yr+9.5+quadratics


 * STUDENT PLANNER 2012 ** **__Topic: QUADRATIC ALGEBRA__** (Chapter 10) **NAME: _ ___**

identifying quadratic equations, quadratic trinomials, quadratic binomials, solving quadratic equations using the Null Factor Law, factorising quadratics, completing the square (extension) |||||| ** VOCABULARY: ** quadratic equations, like terms, expand, solve, null factor law, trinomials, binomials, factorised form, D.O.T.S, perfect squares, sum, product, grouping, factorise, || eso – every second one CAS – graphics calculator || ** Classroom Activities ** || ** Consolidation Tasks ** || ** Enrichment & Extension Activities ** || ** Homework ** || Students will identify which equations are ‘quadratic’ and which are not. In doing so, they will show their understanding of what a quadratic equation is.
 * ** In this topic you will explore the following concepts **
 * || // Abbreviations //
 * ** 1 ** || ** Learning Outcome – What is a Quadratic Equation? **

Students will use the Null Factor Law to solve quadratic equations || Worked Examples Pg 411 Ex 10B Q1abdegin Q4a || Pg 408 Ex 10A Q1 Puzzle 112
 * Learning Outcome - Solving Quadratic Equations **

There is a PowerPoint for simple ‘taking out a common factor’ and it can be accessed at http://drp.bo/?MGSCYr9Maths

Maths Online à Quadratic Equations à Factored Equations à worksheet

Puzzle 115 || Pg 411 Ex 10B Q5, Q6, Q7 || 30 minutes to Finish exercises, Puzzle 112 Puzzle 114, and review work || Students will recognise two specific patterns of algebraic expressions and use this knowledge to assist in factorising expressions. The two patterns are: - The ‘difference of two squares’ rule
 * ** 2 ** || ** Learning Outcome - Factorising and Expanding Patterns **

- The ‘perfect square’ rule || Notes & Worked Examples Pg 414 Ex 10C Q1, Q2, Q3, Q4, Q5, Q6

Pg 418 Ex 10D Q1abcdefgh, Q2abcdkl, Q4 || Maths Online à Algebra à Factorisation à Difference of Two Squares à worksheet || Pg 415 Ex 10C Q8, Q9 || 30 minutes to Finish Ex 10C, Ex 10D || Please view PowerPoint. Access it at [] || Puzzle 91 ||   || 30 minutes to catch up on exercises, worksheets and review work || Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form. || Worksheets: ‘Sums & products with directed numbers’ ‘Introducing Factorising Quad Trinomials’ ||  ||   || 30 minutes to catch up on exercises and review work || Students will apply the ‘sum and product’ method so that they can express quadratic trinomials in factor form. || Worksheets: Factorising QTs for monic quadrtics (a=1) Sheet 1 & Sheet 2 || Pg 421 Ex 10E Choose 7 questions || Pg 421 Ex 10E Q31
 * ** 3 ** || ** Catch up Lesson ** || Taking out a common factor review….
 * ** 4 ** || ** Learning Outcome - Factorising Quadratic trinomials **
 * ** 5 ** || ** Learning Outcome - Factorising Quadratic trinomials continued **

Puzzle 114 || 30 minutes to catch up on exercises and review work || Students will apply the process of ‘grouping 2 and 2’ so that they can express quadratic trinomials in factor form [Alternative method may also be explored] || Worksheets: Sheet 3 & Sheet 4 || Pg 424 Ex 10F Q1 Choose 3 questions Q2 Choose 3 questions || Puzzle 116 || 30 minutes to catch up on exercises and review work || Students will apply what they have learnt in the last 6 lessons to solve quadratic equations. || Pg 427 Ex 10G Q1 eso, Q2 eso, Q3 || Website [] || Pg 427 Ex 10G Q4, Q5
 * ** 6 ** || ** Learning Outcome - Factorising Quadratic trinomials **
 * ** 7 ** || ** Learning Outcome - Solving Quadratic equations with 3 terms **

‘Completing the Square’ worksheet || Start revising for the test. (30 minutes) || Students will convert sentences into math terms and then apply what they have learnt in this topic to solve worded problems. || Notes & Worked examples Pg 431-432 Ex 10I Q1, Q4, Q6, Q7, Q8, Q9, Q11 || || Pg 432 Ex 10I Q13, Q14
 * ** 8 ** || ** Learning Outcome - Applications using Quadratic equations **

Pg 438 Ex 10J || Chapter Review and Own Revision ||
 * ** 9 ** || ** Catch up lesson & Revision ** ||  ||   || Extension question || Own Revision ||
 * ** 10 ** || ** Assessment – Test ** ||  ||   ||   || Organise notebook, ready for next topic ||

__Extension Question for lesson 9__ Economics tells us that the cheaper an item the more items we will sell. Maddi is on a committee that is trying to raise money for World Challenge 2011 by selling traditional Moroccan craft items. Maddi needs to raise at least $800 for the Challenge. At $20 each, 30 craft items will be sold. For every $1 reduction in the price of the items, 5 more will be sold. In what price range should they be sold?
 * 1) Let the discount in the price of the craft items be //x//. The price of the items will be given by (20 − //x//). The number of items sold will be 30 + 5//x//. The income from sales will be given by the price × the number sold. Write an expression for the income.


 * 1) Maddi needs to raise at least $800 for the Challenge. Therefore, the income must equal $800. Form a quadratic equation by expanding (20 − //x//)(30 + 5//x//) = 800 and rewriting the equation in standard form.


 * 1) Factorise and solve the quadratic equation to find two prices between which the Moroccan craft items should be priced.


 * 1) Examine the equation in more detail to find the price at which the income will be greatest, and find what this maximum income is equal to.