1. We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately solve quadratic equations by completing the square. (Grades A-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. BRAIN IN GEAR Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills Work out the following Mathematical anagrams: TASK EXTENSION Develop your own Mathematical anagrams as above as a creative thinker. DURAATICQ NOETIFFICCE GEARERRAN EXAMPLE DITDIONA can be rearranged to make ADDITION Quadratic Coefficient Rearrange

3. Write in standard form: 57.6 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) 5) 4) 6) Solve: 2x + 5y = 15 3x - 2y = 13 Distance = 925miles Speed = 74mph Time = ……….minutes Write the bearing. Find the sum of one exterior angle in an regular decagon and one exterior angle in a regular hexagon? Area shaded black? 8m Work out the perimeter 15cm 8cm N 4cm =5.76x 10 1 = 925 74 =12.5hours 750 Area of circle – Area of triangle Π x r x r- 8 x 4 2 b x h 2 = 3.14 x 7.5 x 7.5 - = 176.625 - 16 = 160.6cm 2 075° 4x + 10y = 30 15x - 10y = 65 + 19x = 95 x = 5 10 + 5y = 15 5y = 5 y = 1 8m Π x d 4 + r = 3.14 x 16 4 + 8 = 28.56m Decagon → 360 10 =36° Hexagon → 360 6 =60°

4. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE EXAMPLE 1 ) ax + bx + c 2 = x + b 2 2 ( - b 2 ( ) 2 + c (a) Rewrite the following in the form (x a) b + - + - 2 x + 6x - 11 2 (b) x - 8x + 5 2 Write down the formula first (x + ) – ( ) + c b 2 b 2 2 2 b = 6c = -11 Substitute in the values for b and c ( x + 6 2 ) 2 – ( 6 2 ) 2 + - 11 ( x + 3 ) 2 – ( 3 ) 2 ( x + 3 ) 2 – 9 ( x + 3 ) 2 - 20 Write down the formula first (x + ) – ( ) + c b 2 b 2 2 2 b = -8c = 5 Substitute in the values for b and c ( x + -8 2 ) 2 – ( 2 ) 2 + 5 ( x - 4 ) 2 – ( -4 ) 2 + 5 ( x - 4 ) 2 – 16 + 5 ( x - 4 ) 2 - 11

5. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 1 (GRADE A) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE Rewrite the following in the form (x a) b + - + - 2 x + 4x - 2 2 x + 12x - 7 2 x - 6x + 5 2 x - 8x + 11 2 x + 2x - 9 2 x + 10x + 6 2 x - 14x - 12 2 x - 20x + 15 2

6. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE EXAMPLE 2 ) ax + bx + c 2 = x + b 2 2 ( - b 2 ( ) 2 + c Solve by completing the square. Leave your answer in the form a + - x - 6x – 3 = 0 2 b 2 Write down the formula first (x + ) – ( ) + c = 0 b 2 b 2 2 2 b = -6c = -3 Substitute in the values for b and c ( x + -6 2 ) 2 – ( 2 ) 2 + - 3 = 0 ( x - 3 ) 2 – ( -3 ) 2 = 0 ( x - 3 ) 2 – 9- 3 = 0 ( x - 3 ) 2 - 12 = 0 ( x - 3 ) 2 - 12 = 0 ( x - 3 ) 2 = 12 x - 3 = + - x = 3 + - 4 3 2 3

7. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 2 (GRADE A*) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE x + 2x – 5 = 0 2 x - 6x + 4 = 0 2 x + 10x + 7 = 0 2 x - 4x - 2 = 0 2 x + 12x + 3 = 0 2 x - 14x – 4 = 0 2 x - 2x - 7 = 0 2 x + 8x - 11 = 0 2 Solve the following by completing the square. Leave your answers in surd form.

8. 10 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE EXAMPLE 3 ) ax + bx + c 2 = x + b 2 2 ( - b 2 ( ) 2 + c Solve by completing the square. Give your answer to 2 decimal places. x + 2x – 9 = 0 2 2 Write down the formula first (x + ) – ( ) + c = 0 b 2 b 2 2 2 b = 2c = -9 Substitute in the values for b and c ( x + 2 2 ) 2 – ( 2 2 ) 2 + - 9 = 0 ( x + 1 ) 2 – ( 1 ) 2 - 9 = 0 ( x + 1 ) 2 – 1- 9 = 0 ( x + 1 ) 2 - 10 = 0 ( x + 1 ) 2 - 10 = 0 ( x +1 ) 2 = 10 x + 1 = + - x = + - x = +10x = -10 x = 2.16 x = -4.16

9. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 3 (GRADE A*) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE x + 2x – 3 = 0 2 x - 4x + 2 = 0 2 x + 10x + 12 = 0 2 x - 6x - 13 = 0 2 x + 10x + 15 = 0 2 x - 16x – 13 = 0 2 x - 2x - 21 = 0 2 x + 2x - 9 = 0 2 Solve the following by completing the square. Round your answers to 2d.p. where appropriate.

10. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION 1 (GRADE A*) 1) 2) 3) 5)6) 7) COMPLETING THE SQUARE Solve the following by completing the square. Leave your answers in surd form. 2x + 4x – 8 = 0 2 2x + 12x – 20 = 0 2 3x - 12x + 9 = 0 2 5x + 30x = 45 2 x + 3x – 2 = 0 2 x - 5x = -3 2 Divide by 2 throughout Divide by 3 throughout Divide by 5 and change RHS = 0 Make RHS = 0

11. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION 2 (GRADE A*) COMPLETING THE SQUARE Rearrange the following statements to give the complete solution, using the method of completing the square to the equation: ax + bx + c = 0 2 H, C, B, E, D, J, A, F, G, I

12. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Draw a 3 x 3 grid as shown below: Place any nine answers below into the grid (repeats forbidden) -8-3D6 -4.54 -2 A 2 B -9 -10 C 7 -50 3

13. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x + 4x + 5 = 0 2 (x + ?) + 1 = 0 2 2

14. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x + 14x + 48 = 0 2 (x + ?) - 1 = 0 2 7

15. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 6x - 16 = 0 2 (x + ?) - 25 = 0 2 -3

16. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Which is answer is correct in surd form: x + 4x + 3 = 0 2 A) x = -2 1 - + B) x = 2 1 - + C) x = -2 7 - + D) x = -2 7 - +

17. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 20x - 44 = 0 2 (x + ?) - 144 = 0 2 -10

18. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 16x + 64 = 0 2 (x + ?) = 0 2 -8

19. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Which is answer is correct in surd form: x - 8x + 7 = 0 2 C) x = 4 9 - + B) x = -4 9 - + A) x = -4 23 - + D) x = 4 23 - +

20. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 9x + 20 = 0 2 (x + ?) + 40.25 = 0 2 -4.5

21. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 8x + 18 = 0 2 (x - 4) + ? = 0 2 -2

22. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x + 4x + 7 = 0 2 (x + 2) + ? = 0 2 3

23. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Which is answer is correct in surd form: x - 4x - 12 = 0 2 C) x = -2 16 - + B) x = -2 8 - + A) x = 2 8 - + D) x = 2 16 - +

24. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x + 6x + 15 = 0 2 (x + 3) + ? = 0 2 6

25. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x + 12x + 27 = 0 2 (x + 6) + ? = 0 2 -9

26. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 18x + 31 = 0 2 (x - 9) + ? = 0 2 -50

27. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Which is answer is correct in surd form: x + 10x + 24 = 0 2 C) x = -5 1 - + B) x = 5 1 - + A) x = -5 -1 - + D) x = -5 49 - +

28. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 1 – BINGO COMPLETING THE SQUARE Find the value of ? below: x - 12x + 40 = 0 2 (x - 6) + ? = 0 2 4

29. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 2 – ASSESSING UNDERSTANDING Bogdar rewrites the expression x + px + q by completing the square. He correctly does this and gets (x – 7) – 52. What are the values of p and q? COMPLETING THE SQUARE 2 2 (x – 7) – 52 2 = (x – 7)(x – 7) – 52 = x 2 + 49 - 7x - 52 = x 2 - 14x - 3 p q p = -14 and q = -3

30. 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 completing the square. What grade are we working at?

31. PLENARY ACTIVITY 1 – CONNECT 4 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose.

32. PLENARY ACTIVITY 1 – CONNECT 4 ANSWERS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose. {-3, -1} {4, -2} {-2, 6} {8, -6} {-2, -10} {12, -4} {7, -9} {5, 3} {-3, -7} {3, -1} {-1, 5} {1.27, -17.27} {4.83, -6.83} {9.16, 2.84} {5.56, -7.56} {-1.28, -11.72} {11.52, -2.52} {-5.61, 1.61} {-7, 1} {-5.45, -0.55} {-1} {-3.41, -0.59} {-5.41, -2.59} {-8.36, 0.36} {-6.74, -0.74} {-2, 0} {-3.73, -0.27} {4.41, 1.59} {6.32, -0.32} {7.16, 0.84} {9, -1} {9.24, 0.76} {11.08, -1.08} {11.57, 0.43} {3.45, -1.45} {5.32, -1.32}

33. PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills (a) Find the values of a and b such that: COMPLETING THE SQUARE 1) x + 6x – 3 = (x + a) + b 2 2 (2 marks) (b) Hence, or otherwise, solve the equation: giving your answers in surd form. x + 6x – 3 = 0 2 (3 marks) (x + ) – ( ) + c = 0 b 2 b 2 2 2 b = 6c = -3 ( x + 6 2 ) 2 – ( 6 2 ) 2 + - 3 = 0 ( x + 3 ) 2 – ( 3 ) 2 - 3 = 0 ( x + 3 ) 2 – 9- 3 = 0 ( x + 3 ) 2 - 12 = 0 ab a = 3 and b = -12 ( x + 3 ) 2 - 12 = 0 12 ( x + 3 ) 2 - 12 = 0 ( x +3 ) 2 = 12 x + 3 = + - x = -3 + - 4x = + - 3 2 x = + - 3

34. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about solving quadratic equations by completing the square. 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?

35. . 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

36. 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

37. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 1 (GRADE A) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE Rewrite the following in the form (x a) b + - + - 2 x + 4x - 2 2 x + 12x - 7 2 x - 6x + 5 2 x - 8x + 11 2 x + 2x - 9 2 x + 10x + 6 2 x - 14x - 12 2 x - 20x + 15 2

38. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 2 (GRADE A*) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE x + 2x – 5 = 0 2 x - 6x + 4 = 0 2 x + 10x + 7 = 0 2 x - 4x - 2 = 0 2 x + 12x + 3 = 0 2 x - 14x – 4 = 0 2 x - 2x - 7 = 0 2 x + 8x - 11 = 0 2 Solve the following by completing the square. Leave your answers in surd form.

39. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK 3 (GRADE A*) 1) 2) 3) 4) 5) 6) 7) 8) COMPLETING THE SQUARE x + 2x – 3 = 0 2 x - 4x + 2 = 0 2 x + 10x + 12 = 0 2 x - 6x - 13 = 0 2 x + 10x + 15 = 0 2 x - 16x – 13 = 0 2 x - 2x - 21 = 0 2 x + 2x - 9 = 0 2 Solve the following by completing the square. Round your answers to 2d.p. where appropriate.

40. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION 1 (GRADE A*) 1) 2) 3) 5)6) 7) COMPLETING THE SQUARE Solve the following by completing the square. Leave your answers in surd form. 2x + 4x – 8 = 0 2 2x + 12x – 20 = 0 2 3x - 12x + 9 = 0 2 5x + 30x = 45 2 x + 3x – 2 = 0 2 x - 5x = -3 2

41. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION 2 (GRADE A*) COMPLETING THE SQUARE Rearrange the following statements to give the complete solution, using the method of completing the square to the equation: ax + bx + c = 0 2

42. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills MINI-PLENARY 2 – ASSESSING UNDERSTANDING Bogdar rewrites the expression x + px + q by completing the square. He correctly does this and gets (x – 7) – 52. What are the values of p and q? COMPLETING THE SQUARE 2 2

43. PLENARY ACTIVITY 1 – CONNECT 4 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills COMPLETING THE SQUARE Connect 4 counters in a horizontal, vertical or diagonal line by correctly completing the square of the sum you choose.

44. PLENARY ACTIVITY 2 – GRADE A* EXAM QUESTION Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills (a) Find the values of a and b such that: COMPLETING THE SQUARE 1) x + 6x – 3 = (x + a) + b 2 2 (2 marks) (b) Hence, or otherwise, solve the equation: giving your answers in surd form. x + 6x – 3 = 0 2 (3 marks)