Revision sheet

Equivalent expressions

Distribute to every term; combine like terms with their signs.

Watch out: a minus before parentheses changes every sign inside.

Linear equations

Do the same to both sides until $x$ is alone.

Watch out: distribute to every term.

Inequalities

Solve as an equation; flip when multiplying or dividing by a negative.

Watch out: check with a number from your answer.

Arithmetic sequences

• Add $d$ each time: $a_n = a_1 + (n - 1)d$.
• $d = \dfrac{a_q - a_p}{q - p}$.

Watch out: $n - 1$ steps from $a_1$ to $a_n$.

Geometric sequences

• Multiply by $r$ each time: $a_n = a_1 r^{\,n-1}$.
• $r$ = a term divided by the one before.

Watch out: the exponent is $n - 1$.