Mr Nguyen VCE Maths Methods 11

Objective: to visualise odd and even functions. to prove odd and even functions using function notation/substitution.

Objective: to identify the different representations of quartic function; factorise and sketch these graphs

objectives: given a graph, find the equation of the cubic function. given an equation with unknowns 'a' and 'b' and a point (x,y), find the equation. click on the link to explore these cubic graphs y=ax^3  y=a(x-h)^3 +k y=a(x-b)(x-c)(x-d) y=ax^3+bx^2+cx+d y=a(x-b)(x-c)^2 question 9a) question 2

objective: able to sketch three types of cubic functions, and solve the inequalities equation.

objective: to recognise the general equation of cubic graphs where a is the dilation factor from the x-axis and (h,k) is the point of inflection

Objectives: similar to ex 6C, we need to factorise the cubic equation and apply the Null Factor Law learned in chapter 3-Quadratics.  Case 1: factors form. Use Null factor loaw Case 2: groupings- factorise the first two terms, factor out the common factor, and finally null factor law case 3: apply factor theorem, long division, cross method and finally null factor law

Here, you will learn how to factorise polynomials of degree 3 and above. In chapter 3, you've learned how to factorise quadratic equations using a variety of techniques. These were: cross method, common factors, completing the square, the quadratic equation. However, when it comes to polynomials of higher power, those strategies don't apply to it. In this exercise, we will learn about the Remainder Theorem and the Factor theorem. These two provide the foundation for factorising polynomials. You will also need to be strong in long division in the previous exercise in order to be successful in this section.

objective: - to be able to divide two polynomials using the Long Division method with and without a remainder - to be able to divide two polynomials using the Synthetic division method with and without a remainder notes: Practice: Exercise 6B questions 1-7                                                              homework: Excel unit 5 Tutorial videos Long division long division with divisor = polynomial degree >1 long division when divisor is (ax+b) synthetic division of polynomials 

Objective:  -recognize and identify polynomial functions -able to perform arithmetic operations for polynomials Task 1: write the notes Task 2: Practice questions 6A- 2,5,6,7              Homework: Excel sheet 1,2,3,4

Objectives: >Identify the general equation of circles >identify the centre (h,k) and the radius >sketch the circle relation >advanced: applying Complete the square method to factorise the circle relation Task 1: click here explore how the values of (h,k) influences the centre of the circle explore how the value 'r' influences the shape of the circle Task 2: click here What is the centre of this circle? what is the radius of this circle? Can you rewrite the relation into the general circle equation? What method could we use? Notes:

Task 1:  circle patterns click here In this activity, students notice similarities and differences in a set of circles. They use this information to practice writing equations of circles that extend a given pattern or match a given set of conditions. Task 2: domain and range click here This activity will encourage student creativity while also helping them review a) function inequalities, and b) domain and range restrictions.

Objectives identify the equation of the square root relation identify the dilation factor and the translation factors recognize the shape of the relation and its reflection in both x and y axis Exercise 4C: Q1,2 Task 1: Investigating the variables a,h,k click here Play around with the variables and answer the following questions in your book Describe the graph graph when you increase and decrease 'a' Describe the graph graph when you change 'h' and 'k' what conclusion can you make about the coordinate (h,k) from the equation Task 2: Investigating the reflection of the graph in x-y axis click here Play around with the variables and answer the following questions in your book Describe the graph when 'a' is negative Describe the graph the graph when 'b' is negative Describe the graph when both 'a' and 'b' are negative Describe the graph when you change 'b' Task 3: Investigating dilation fa...

Objectives: identify the equation of a truncus identify the dilation factor, horizontal and vertical asymptotes of a truncus recognise the shape of a truncus Task 1:  click here Play around with 'a','h,' and 'k'. Write down how the variables change the overall shape of the graph as you increase and decrease (negative) it.  Task 2: Take notes Task 3: Read the examples and attempt question 1, 3

Objectives: investigate the graph of a hyperbola including the dilation factor, vertical and horizontal asymptotes by exploring Desmos watch the tutorial video on how to sketch the graphs Read the examples 1,2 Task 1: Click here Play around with the variables a, h, k. In your book: Explain what happens to the graph as you increase and decrease these variables Task 2: Copy the notes Task 3: Read example 1. Attempt question 1. page 149.