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Algebra and functions formulae

The 7 results the algebra and functions notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 7, 6 are yours to memorise and 1 is a working line the notes derive in front of you.

Years 12-13 · 3 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

3 lessons

Indices and surds

ax×ay=ax+ya^{x} \times a^{y} = a^{x+y}NOT IN THE BOOKLET: LEARN ITConditionsSame base throughout, with a > 0 whenever the indices are not integers.
ax÷ay=ax-ya^{x} \div a^{y} = a^{x-y}NOT IN THE BOOKLET: LEARN ITConditionsSame base throughout, a ≠ 0, and a > 0 whenever the indices are not integers.
(ax)y=axy(a^{x})^{y} = a^{xy}NOT IN THE BOOKLET: LEARN ITConditionsa > 0. For a negative base the rule can fail once the indices are not integers.
xy=xy\sqrt{xy} = \sqrt{x}\sqrt{y}NOT IN THE BOOKLET: LEARN ITConditionsx ≥ 0 and y ≥ 0. It fails for negative radicands: √(−1)√(−1) is not √1.

Quadratic functions

ax2+bx+c=a(x+b2a)2+(c−b24a)ax^{2} + bx + c = a(x + \frac{b}{2a})^{2} + (c − \frac{b^{2}}{4a})NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsa ≠ 0.
x=−b±b2−4ac2ax = \frac{−b \pm \sqrt{b^{2} − 4ac}}{2a}NOT IN THE BOOKLET: LEARN ITConditionsa ≠ 0, and real roots need b² − 4ac ≥ 0.

Polynomials and the factor theorem

f(a)=0⇔(x−a) is a factor of f(x)f(a) = 0 \iff (x − a) \text{ is a factor of } f(x)NOT IN THE BOOKLET: LEARN ITConditionsf(x) a polynomial.

Every formula in the library is indexed by unit on the equation index, and the algebra and functions notes are where these results are derived and used. The 6 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Coordinate geometry formulae