Maths1,134 views·Updated May 26, 2026·2 pages

Mastering Quadratics: Knowledge Organizer for GCSE AQA

Luck@imbored2999

Ever wondered why algebra seems to follow patterns everywhere? Quadratics... Show more

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Year 9 Mathematics Knowledge Organiser - Unit 2: Quadratics

Keywords
Expanding brackets means removing the brackets.
Factorising means putt

Expanding and Factorising Quadratics

Think of expanding brackets like unpacking a suitcase - you're taking everything out and spreading it around. When you see something like 4 $a+6$ , multiply the 4 by everything inside those brackets to get 4a + 24.

Factorising works the opposite way - you're packing things back into the suitcase by finding the Highest Common Factor (HCF). For example, 4x + 12 becomes 4 $x + 3$ because 4 divides into both terms perfectly.

The real fun starts with double brackets like $x-5$ $x+2$ . You need to multiply everything in the first bracket by everything in the second bracket - think of it as making sure everyone at two different tables meets everyone at the other table. This gives you x² - 3x - 10 after collecting like terms.

Top Tip: Always check your factorising by expanding the brackets back out - if you get your original expression, you've nailed it!

Squared brackets like $x+3$ ² are just the same bracket multiplied by itself twice. The difference of two squares pattern $like x² - 16$ has a special shortcut: it always factors as $x+4$ $x-4$ .

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Solving Quadratic Equations and Sequences

Quadratic equations are like puzzles where you're hunting for the mystery values of x that make everything equal zero. The standard form ax² + bx + c = 0 might look scary, but it follows a reliable three-step process: rearrange, factorise, then solve.

Once you've factorised your equation into something like $x-4$ $x-2$ = 0, you're nearly there. Since anything multiplied by zero equals zero, either x-4 = 0 or x-2 = 0, giving you x = 4 or x = 2.

Sequences are number patterns that follow rules, and they're everywhere in maths. Linear sequences increase by the same amount each time (the common difference), while quadratic sequences have a constant second difference when you look at how the gaps between terms change.

Quick Check: For any quadratic sequence, find the first differences, then the second differences - if the second differences are constant, you've got a quadratic sequence!

Finding the nth term lets you calculate any term in the sequence without writing out hundreds of numbers. For linear sequences, use the format an + b, and for quadratic sequences, use an² + bn + c. The key is methodically working through the differences and checking your answer works.

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Maths1,134 views·Updated May 26, 2026·2 pages

Mastering Quadratics: Knowledge Organizer for GCSE AQA

Luck@imbored2999

Ever wondered why algebra seems to follow patterns everywhere? Quadratics are like the building blocks of advanced maths - they're expressions where variables get squared (raised to the power of 2). Mastering how to expand, factorise, and solve these expressions... Show more

of 2

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Expanding and Factorising Quadratics

Top Tip: Always check your factorising by expanding the brackets back out - if you get your original expression, you've nailed it!

of 2

Sign up to see the content. It's free!

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Solving Quadratic Equations and Sequences

Once you've factorised your equation into something like $x-4$ $x-2$ = 0, you're nearly there. Since anything multiplied by zero equals zero, either x-4 = 0 or x-2 = 0, giving you x = 4 or x = 2.

Quick Check: For any quadratic sequence, find the first differences, then the second differences - if the second differences are constant, you've got a quadratic sequence!