Use arithmetic operations including integer division, modulus and exponentiation, relational operators, and the Boolean operators AND, OR and NOT, and understand operator precedence.

What this dot point is asking

AQA wants you to use arithmetic operators (including integer division and modulus), relational operators that produce a Boolean result, and the logical operators AND, OR and NOT, and to apply operator precedence correctly.

Arithmetic operators

• Addition, subtraction, multiplication: the usual operators on integers and reals.
• Real division (/): gives a real result, so $7 / 2 = 3.5$.
• Exponentiation: raises to a power, so $2^{10} = 1024$.
• DIV and MOD: integer division and remainder, used for digit extraction, wrapping values round (as in a circular queue) and divisibility tests.

DIV and MOD together are powerful for breaking numbers apart. Repeatedly applying $n \,\text{MOD}\, 10$ extracts the last digit and $n \,\text{DIV}\, 10$ removes it, which is exactly how a number is converted to its individual digits or to another base. This pairing appears constantly in exam algorithms, so it is worth being fluent with both.

Relational and Boolean operators

Relational operators compare two values and return a Boolean: $=$ (equal), $\neq$ (not equal), $<$, $>$, $\leq$ and $\geq$. The result is True or False, which is why a condition in an IF or WHILE is really a Boolean expression.

A useful related idea is short-circuit evaluation, used by many languages: in A AND B, if A is False the whole expression must be False, so B is not even evaluated; in A OR B, if A is True then B is skipped. This both saves time and lets a programmer guard a risky test, for example checking a list is non-empty before accessing its first element in the same condition.

Operator precedence

When several operators appear in one expression, precedence decides the order: brackets first, then exponentiation, then *, /, DIV and MOD, then + and -, and finally the relational and Boolean operators. So $2 + 3 \times 4 = 14$, not $20$, because multiplication is done before addition. Operators of equal precedence are evaluated left to right. Use brackets to make the intended order explicit and the expression readable, even where they are not strictly required.