M3 - Thinker

Powers and roots

a^n = a x a x ... (n times) ; sqrt(a^2) = a

A power is repeated multiplication. A square root undoes a square.

Scientific notation

a x 10^n with 1 <= a < 10

Write very large or very small numbers as a number between 1 and 10 times a power of ten.

Percentage increase and decrease

change% = (new - old) / old x 100

Compare the change to the original amount.

Perimeter and area

perimeter = sum of sides; rectangle area = l x w

Perimeter is the distance around a shape, area is the surface inside it.

Area of a triangle

area = (base x height) / 2

Half the base times the perpendicular height.

Circle area and circumference

area = pi r^2 ; circumference = 2 pi r

Pi is roughly 3.14. The diameter is twice the radius.

Angle rules

triangle = 180 deg; straight line = 180 deg; full turn = 360 deg

Angles in a triangle add to 180. On a straight line they add to 180. Angles at a point add to 360.

Volume

box = l x w x h; cylinder = pi r^2 h

Volume measures the space inside a solid, in cubic units.

Symmetry

A shape has a line of symmetry when it folds exactly onto itself.

Coordinates

A point (x, y) gives the horizontal then vertical position. x comes before y.