PLC Papers Created For:

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1 PLC Papers Created For: Quadratics intervention

2 Deduce quadratic roots algebraically 1 Grade 6 Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 Question 2. a) Factorise x 2 13x + 36 b) Hence, or otherwise, solve the equation x 2 13x + 36 = 0 (2) (1)

3 Question 3. Solve the equation 2x 2 6x -1 = 0 Give your answers to two decimal places. You must show your working. (Total 4 marks) Total /10

4 Factorising quadratic expressions 1 Grade 5 Objective: Factorise a quadratic expression of the form ax 2 + bx + c including the difference of two squares Question 1. Factorise the expression x 2-6 x + 5 Question (Total 2 mark) Factorise the expression x 2 - x - 12 Question 3... (Total 2 mark) Factorise the expression x x + 30 Question 4... (Total 2 mark) Factorise the expression x (Total 2 mark) Question 5 Factorise the expression x 2-49y 2... (Total 2 mark) Total marks / 10

5 Factorising difficult quadratic expressions 1 Grade 7 Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2 +10x+16 (2 Marks) Question 2 Factorise 3x 2 +11x+6 (3 Marks) Question 3 Factorise 4x 2-16 (2 Marks) Question 4 Factorise 4x 2-15x-4 (3 Marks) Total marks / 10

6 Quadratic equations (factorisation) 1 Grade 6 Objective: Solve quadratic equations by factorising. Question 1. Solve: a) = 0 b) = 0 (1) (1) c) = 0 (1) d) 2 25 = 0 (1) (Total 4 marks)

7 Question 2. Solve ( + 5) = 24 Question 3. Solve by factorising = 0 TOTAL /10

8 Quadratic equations (graphical methods) 1 Grade 6 Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = for values of x from 5 4. Plot the graph using 5 4 and b) Use your graph to estimate the solutions of the two roots of =0

9 Question 2. a) Complete the table below to work out values for the graph of = for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when =1.5

10 Question 3. a) Using suitable axes draw the graph of = for 2 5 b) What is the value of when = 0.5 c) For what values of x does 2 4 2= 4 (Total 4 marks) TOTAL /10

11 Quadratic equations (quadratic formula) 1 Grade 7 Objective: Solve quadratic equations by using the quadratic equation formula. Question 1. Solve = 0. Give your answer to 2 decimal places. = or = Question 2. Solve = 0. Give your answer to 3 significant figures. = or =

12 Question 3. Solve 2 ( 3) = 10 Leave your answer in surd form. = (Total 4 marks) TOTAL /10

13 PLC Papers Created For: Quadratics intervention

14 Deduce quadratic roots algebraically 1 Grade 6 Solutions Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 (x 5) (x - 3) = 0 (M1) x = 5 x = 3 Question 2. a) Factorise x 2 13x + 36 (x 9)(x 4) (M2) b) Hence, or otherwise, solve the equation x 2 13x + 36 = 0 (2) (x 9)(x 4) = 0 x = 9 x = 4 (1)

15 Question 3. Solve the equation 2x 2 6x -1 = 0 Give your answers to two decimal places. You must show your working. a =2; b = -6 c = -1 x = 6 ± ( 6)2 (4 2 1) ± (36+8) x = 4 +6 ± (44) x = (M1) 4 x = 3.16 x = (M1) (Total 4 marks) Total /10

16 Factorising quadratic expressions 1 Grade 5 Solutions Objective: Factorise a quadratic expression of the form ax 2 + bx + c including the difference of two squares Question 1. Factorise the expression x 2-6 x + 5 Question 2. Factorise the expression x 2 - x - 12 (x-1)(x-5) (x-4)(x+3)... (Total 2 mark) Question 3... (Total 2 mark) Factorise the expression x x + 30 Question 4 Factorise the expression x 2-81 (x + 10)(x + 3) (x+9)(x-9)... (Total 2 mark)... (Total 2 mark) Question 5 Factorise the expression x 2-49y 2 (x+7y)(x-7y)... (Total 2 mark) Total marks / 10

17 Factorising difficult quadratic expressions 1 Grade 7 Solutions Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2 +10x+16 (x+8)(x+2) A2 (2 Marks) Question 2 Factorise 3x 2 +11x+6 = 3x 2 +9x+2x+6 M1 = 3x(x+3) + 2(x+3) M1 = (3x+2)(x+3) A1 (3 Marks) Question 3 Factorise 4x 2-16 = 4(x 2-4) M1 = 4(x+2)(x-2) A1 (2 Marks) Question 4 Factorise 4x 2-15x-4 = 4x 2-16x+x-4 M1 = 4x(x-4) + (x-4) M1 = (4x+1)(x-4) A1 (3 Marks) Total marks / 10

18 Quadratic equations (factorisation) 1 Grade 6 SOLUTIONS Objective: Solve quadratic equations by factorising. Question 1. Solve: a) = 0 ( + 9)( + 6) = 0 = 9 = 6 b) = 0 ( 7)( + 5) = 0 = 7 = 5 (1) (1) c) = 0 ( 4)( 7) = 0 = 4 = 7 (1) d) 2 25 = 0 ( + 5)( 5) = 0 = 5 = 5 (1) (Total 4 marks)

19 Question 2. Solve ( + 5) = = 0 (M1) ( + 8)( 3) = 0 (M1) = 8 = 3 Question 3. Solve by factorising = 0 (2 + 3)( + 5) = 0 (M2) = 3 2 = 5 TOTAL /10

20 Quadratic equations (graphical methods) 1 Grade 6 Solutions Objective: Find approximate solutions to quadratic equations using a graph Question 1. a) Complete the table below to work out values for the graph of = for values of x from 5 4. Plot the graph using 5 4 and b) Use your graph to estimate the solutions of the two roots of = (A1

21 Question 2. a) Complete the table below to work out values for the graph of = for values of x from 2 4 then draw the graph. b) Use your graph to find the y-value when = < < 5.5

22 Question 3. a) Using suitable axes draw the graph of = for 2 5 b) What is the value of when = c) For what values of x does = and (Total 4 marks) TOTAL /10

23 Quadratic equations (quadratic formula) 1 Grade 7 SOLUTION Objective: Solve quadratic equations by using the quadratic equation formula. Question 1. Solve = 0. Give your answer to 2 decimal places. = 8± (M1) = or = = 1.18 or = 3.18 (A2) = or = Question 2. Solve = 0. Give your answer to 3 significant figures. = 7± ( 7) (M1) = or = = 6.46 or = 4.13 (A2) = or =

24 Question 3. Solve 2 ( 3) = 10 Leave your answer in surd form = = 0 = 6± ( 6) = 3± 29 2 (M1) (M1) (M1) = (Total 4 marks) TOTAL /10