Irene Mccormack Catholic College s3

Irene McCormack Catholic College

Mathematics Learning Area

Year 10 Specialist Ellective

Program 2017

Resource Materials Mathspace Excel Year 10 Extension Casio Classpad Calculator Other Mathematics Department Resources (provide as required)

Assessments

SEMESTER 1

TESTS (3) 20%

INVESTIGATIONS (2) 10%

RESEARCH PROJECT 5%

SEMESTER EXAM 15%

SEMESTER 2

TESTS (3) 20%

INVESTIGATIONS (2) 10%

RESEARCH PROJECT 5%

SEMESTER EXAM 15%

TOTAL 100% Week Content Resources Assessments

Geometry

Term 1  Review Geometric Terms and concepts Mathspace tasks  Geometric construction 1-4  Proofs Cornerstone 10 Solve problems involving parallel and perpendicular lines Chapter 5 (ACMNA238) Formulate proofs involving congruent triangles and angle properties Pearson 10-10A (ACMMG243) Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)

Circles

5-8  Properties and terms of Circles Test 1 (Week 5)  Area of sector & segment Mathspace tasks determine areas of sectors and segments in circles using exact and Investigation approximate values as appropriate Excel 9 & 10 -Angles in  Arc length Circles determine arc lengths in circles, exactly and approximately Pearson 9 &10- (Week 6)  Latitude & longitude 10A solve practical problems including navigation distances along circles of constant latitude or constant longitude on the surface of the Earth. Salder MAS 3AB  Angles in Circles Prove and apply angle and chord properties of circles (ACMMG272)

Factor and Remainder Theorem

9-10  Review factorising polynomials Mathspace tasks Test 2 (Week Factorise monic and non-monic quadratic expressions and solve a wide 10) Term 2 range of quadratic equations derived from a variety of contexts Excel Extension (ACMNA269) 10 1 Research  Solve polynomials Investigate the concept of a polynomial and apply the factor and Pearson 10-10A Assignment – remainder theorems to solve problems (ACMNA266) Mathematics in Sadler Intro Calc. the Medical or Engineering Industry. Unit Circle and Radian Measure

2-5  Introduce the unit circle to determine sine, cosine and tangent Mathspace tasks Investigation – values. Unit Circle Use the unit circle to define trigonometric functions, and graph them Excel Extension (Week 2) with and without the use of digital technologies (ACMMG274) 10  Convert degrees to radians and radians to degrees. Test 3 (Week establish the relationship between radian measure and degree measure Pearson 10-10A 5/6) of angles and convert from one measure to the other  Use the unit circle to solve trigonometric equations. Sadler MAT 3AB Solve simple trigonometric equations (ACMMG275) Sadler MAS 3AB

6 Revision  How to study for a Maths Exam  Study skills and strategies (Revisit those discussed and used throughout the semester).  Past examination style questions.

7-8 Exam

Polar Coordinates and Graphs

9-10  What is a Polar Coordinate? Mathspace tasks Investigation – develop the concept of polar coordinates (r,) in the plane, where r  0 Polar Graphs  Convert between Cartesian and Polar. Sadler MAS 3AB use the relationship between Cartesian and polar coordinates in the plane to convert from one system to the other.

Introduction to Vectors

Term 3  What is a Vector? Mathspace tasks Test 4 – (Week distinguish between vector and scalar quantities 1-6 5)  Vector notation. Sadler MAS 3AB represent a directed line segment in the plane with magnitude and Investigation - direction using vector notation  Special Vectors Vectors develop the concept of equality of vectors, opposite vectors, unit vectors and the zero vector  Scalar Multiples and Division multiply a vector by a scalar and subdivide line segments internally  Solve basic problems involving vectors.

Logarithms

7-10  Revise index laws Mathspace tasks Research Simplify algebraic products and quotients using index laws (ACMNA231) Assignment –  Indroduce logarithms as the inverse of an exponential equation. Excel Extension Careers with  Logarithmic Laws 10 Tertiary Use the definition of a logarithm to establish and apply the laws of Mathematics. logarithms (ACMNA265) Pearson 10-10A Test 5 – Week Sadler MAS 3AB 10

Functions & Limits

Term 4  Review of basic Funtions Mathspace tasks Test 6 (Week Explore the connection between algebraic and graphical 5/6) 1-5 representations of relations such as simple quadratics, circles and Sadler MAS 3AB exponentials using digital technology as appropriate (ACMNA239) Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267) Solve simple exponential equations (ACMNA270)  Function Notation  What is a Function? v What is a Relation? develop the concept of function composition and obtain expressions for the composites of simple functions  Domain and Range develop the concept of function composition and obtain expressions for the composites of simple functions  Limiting behaviour of Functions. Introduce the concept of a limit. What happens to a function as it approaches , zeros, asymptotes.

6 Revision 7-8 Exams