Use arithmetic operators including integer division and modulus, comparison operators, and the Boolean operators AND, OR and NOT, applying correct operator precedence.

What this dot point is asking

AQA wants you to use arithmetic operators (including integer division DIV and modulus MOD), comparison operators, and the Boolean operators AND, OR and NOT, applying the correct order of precedence.

Arithmetic operators

DIV and MOD work as a pair: for any division, DIV gives how many whole times the divisor fits and MOD gives what is left over. MOD is especially useful for tests such as "is this number even?" (number MOD 2 = 0), "is it divisible by 5?" (number MOD 5 = 0), or wrapping a value around a range (such as turning a 25-hour count into a clock time with hours MOD 24).

Comparison operators

Comparison operators compare two values and return a Boolean (True or False): equal to $=$, not equal to $\ne$, less than $<$, greater than $>$, less than or equal to $\le$, and greater than or equal to $\ge$. They form the conditions inside selection (IF) and iteration (WHILE), where the program needs a True or False answer to decide what to do.

Boolean operators

For example age >= 13 AND age <= 19 is True only for teenagers, because both halves must hold. day = 'Sat' OR day = 'Sun' is True at the weekend, because either is enough.

Operator precedence

Comparison operators in conditions

Comparison operators are what turn data into the True or False answer a program needs to make a decision. Inside an IF or a WHILE, a condition such as score >= passMark is evaluated to a Boolean and the program branches or loops accordingly. The six operators are equal to, not equal to, less than, greater than, less than or equal to, and greater than or equal to. A frequent source of bugs is mixing up "equal to" used as a test with "assignment" used to store a value: in AQA pseudocode the assignment arrow $\leftarrow$ stores a value, while $=$ tests for equality inside a condition.

Combining Boolean operators with comparisons

Real conditions usually combine comparisons with Boolean operators. For example mark >= 40 AND mark < 70 is True for a pass that is not a distinction, and day = 'Sat' OR day = 'Sun' is True at the weekend. NOT inverts a condition, so NOT loggedIn is True when the user is not logged in. As with arithmetic, precedence and brackets matter: NOT is applied first, then AND, then OR, so brackets are used to make the intended logic clear, such as (a OR b) AND c. Building conditions carefully from comparisons and Boolean operators is the heart of writing correct selection and iteration.

Try this

Q1. Calculate $23 \text{ MOD } 4$. [1 mark]

• Cue. 3, because $23 \div 4 = 5$ remainder 3.

Q2. State the result of True AND False and of True OR False. [2 marks]

• Cue. True AND False is False; True OR False is True.