# Year 11 – 10: Quadratic and other Polynomials – South Australia

### SA Year 11 – 10: Quadratic and other Polynomials

# | TOPIC | TITLE | |
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1 | Study Plan | Study plan – Year 11 – 10: Quadratic and other Polynomials | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Factors by grouping | Factors by grouping. | |

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||

3 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

4 | Common fact and diff | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||

5 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

6 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

7 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

8 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |

Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

9 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||

10 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||

11 | Surds | Binomial expansions | |

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. | |||

12 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

13 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

14 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

15 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

16 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

17 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

18 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

19 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

20 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

21 | Quadratic equations | Problem solving with quadratic equations | |

Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||

22 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||

23 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||

24 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||

25 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||

26 | Graphing roots | Graphing irrational roots | |

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational. | |||

27 | Coordinate geometry | Solve by graphing | |

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||

28 | Graphing-polynomials | Graphing complex polynomials: quadratics with no real roots | |

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. | |||

29 | Sum/diff 2 cubes | Sum and difference of two cubes. | |

Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them. | |||

30 | Graphing-cubic curves | Graphing cubic curves | |

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||

31 | Logarithms-Complex numbers | Imaginary numbers and standard form | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction. | |||

32 | Logarithms-Complex numbers | Complex numbers – multiplication and division | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division. | |||

33 | Logarithms-Complex numbers | Plotting complex number and graphical representation | |

Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers. | |||

34 | Algebra-polynomials | Introduction to polynomials | |

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||

35 | Algebra-polynomials | The sum, difference and product of two polynomials. | |

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||

36 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

37 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

38 | Remainder theorem | More on remainder theorem | |

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||

39 | Factor theorem | The factor theorem | |

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||

40 | Factor theorem | More on the factor theorem | |

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||

41 | Factor theorem | Complete factorisations using the factor theorem | |

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||

42 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

43 | Graphs, polynomials | Graphs of polynomials | |

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||

44 | Roots quad equations | Sum and product of roots of quadratic equations | |

Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots. | |||

45 | Roots quad equations | Sum and product of roots of cubic and quartic equations | |

Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations. | |||

46 | Approx roots | Methods of approximating roots | |

Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question. | |||

47 | Newton’s approx | Newton’s method of approximation | |

Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method. | |||

48 | Exam | Exam – Year 11 – 10: Quadratic and other Polynomials | |

Objective: Exam |