Algebra and Expressions

Master like terms, notation, substitution and word problems for MYP 1 Maths

Algebra expression 3x+2 shown as building blocks with labels for coefficient, variable and constant

Subject

Mathematics

Curriculum

IB MYP

Grade

MYP 1

Topic

Algebra and Expressions

Reading

6 min

Difficulty

Foundational

Quick facts

Difficulty

★☆☆☆☆

Exam weight

Core strand — every unit test & investigation task

Prerequisites

Basic arithmetic, order of operations (BIDMAS)

You'll learn

Simplifying, notation, substitution, forming expressions

Revision time

30–40 minutes

Algebra and expressions is the foundational MYP 1 maths topic where letters start standing in for numbers — and it shows up in every unit test and Criterion A/B investigation from here on. Once you understand that an expression like $3 x + 2$ is just a compressed instruction, the rest becomes much easier to manage. This teaser walks through the five ideas examiners test most: combining like terms without silently dropping signs, following algebra's strict writing conventions, turning word problems into expressions, substituting values correctly (including tricky negatives), and telling variables apart from constants. Each section flags the exact trap that costs students marks, so you can avoid it before it happens. For the full worked examples, formula breakdowns and step-by-step practice, the complete revision note is linked at the end.

What you’ll be able to do

✓Identify terms, coefficients, variables and constants in an expression

✓Combine like terms correctly without changing the letter or power

✓Apply algebra's writing conventions (no × symbol, division as a fraction)

✓Translate word problems into algebraic expressions using 'let x = ...'

✓Substitute numeric values into expressions, including negative numbers

✓Explain why unlike terms cannot be combined

✓Simplify expressions arising from perimeter and rate problems

✓Check an expression is fully simplified before finishing a question

Combining Like Terms Without Losing Marks

Like terms have exactly the same letter raised to exactly the same power — $3 x$ and $5 x$ combine, but $3 x$ and $3 x^{2}$ never do. Rearrange first so matching letters sit together, then add or subtract only the coefficients; the letter itself never changes. An expression is 'fully simplified' only once no two remaining terms share a variable part.

Diagram grouping like terms 3x and 5x together separately from 2y and -y before combining

Terms	Like or Unlike?	Why
3x and 5x	Like	Same letter, same power
3x and 3x²	Unlike	Same coefficient but different power
4x and 2z	Unlike	Different letters

Exam tip

On 'show each step' questions, one mark is for rearranging/combining shown explicitly, and one is for the correct final expression — never jump straight to the answer.

Common mistake

Treating $- y$ as if it disappears (e.g. writing $3 y$ instead of $2 y$ ) silently drops a whole term and loses the accuracy mark even if the method looks fine.

Mini summary

Only combine terms with identical letters and powers — grouping first prevents dropped signs.

Algebra's Writing Rules

Algebra has a strict shorthand: $2 \times x$ is written $2 x$ , $b \times a$ is written $ab$ , and $x \times x$ becomes $x^{2}$ — a power, not a coefficient. Division is always shown as a fraction in a final answer, never left with a ÷ symbol. These conventions aren't optional style; markers expect them by default.

Side-by-side comparison of 2x meaning two times x and x squared meaning x times x

Exam tip

Say powers out loud to avoid confusion: $x^{2}$ means 'x times x', while $2 x$ means 'two times x' — they are never interchangeable.

Common mistake

Mixing up 'double x' with 'x squared', e.g. treating $x^{2}$ as $2 x$ when tidying an expression.

Mini summary

Coefficient in front, no × symbol, division as a fraction — the default rules for writing algebra.

Turning Word Problems into Expressions

Start every word problem by writing 'let $x$ = ...' to define what the letter stands for — this sentence is often worth its own mark. Translate each phrase into algebra ('twice the width' becomes $2 w$ ), simplify using like-terms rules, then re-attach units and answer the actual question asked.

Rectangle diagram with sides labelled 2x+3 and x+5 used to calculate perimeter as an expression

Exam tip

In perimeter or area problems, simplify inside brackets before multiplying out, and always distribute across every term in a bracket.

Common mistake

Doubling only one side of a rectangle, or forgetting to distribute a multiplier across both terms in a bracket — e.g. landing on $6 x + 8$ instead of the correct expanded form.

Mini summary

Define the letter, translate the story, simplify, then re-attach units before answering.

Substituting Values Into Expressions

Substitution means replacing every occurrence of a letter with its given value — write $3 x$ as $3 \times (4)$ first rather than skipping straight to the result. Brackets protect negative values, so substituting $x = - 2$ into $x^{2}$ must be written $(- 2)^{2} = 4$ , never $- 2^{2} = - 4$ . If a letter appears more than once, every occurrence must be replaced.

Substitution steps showing x replaced by (-2) with brackets before squaring

Exam tip

Follow BIDMAS exactly after substituting — multiplying before adding matters just as much as it does with plain numbers.

Common mistake

Adding before multiplying, e.g. computing $6 \times (4 + 16)$ instead of $6 \times 4 + 16$ , which gives a completely wrong answer from ignoring BIDMAS.

Mini summary

Substitute with brackets, replace every occurrence, then apply BIDMAS carefully.

Variables vs Constants

In $y = 3 x + 6$ , $x$ and $y$ are variables that change together, $3$ is the coefficient of $x$ , and $6$ is a constant that never changes. A constant never has a letter attached; a coefficient always sits directly in front of one. On a graph of $y = m x + c$ , the constant $c$ is exactly the $y$ -intercept, where $x = 0$ .

Line graph y=3x+6 with the y-intercept at 6 labelled as the constant

Exam tip

Two variables in the same equation don't have to change at the same rate — the coefficient controls that rate.

Mini summary

Coefficients scale variables; constants stay fixed and mark the y-intercept on a graph.

Quick formula sheet

a x + b x = (a + b) x

Add or subtract only the coefficients of matching like terms; the letter never changes. — Same letter, same power — only the numbers in front get added.

2 \times x = 2 x

A number multiplied by a letter is written with the coefficient in front, no × symbol. — Numbers jump in front of letters, no times sign needed.

x \times x = x^{2}

A letter multiplied by itself is written as a power, not a coefficient. — Say it out loud: 'x times x', never 'two x'.

x \div 4 = \frac{x}{4}

Division is always shown as a fraction in a final algebraic answer. — No ÷ symbol survives to the final answer — it becomes a fraction.

P = 2 (l + w)

Perimeter of a rectangle; substitute numeric or algebraic values for length and width. — Double the sum of the two different sides.

Practice questions

Easy

Simplify $4 x + 3 x$ .
Write $5 \times y$ using correct algebraic notation.
Identify the coefficient and constant in $7 x + 2$ .

Medium

Simplify $3 a + 2 b + a + 4 b$ and explain why the result cannot be simplified further.
A rectangle has sides $x + 4$ cm and $2 x + 1$ cm. Write a simplified expression for its perimeter.
Substitute $x = - 3$ into $x^{2} + 2 x$ , showing brackets around the substituted value.

Challenge

Simplify $5 x + 3 y + 2 x - y$ and identify the trap a student might fall into with the $- y$ term.
A toy car moves from point A(1,2) to point B(4,8) on a distance–time graph. Calculate its speed using the gradient.
Explain, using an example, why $4 x$ and $2 z$ can never be combined into a single term.

Frequently asked questions

What is the difference between a term and an expression?+

A term is a single number, letter, or product of numbers and letters separated by + or -. An expression is made of one or more terms combined together, with no equals sign.

How do I know if two terms are like terms?+

Like terms must have the exact same letter raised to the exact same power. $3 x$ and $5 x$ are like terms, but $3 x$ and $3 x^{2}$ are not, even though they share a coefficient.

Why can't I combine $4x$ and $2z$ into one term?+

They have different letters, so their variable parts don't match. Only terms with an identical letter and power can be combined — different letters mean the expression is already fully simplified.

How do I substitute a negative number correctly?+

Put the value in brackets before applying any power or operation, e.g. substitute $x = - 2$ into $x^{2}$ as $(- 2)^{2} = 4$ , never $- 2^{2} = - 4$ .

What's the difference between a coefficient and a constant?+

A coefficient is the number multiplying a letter, like the 3 in $3 x$ . A constant is a fixed number with no letter attached, like the 6 in $3 x + 6$ .

Why is 'let x = ...' important in word problems?+

Defining what the letter represents is often its own mark in longer questions, and it keeps your algebra tied clearly to the real-world quantity you're modelling.

Get the Full MYP 1 Algebra and Expressions Revision Notes

Complete worked examples for every trap covered here, step by step Full breakdown of notation rules, substitution and word-problem strategies Original mock papers and exam-style questions with mark-scheme style guidance Printable formula sheet and mistake checklist for fast revision

Get the Algebra and Expressions notes on RevisionPrep →

Maths: Ratio, Proportion & Percentages Maths: Patterns, Sequences & Algebraic Thinking Maths : Geometry – Properties of Shape