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31 GCSE subtopics currently available

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Number / Number & Place Value

Number / Integer Arithmetic

Number / Fractions

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Number / Bounds & Accuracy

Algebra / Expressions

Algebra / Equations

Algebra / Sequences

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Algebra / Simultaneous Equations

Algebra / Quadratics

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Ratio & Proportion / Direct Proportion

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Solving Quadratics by Factorising

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Algebra - Quadratics - Completing the Square

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A quadratic written in the form (x+a)(x + a)² + b.
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For y=(x+a)y = (x + a)² + b, the turning point is (−a,b)(-a, b).
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Prior Knowledge

2 questions[2 marks]
Section options
  1. More
    1.
    Expand (x+2)(x + 2)⁠(x+3)(x + 3).
    (1)
  2. More
    2.
    Expand (x−4)(x - 4)⁠(x+1)(x + 1).
    (1)
Example options

Fluency

3 questions[3 marks]
Section options
  1. More
    3.
    Rewrite x2+6x+5x^2 + 6x + 5 in completed square form.
    (1)
  2. More
    4.
    Rewrite x2−8x+3x^2 - 8x + 3 in completed square form.
    (1)
  1. More
    5.
    Rewrite x2+10x+7x^2 + 10x + 7 in completed square form.
    (1)

Standard Practice

3 questions[6 marks]
Section options
  1. More
    6.
    Solve x2+6x+2=0x^2 + 6x + 2 = 0 by completing the square.
    (2)
  2. More
    7.
    Solve x2−4x−1=0x^2 - 4x - 1 = 0 by completing the square.
    (2)
  1. More
    8.
    Find the turning point of y=x2+4x+1y = x^2 + 4x + 1.
    (2)

Problem Solving

2 questions[6 marks]
Section options
  1. More
    9.
    Find the minimum value of y=x2−6x+11y = x^2 - 6x + 11 by completing the square.
    (3)
  1. More
    10.
    A quadratic is given by y=x2+8x+10y = x^2 + 8x + 10. Find its turning point.
    (3)

Answers

Prior Knowledge
  1. 1.x2+5x+6x^2 + 5x + 6
  2. 2.x2−3x−4x^2 - 3x - 4
Fluency
  1. 3.(x+3)(x + 3)² - 4
  2. 4.(x−4)(x - 4)² - 13
  3. 5.(x+5)(x + 5)² - 18
Standard Practice
  1. 6.x=−3x = -3 ± √7
  2. 7.x=2x = 2 ± √5
  3. 8.(-2, -3)
Problem Solving
  1. 9.Minimum value is 2
  2. 10.(-4, -6)

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Using the Quadratic FormulaSolving Quadratics by FactorisingSolving Simultaneous Equations AlgebraicallyEquations with BracketsEquations with FractionsForming & Solving EquationsNth Term of Quadratic SequencesGradient from CoordinatesEquation of a Line from Gradient & PointDividing in a Given RatioSolving Direct Proportion ProblemsFactorising QuadraticsView all topics