Mathematical Expressions: Revision Notes (Computer Science Principles 3.3)

Recap

• An expression (value, variable, operator, or procedure call that returns a value) is evaluated to a single value.
• Operators in the notation: +, -, *, /, MOD. Assume a ≥ 0 and b > 0 for a MOD b.
• Order: brackets, then *, /, MOD (same level, left to right), then +, - (same level, left to right).
• a MOD b is the remainder when a is divided by b: 17 MOD 5 = 2.
• 17 / 5 is 3.4, not 3.

Key relationships

Task	Expression	Example
Even test	n MOD 2 = 0	10 MOD 2 = 0 is true
Divisible by d	n MOD d = 0	21 MOD 7 = 0 is true
Last digit	n MOD 10	4826 MOD 10 = 6
Wrap on 24-hour clock	(h + k) MOD 24	(21 + 8) MOD 24 = 5
Whole hours from minutes	(m - m MOD 60) / 60	(135 - 15) / 60 = 2
Smaller than divisor	a MOD b = a when a < b	3 MOD 7 = 3

Assumptions

• a MOD b is only used with an integer a ≥ 0 and an integer b > 0.
• / gives a real-number result (7 / 2 is 3.5).
• Statements run top to bottom and variables hold their most recent values.

Method for evaluating an expression

1. Replace each variable with its current value.
2. Scan for brackets and evaluate inside them first.
3. Evaluate every *, / and MOD from left to right.
4. Evaluate every + and - from left to right.
5. Check the result is sensible: a remainder must be smaller than the divisor.

Mistakes to avoid

• Treating MOD as lower precedence than *.
• Giving the quotient instead of the remainder.
• Rounding 17 / 5 to 3.
• Doing + before *, or going right to left on equal precedence.
• Expecting a MOD b to reach b.

Worked mini-example

x ← 14
y ← x MOD 5 + x / 2 * 3
DISPLAY(y)

Output: 25

14 MOD 5 = 4; 14 / 2 = 7, 7 * 3 = 21; 4 + 21 = 25.

Quick self-check

1. Evaluate 8 + 6 MOD 4 * 3.
2. Which expression tests whether n is a multiple of 5?
3. A clock shows hour h on a 12-hour dial numbered 0 to 11. Write the hour after k more hours.

Answers

1. 6 MOD 4 = 2, 2 * 3 = 6, 8 + 6 = 14.
2. n MOD 5 = 0.
3. (h + k) MOD 12.

Where marks are won and lost

Expect short evaluation tasks: work out the value of an expression or the value left in a variable after a few assignments. Marks go to candidates who respect precedence (MOD with * and /) and the left-to-right rule. Another favourite is a “which expression” question: choose the expression that gives the last digit, tests divisibility, or wraps a value to a clock. Practise the patterns in the key-relationships table until you can write them without looking.

Back to the full study guide for worked examples and explanations.