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Horace Miles
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1 PLC Papers Created For: Year 11 Topic Practice Paper: Factorising Quadratics

2 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 Question 2 Factorise 3x 2 +11x+6 Question 3 Factorise 4x 2-16 Question 4 Factorise 4x 2-15x-4 Total marks / 10

3 Factorising difficult quadratic expressions 2 Grade 7 Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2-17x+30 Question 2 Factorise 5x 2 +14x+8 Question 3 Factorise 9x 2-25 Question 4 Factorise 5x 2-8x-4 Total marks / 10

4 Factorising difficult quadratic expressions 3 Grade 9 Objective: Factorise a quadratic expression in the form ax 2 + bx + c Flats are squares of edge. Rods are rectangles long and wide. Small squares have edges that are 1cm. Flats 6 flats, 7 rods and 2 small squares are arranged to form a rectangle. Rods Small squares a) Write a quadratic expression for the area of the rectangle b) Factorise the expression. (3) c) Hence decide how the pieces can be arranged to form the rectangle and show the arrangement on a sketch diagram. (4) (3) (Total 10 marks) Total /10

5 Factorising difficult quadratic expressions 4 Grade 9 Objective: Factorise a quadratic expression in the form ax 2 + bx + c A rectangle is (2x + 3) cm long and (2x 3) cm wide. The perpendicular height of a triangle is (x 1) cm and the base is (3x 1) cm long The area of the rectangle is 7cm 2 bigger than the area of the triangle. Find the perpendicular height of the triangle. (Total 10 marks) Total /10

6 PLC Papers Created For: Year 11 Topic Practice Paper: Factorising Quadratics

7 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 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 Question 3 Factorise 4x 2-16 = 4(x 2-4) M1 = 4(x+2)(x-2) A1 Question 4 Factorise 4x 2-15x-4 = 4x 2-16x+x-4 M1 = 4x(x-4) + (x-4) M1 = (4x+1)(x-4) A1 Total marks / 10

8 Factorising difficult quadratic expressions 2 Grade 7 Solutions Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2-17x+30 (x-15)(x-2) A2 Question 2 Factorise 5x 2 +14x+8 5x 2 +10x +4x+8 5x(x+2) +2(x+2) M1 (5x+2)(x+2) A2 Question 3 Factorise 9x 2-25 (3x+5)(3x-5) A2 Question 4 Factorise 5x 2-8x-4 5x 2-10x +2x-4 5x(x-2) +2(x-2) M1 (5x+2)(x-2) A2 Total marks / 10

9 Factorising difficult quadratic expressions 3 Grade 9 Solutions Objective: Factorise a quadratic expression in the form ax 2 + bx + c Flats are squares of edge. Rods are rectangles long and wide. Small squares have edges that are 1cm. Flats 6 flats, 7 rods and 2 small squares are arranged to form a rectangle. Rods Small squares a) Write a quadratic expression for the area of the rectangle Area = 6x 2 + 7x + 2 b) Factorise the expression. (2x + 1) (3x + 2) 3M for fully correct expression 2M if 2 terms are correct 1M for any quadratic expression 4M if both factors are completely correct 3M if 3 terms are correct 2M if one factor is completely correct 1M for an attempt to factorise is seen (3) (Allow FT from their quadratic expression) (4) c) Hence decide how the pieces can be arranged to form the rectangle and show the arrangement on a sketch diagram. 1M correct width 1M correct length 1M shapes shown inside rectangle (Allow FT from their quadratic expression) (3) (Total 10 marks) Total /10

10 Factorising difficult quadratic expressions 4 Grade 9 Solutions Objective: Factorise a quadratic expression in the form ax 2 + bx + c A rectangle is (2x + 3) cm long and (2x 3) cm wide. The perpendicular height of a triangle is (x 1) cm and the base is (3x 1) cm long The area of the rectangle is 7cm 2 bigger than the area of the triangle. Find the perpendicular height of the triangle. Rectangle A + 7 = (2x + 3)( 2x 3) 2A + 14 = 2(2x + 3)( 2x 3) Triangle A = ½ (x 1)(3x 1) 2A = (x 1)(3x 1) 14 = 2(2x + 3)( 2x 3) (x 1)(3x 1) 14 = 2 ( 4x 2 9 ) ( 3x 2 4x + 1 ) 14 = 8x x 2 + 4x 1 14 = 5x 2 + 4x 19 0 = 5x 2 + 4x 33 0 = (5x 11)(x + 3) Writes correct expression for areas Attempts to use area of rectangle is bigger Writes correct equation Expands equation Simplifies equation Writes equation in ax 2 + bx + c = 0 form Factorises Finds both values of x Discards x = 3 Finds height of triangle x = 3 (no solution this would give negative height) x = 2.2 Height of triangle = = 1.2 cm (Total 10 marks) Total /10

PLC Papers Created For:

PLC Papers Created For: Quadratics intervention Deduce quadratic roots algebraically 1 Grade 6 Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 Question