Formulas and rules

Ratio and proportion

a : b ; total / (a + b) = one part

A ratio compares amounts. To share in a ratio, find one part then multiply.

Reverse percentage

original = final / multiplier

To find the original price after a change, divide by the multiplier.

Algebraic notation

2x means 2 times x. x^2 means x squared. Like terms can be collected.

Expanding brackets

a(b + c) = ab + ac

Multiply the term outside by every term inside.

Factorising

ab + ac = a(b + c)

Take the highest common factor outside the brackets.

Solving linear equations

ax + b = c -> x = (c - b) / a

Do the same operation to both sides to keep the balance and isolate x.

Sequences

arithmetic: u_n = a + (n-1)d ; geometric: u_n = a x r^(n-1)

Arithmetic sequences add a constant, geometric ones multiply by a constant.

Pythagoras theorem

a^2 + b^2 = c^2

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Thales theorem

AM/AB = AN/AC = MN/BC

A line parallel to one side of a triangle cuts the other two sides proportionally.

Mean

mean = sum of values / number of values

The mean averages the data.

Median, mode and range

Median is the middle value when ordered. Mode is the most frequent. Range is highest minus lowest.

Probability

P = favourable outcomes / total outcomes

Probability runs from 0 (impossible) to 1 (certain).