MYP · Mathematics (Standard) MYP Year 5

Sequences Patterns and Functions

MYP Year 5 Mathematics — Patterns strand (key concept: Form; related concepts: Generalization, Representation)

24 min readStandardCore recurring strand — tested across on-screen tasks, Criterion B pattern investigations and Criterion D real-world modelling questions

Sequences, patterns and functions are the same mathematical object wearing different clothes. A sequence like $102, 106, 110, 114, \dots$ is just a function $U_{n}$ whose domain is restricted to positive whole numbers — plug in the position, get the value out. Every question in this topic is really testing one skill: can you spot the rule linking position to value, write it correctly, and know exactly which numbers are allowed to go in?

Overview — the shape of this topic

What this topic actually tests

Once you see a sequence as a function of position, 'deduce the formula', 'evaluate $f (3)$ ', and 'find the range' all become versions of the same skill: read the rule, apply it correctly, and know which values of $n$ or $x$ are actually allowed in.

Spot the pattern type first — constant first difference means arithmetic (linear); constant second difference means quadratic. Get this wrong and every formula built on it is wrong.
Translate word problems into $U_{1}$ and $d$ before touching any formula — most marks are lost before any algebra even starts.
Composite and inverse functions are about order and reversal: $(f \circ g) (x) \neq = (g \circ f) (x)$ in general, and $f^{- 1}$ undoes exactly what $f$ did.
Domain and range questions are usually about context, not algebra: how many houses actually exist, how many parking spaces there are, what values of $n$ make physical sense.

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

Command terms that drive this topic

Command term	What it demands	AO	Mark-earning move
Deduce	Reach a value or rule using given data, with brief supporting evidence	MYP Criterion B	Appears in Q1, Q4, Q5, Q8 — you must show at least one subtraction (e.g. $106 - 102 = 4$ ) before stating $d$ ; a bare number with no working is often marked 'answer only'.
Calculate	Obtain a numerical answer with working shown	MYP Criterion A	Skipping the substitution line (e.g. going straight to a final salary/value with no $U_{1} + (n - 1) d$ shown) loses the method mark even if the number is right.
Justify	Support a yes/no decision with a specific number from the problem	MYP Criterion D	In the bus questions (Q5, Q8) 'yes because it's soon' scores zero; 'wait time = 7 min ≤ 10 min, so yes' scores full marks.
Advise	Give a recommendation plus the calculation that supports it	MYP Criterion D	Q4 and Q7 need the decision AND the exact n-value or comparison that proves it — the decision alone is not enough.
Show that	Display every step of a result you are already told, not just assert it	MYP Criterion B	For 'show second differences are constant' (Q6) you must write the actual subtractions $6 - 4 = 2$ , $8 - 6 = 2$ , $10 - 8 = 2$ — stating 'they're all 2' loses the demonstration mark.
State / Write down	Give the answer directly, no working required	MYP Criterion A	The answer must match the exact form asked — Q3(a) wants three separate values $V_{0}, V_{1}, V_{2}$ , not one formula.

Key point

A sequence is a function in disguise:

U_{n} = f (n)

. If you can write the rule linking

n

U_{n}

, you can answer nearly every question in this topic — the hard part is always spotting the rule, not applying it.

Overview

Sequences Patterns and Functions

Overview — the shape of this topic

What this topic actually tests

The shape of the chapter

Command terms that drive this topic