MYP · Mathematics (Extended) MYP Year 4

Sequences Patterns and Functions

17 min readExtendedCore strand of MYP Extended Mathematics — assessed under Criterion A (Knowing & Understanding) and Criterion D (Applying Mathematics in Real-Life Contexts); recurs across unit tests and the on-screen eAssessment 'Patterns' strand.

Every pattern you've clocked since Year 7 — tile arrangements, bouncing-ball heights, bus timetables — is a function wearing a disguise: something goes in (a position number $n$ , or an input $x$ ), a rule acts on it, and something comes out (a term value, or $f (x)$ ). This chapter gives you the formal machinery to describe that precisely instead of just eyeballing 'it goes up by 6 each time': arithmetic and geometric sequences, the general term formula, function notation, composite and inverse functions, and domain/range.

Overview

Why this chapter exists

A sequence is an ordered list of numbers ( $u_{1}, u_{2}, u_{3}, \dots$ ); a series is what you get when you add them up. Two families dominate this course: arithmetic (constant difference $d$ ) and geometric (constant ratio $r$ ). Functions generalise the same idea for continuous inputs — write $f (x)$ instead of $u_{n}$ — and open up new questions: what can you legally put in (domain), what comes out (range), and can you chain or reverse the rule (composite/inverse functions)?

Real exam contexts recycle the same skeleton every time: identify the pattern type, build the general formula, then use it to answer a specific question about the situation (a target value, a capacity limit, a day number).
Arithmetic sequences and straight-line functions are literally the same mathematical object — $u_{n} = d n + (u_{1} - d)$ has exactly the shape $y = m x + c$ .
Domain, range, composite and inverse functions extend the idea of 'a rule with inputs and outputs' beyond whole-number term positions to any real-number $x$ .

Mind map of Sequences Patterns and Functions centred on Sequences, Patterns & Functions.

Command terms that actually appear on this topic

Command term	What it demands	AO	Mark-earning move
Deduce	Reach a conclusion using the given information, showing the specific step (usually a subtraction or substitution) that gets you there.	Reasoning	The mark is for the shown step (e.g. $108 - 102 = 6$ ), not for the bare final value.
Justify	Support a conclusion with explicit numerical evidence and a concluding sentence answering the actual question.	Reasoning/communication	Calculation alone without a stated yes/no or comparison sentence often scores zero on a 1-mark item.
Advise	Give a clear recommendation to the person/organisation in the context, backed by a calculation.	Application	Mark awarded for the explicit recommendation tied to a number, not the number alone.
Calculate	Obtain a numerical answer, showing the method used.	Knowledge/application	Working must be visible — a correct final answer with no method can lose method marks on multi-mark items.
Construct	Build a mathematical statement, formula, or representation from given information.	Application	Wants an actual formula in terms of n (or x), not a description in words.
State	Give a short answer with no working required.	Knowledge	Still needs correct notation (e.g. $x \geq 3$ , not 'x is more than 3') to earn the mark.
Analyse	Break down the given model to identify a relationship and interpret its meaning in context.	Application/interpretation	Needs the calculation AND a sentence saying what it means in the real-world context.

Key point

Every 'Justify' or 'Advise' question in this topic wants the same three moves: state the rule, substitute the actual numbers from the question, then finish with one sentence answering exactly what was asked. Skipping that last sentence is the single most common way to drop the mark even when the arithmetic is flawless.

Overview

Sequences Patterns and Functions

Overview

Why this chapter exists

The shape of the chapter

Command terms that actually appear on this topic