Understand the need for and be able to follow and write algorithms that…

The idea

Algorithms need operators to turn stored data into decisions and results. Arithmetic operators compute values: addition combines, subtraction finds a difference, multiplication scales, division gives a quotient, modulus returns the remainder, integer division discards the fractional part, and exponentiation raises a base to a power such as 2³ = 8. Relational operators compare two values and yield true or false: equal to, less than, greater than, not equal to, less than or equal to, greater than or equal to. Logical operators combine or invert Boolean results: AND is true only when both inputs are true, OR is true when at least one is true, and NOT reverses a single Boolean.

For example: A program accepts a score, then tests score ≥ 50 AND score ≤ 100 to decide whether the mark is valid.

What earns the marks

• Addition combines two values, for example total ← total + price.
• Subtraction finds a difference, for example change ← paid − cost.
• Multiplication scales a value, for example area ← length × width.
• Division produces a quotient that may include a fractional part, for example average ← total ÷ count.
• Modulus returns the remainder after division, for example 17 MOD 5 gives 2.
• Integer division discards the fractional part, for example 17 DIV 5 gives 3.
• Exponentiation raises a base to a power, for example 2³ = 8.
• Relational operators compare values and produce true or false: equal to, less than, greater than, not equal to, less than or equal to, greater than or equal to.
• AND is true only when both operands are true; OR is true when at least one operand is true; NOT reverses a Boolean value.
• A correct answer selects the operator whose meaning matches the stated task, such as using modulus to test divisibility.

Common mistakes and how to put them right

• Confusing modulus with division.

  Put it right: Modulus returns the remainder, so 17 MOD 5 is 2, while 17 DIV 5 is 3.

• Treating integer division as ordinary division.

  Put it right: Integer division discards the fractional part, so 17 DIV 5 is 3, not 3.4.

• Assuming OR is true only when exactly one operand is true.

  Put it right: OR is true when at least one operand is true, so true OR true is true.

• Reading NOT as a comparison rather than an inversion.

  Put it right: NOT reverses a single Boolean value, so NOT true is false.

Exam tips

• Underline the key word in the question, such as remainder, quotient or power, before choosing an operator.
• Work out each expression step by step, applying brackets and operator precedence before comparing values.
• Check Boolean expressions by substituting true and false for each operand and evaluating the logical operators last.