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- GCE N(A)-Level A Maths
- Factorisation

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Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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Get Started Now- Lesson: 1a7:46
- Lesson: 1b3:44
- Lesson: 212:53
- Lesson: 311:39

Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

Basic concepts: Factoring trinomials, Solving quadratic equations using the quadratic formula, Completing the square, Shortcut: Vertex formula,

Related concepts: Even and odd functions, What is a polynomial function?, Characteristics of polynomial graphs,

- 1.From the graph of the parabola, determine the:

• vertex

• axis of symmetry

• y-intercept

• x-intercepts

• domain

• range

• minimum/maximum value

a)

b)

- 2.Identifying Characteristics of Quadratic function in General Form: $y = ax^2 + bx+c$

$y = 2{x^2} - 12x + 10$ is a quadratic function in general form.

i) Determine:

• y-intercept

• x-intercepts

• vertex

ii) Sketch the graph. - 3.Identifying Characteristics of Quadratic Functions in Vertex Form: $y = a(x-p)^2 + q$

$y = 2{\left( {x - 3} \right)^2} - 8$ is a quadratic function in vertex form.

i) Determine:

• y-intercept

• x-intercepts

• vertex

ii) Sketch the graph.

5.

Factorisation

5.1

Factorise by taking out the greatest common factor

5.2

Factorise by grouping

5.3

Factorising perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$

5.4

Factorising difference of squares: $x^2 - y^2$

5.5

Factorise trinomials

5.6

Solving polynomials with unknown coefficients

5.7

Solving polynomials with unknown constant terms

5.8

Properties and graphs of quadratic functions

5.9

Factorising difference of cubes: $a^3-b^3$

5.10

Factorising sum of cubes: $a^3+b^3$

We have over 1080 practice questions in GCE N(A)-Level A Maths for you to master.

Get Started Now5.1

Factorise by taking out the greatest common factor

5.2

Factorise by grouping

5.3

Factorising perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$

5.4

Factorising difference of squares: $x^2 - y^2$

5.5

Factorise trinomials

5.6

Solving polynomials with unknown coefficients

5.7

Solving polynomials with unknown constant terms

5.8

Properties and graphs of quadratic functions