Revision sheet

Square and cube roots

$\sqrt{a}$: side of a square of area $a$; $\sqrt[3]{a}$: edge of a cube of volume $a$.

Watch out: a root is not half or a third.

Rational and irrational

Ends or repeats: rational. Neither: irrational.

Watch out: a repeating decimal is a fraction over 9, 99, …

Pythagorean theorem

$a^2 + b^2 = c^2$, with $c$ the hypotenuse.

Watch out: for a leg, subtract the squares.

Converse and applications

$a^2 + b^2 = c^2$ means right angle; distances are hypotenuses.

Watch out: always test with the longest side as $c$.

Distance and midpoint

$d = \sqrt{\Delta x^2 + \Delta y^2}$; midpoint = average of the coordinates.

Watch out: average, not half the difference.