1.3 Quadratic Expressions and Equations 1

• Expansion of algebraic expressions to form quadratics
• Factorisation of quadratic expressions
• Solving quadratic equations by factorisation
• Forming and solving quadratic equations from real situations

• expand expressions to obtain quadratic expressions
• factorise quadratic expressions
• solve quadratic equations by factorisation
• apply quadratic equations to real life situations

“How are quadratic expressions used in real life?”

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1. Expanding and factorising
   40 min · 2 practice tasks · quiz
   Multiplying two brackets out, and putting an expression back into brackets.
2. Solving quadratic equations
   40 min · 2 practice tasks · quiz
   Why a quadratic usually has two answers, and how to find them by factorising.
3. Forming quadratic expressions
   40 min · 1 practice tasks · quiz
   Turning a sentence about lengths, products or consecutive numbers into ax² + bx + c.
4. Quadratic identities from area
   40 min · 1 practice tasks · quiz
   Why (a + b)², (a - b)² and (a + b)(a - b) expand the way they do, seen as areas.
5. Using identities with numbers
   40 min · 1 practice tasks · quiz
   Computing squares and products near a round number by rewriting them as identities.
6. Taking out a common factor
   40 min · 1 practice tasks · quiz
   Always look for a common factor before hunting for two brackets.
7. Difference of two squares
   40 min · 1 practice tasks · quiz
   x² - a² factorises as (x - a)(x + a), including when the squares hide coefficients.
8. Perfect-square trinomials
   40 min · 1 practice tasks · quiz
   Recognising x² + 2ax + a² as (x + a)², the identity the other way round.
9. Factorising when a is not 1
   40 min · 1 practice tasks · quiz
   Splitting the middle term of ax² + bx + c and grouping, so the grid still closes.
10. Completing the square
    40 min · 1 practice tasks · quiz
    Forcing x² + bx into a perfect square by adding the missing corner, then rewriting.
11. Forming quadratic equations
    40 min · 1 practice tasks · quiz
    Writing a quadratic equation from given roots, from a sum and product, and from a sentence.
12. Solving harder quadratic equations
    40 min · 1 practice tasks · quiz
    Rearranging first, common factors, a not 1, brackets that are not yet zero, and a repeated root.
13. The parabola and its intercepts
    40 min · 1 practice tasks · quiz
    The graph of a quadratic is a parabola; its x-intercepts are the roots you already know how to find.
14. Quadratics in real life
    40 min · 1 practice tasks · quiz
    Forming and solving quadratics for plots, ages, consecutive numbers, a ladder, and a selling price.