1. We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately solve quadratic equations by using the quadratic formula. (Grade A) Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curricular links? www.mistrymaths.co.uk

2. LEARNING JOURNEY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills

3. STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION TASK 1) 2) 3) 4) Factorise: 16y 2 + 20y 5) Factorise and simplify: x 2 + 4x – 5 x 2 + 5x – 6 6) Solve Factorise: x 2 – 5x – 14 Factorise: x 2 – 10x + 24 Factorise: h 2 – 81 Factorise and simplify: x 2 – 25_ x 2 + 5x 2x 2 – 32 = 0 = 4y(4y + 5)= (x – 7)(x + 2) = (x – 4)(x – 6) = (h + 9)(h - 9) = (x + 5)(x - 1) (x + 6)(x - 1) = x + 5 x + 6 = (x + 5)(x - 5) x(x + 5) = x - 5 x ÷ 2 x 2 – 16 = 0 (x + 4)(x – 4) = 0 x = -4 or x = 4

4. X = Which ones are you using? Quadratic Formula Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills EXAMPLES Solve the following equations by using the quadratic formula: (b) (a)2x 2 + 3x - 20 = 0 5x 2 - 11x - 4 = 0 a = 2b = 3 b 2 QUADRATIC FORMULA x = -b + - - 4ac 2a c = -20 X = - 3 - + 3 2 - 4 x 2 x -20 2 x 2 X = - 3 - + 9 + 160 4 X = - 3 - + 169 4 X = - 3 + 169 4 X = 2.5 OR X = - 3 - 169 4 X = - 4 a = 5b = -11c = -4 - -11 - + (-11) 2 - 4 x 5 x -4 2 x 5 11 - + 121 + 80 10 11 - + 201 10 X = 11 + 201 10 X = 2.52 (2d.p.) OR X = 11 - 201 10 X = - 0.32 (2d.p.)

5. Quadratic Formula Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 1 (GRADE A) 1) Solve the following using the quadratic formula: (a) (b) (c)(d) 1 5 3 5 5 13 1 5 13 2 -0.70 -4.30 1 9 -2 9 9 1 1 9 89 2 0.22-9.22 2 3 -5 3 3 2 2 3 49 4 1 -2.5 3 8 8 8 3 3 8 76 6 0.12 -2.79

6. Quadratic Formula Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 2 (GRADE A) EXTENSION (GRADE A) 1) Solve the following using the quadratic formula: a)2x + x - 8 = 0 b) 3x + 5x + 1 = 0 c) x - x − 10 = 0 d) 5x + 2x - 1 = 0 e) 7x + 12x + 2 = 0 f) 3x + 11x + 9 = 0 g) 4x + 9x + 3 = 0 h) 6x + 22x + 19 = 0 i) x + 3x – 6 = 0 j) 3x - 7x + 1 = 0 2 2 2 2 2 2 2 2 2 2 x = 1.77 or x = -2.27 x = -0.23 or x = -1.43 x = 3.7 or x = -2.7 x = 0.29 or x = -0.69 x = -0.19 or x = -1.53 x = -1.23 or x = -2.43 x = -0.41 or x = -1.84 x = -1.39 or x = -2.27 x = 1.37 or x = -4.37 x = 2.18 or x = 0.15 k) 2x + 11x + 4 = 0 l) 4x + 5x - 3 = 0 m) 4x - 9x + 4 = 0 n) 7x + 3x - 2 = 0 o) 5x - 10x + 1 = 0 2 2 2 2 2 x = -0.39 or x = -5.11 x = 0.44 or x = -1.69 x = 1.64 or x = 0.61 x = 0.36 or x = -0.79 x = 1.89 or x = 0.11 1) Mavis is solving a quadratic equation using the quadratic formula. She correctly substitutes in values for a, b and c to get: What is the equation Mavis is trying to solve? 2) Junior uses the quadratic formula to solve: Sienna uses factorisation to solve: They both find something unusual in their solutions. Explain what this is. x 2 - 3x - 7 = 0

7. 23 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY – SPOT THE MISTAKES Quadratic Formula The student has solved the equation using the quadratic formula. Find the mistakes below: 4x 2 - 5x - 3 = 0 a = 4b = -5c = -3 X = - 5 - + (-5) 2 - 4 x 4 x -3 2 x 4 -5 - + -25 + 48 6 -5 - + 6 X = -5 + 23 6 X = -0.03 (2d.p.) OR X = -5 - 23 6 X = - 1.63 (2d.p.)

8. DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately solve quadratic equations by using the quadratic formula. What grade are we working at?

9. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY 1 – EXAM QUESTION (GRADE A) Solve the equation Quadratic Formula 4x 2 - 5x - 3 = 0 Give your answer correct to two decimal places. You must show your working. (3 marks) X = a = 4b = -5 c = -3 - -5 - + (-5) 2 - 4 x 4 x -3 2 x 4 5 - + 25 + 48 8 5 - + 73 8 X = 5 + 73 8 X = 1.69 (2d.p.) OR X = 5 - 73 8 X = - 0.44 (2d.p.)

10. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY 2 – DISCRIMINANT (GRADE A*) Quadratic Formula Find the discriminant b - 4ac of the equation and explain what the result tells us 2 x 2 + 3x + 5 = 0 b - 4ac 2 a = 1 b = 3 c = 5 = 3 2 -4 x 1 x 5 = 9 - 20 = - 11

11. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about using the quadratic formula to solve equations. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?

12. . How well do you understand the task? I don’t understand I nearly understand I fully understand Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? SELF ASSESSMENT Plenary Activity www.mistrymaths.co.uk

13. SELF ASSESSMENT Plenary Activity On your post it notes… Think about how you can improve your work. On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If) Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? www.mistrymaths.co.uk