.92.3.10 | define the imaginary number i as a root of the equation x2=-1represent complex numbers in the rectangular form; a + bi where a and b are the real and imaginary parts determine and use complex conjugates perform complex number arithmetic: addition, subtraction, multiplication and division | Chapter 13OTL 29 | |
| The complex plane | |||||
| 8 | 3 Sep | 2.3.112.3.122.3.13 | consider complex numbers as points in a plane, with real and imaginary parts, as Cartesian coordinates examine addition of complex numbers as vector addition in the complex planedevelop and use the concept of complex conjugates and their location in the complex plane | Chapter 13OTL 29 | |
| Roots of equations | |||||
| 9 | 10 Sept | 2.3.142.3.152.3.16 | use the general solution of real quadratic equationsdetermine complex conjugate solutions of real quadratic equations determine linear factors of real quadratic polynomials | Chapter 13OTL 29 | |
| 10 | 17 Sept | Revision | Test 6(7%) | ||
| Term 4 | Weekcommencing | Topic | Reference:Chapter/Topic | Assess-ment | |
| 1 | 8 Oct | Revision | |||
| 2 | 15 Oct | SEMESTER TWO EXAMINATIONS | |||
| 3 | 22 Oct | SEMESTER TWO EXAMINATIONS | |||
Mathematics Specialist: Assessment Outline: Year 11, 2018
| Item | Type | Topic | Year weighting | Approximate timing |
| Test 1 | Response | Combinatronics & Geometry1.3.1-1.3.5, 1.1.1-1.1.9 | 5% | Term 1, Week 4 |
| Investigation 1 | Investigation | Combinatonics | 6% | Term 1, Week 6 |
| Test 2 | Response | Vectors & Geometry1.2.1-1.2.9, 1.3.6-1.3.15 | 7% | Term 1, Week 9 |
| Investigation 2 | Investigation | Vectors/Geometry | 7% | Term 1, Week 11 |
| Test 3 | Response | Geometry & Vectors1.2.10-1.2.14, 1.3.16-1.3.18 | 7% | Term 2, Week 3 |
| Semester 1 Examination | Examination | Unit 1 | 16% | Term 2, Week 5/6 |
| Totals | 48% | |||
| Investigation 3 | Investigation | Trigonometry | 7% | Term 2, Week 9 |
| Test 4 | Response | Trigonometry2.1.1-2.1.9 | 7% | Term 3, Week 1 |
| Test 5 | Response | Matrices2.2.1-2.2.10 | 7% | Term 3, Week 5 |
| Test 6 | Response | Real and Complex numbers2.3.1-2.3.16 | 7% | Term 3, Week 10 |
| Semester 2 Examination | Examination | Unit 1 & 2 | 24% | Term 4, Week 2/3 |
| Totals | 52% |
Types: Relative to time allocation
Response 40% 1. Combinatorics 10% 4.Trigonometry 15%
Investigation 20% 2. Vectors 20% 5. Matrices 17%
Examination 40% 3. Geometry 20% 6. Real and Complex nos. 18%