Algebra Clinic: Every Algebra Lesson, in the Right Order

All the Mathematics algebra lessons in one place, in a sensible order: from what letters mean, through equations and traps, to WASSCE word problems.

Algebra is where many students first start to feel lost in maths. A sign changes, a bracket disappears, and suddenly nothing makes sense. The good news is that most algebra trouble comes from a few small gaps, and every one of them can be fixed.

Start at the top if algebra has always felt confusing. If you already know your weak spot, jump straight to that section.

Practise algebraic reasoning →

Algebra in one page

Algebra is the language the rest of Core Maths is written in. Weak algebra shows up everywhere: in simple interest, in graphs, in mensuration. The good news is that most algebra mistakes come from a handful of foundation habits. Here they are, in the order you should fix them.

Algebra as a ladder: number sense, signs, like terms, brackets and substitution, solving equations, then word problems and simultaneous equations
Algebra is a ladder. A missing rung makes every higher step shaky.

1. The sign belongs to the term after it

Splitting 5x − 3 + 2x − 7 into signed terms to get 7x − 10, with the sign rules for multiplication and the bracket trap
Carry each sign with its term.

2. Collect only like terms

Sorting 4a + 3b − 2a + 5b into a-terms and b-terms to get 2a + 8b, with the traps 10ab and 5x²
Sort the terms, then combine.

3. Solve equations by balancing

Whatever you do to one side, do to the other. Undo the operations in reverse order.

2x + 5 = 17 \;\Rightarrow\; 2x = 12 \;\Rightarrow\; x = 6
Balance scale with 2x + 5 on one side and 17 on the other; subtract 5 from both sides, then divide both by 2, giving x = 6
Keep the scale balanced.

4. Change the subject of a formula

Making t the subject of v = u + at by undoing the operations in reverse order: t = (v − u) ÷ a
Undo the operations in reverse order.

5. Simultaneous equations

Solving x + y = 10 and x − y = 4 by adding to eliminate y: x = 7, y = 3, checked in both equations
Add or subtract to eliminate one letter.

6. Turn words into maths

Table translating phrases like “5 more than x” into x + 5, with a worked word problem giving 16 and 24
Translate the story phrase by phrase.

Start here: the foundations

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Sign Errors in Mathematics: 9 Ways to Avoid Them

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9 Ways to Stop Mixing Up Expressions and Equations

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Working with expressions

When to Expand, Factorise or Simplify: 7 Quick Checks

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Substitution in Maths: 9 Costly Mistakes to Avoid

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10 Algebra Rules Every SHS Student Should Know

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Solving equations

Linear Equations: 5 Steps to Solve Without Guessing

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10 Steps to Solve Linear Equations Without Guessing

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8 Ways to Solve Equations Step by Step

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Making a Subject: 7 Reasons Students Lose Marks

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Simultaneous Equations: 7 Hidden Gaps Behind Wrong Answers

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Traps and mistakes that cost marks

Algebra Traps: 8 Ways Students Lose Easy Marks

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Algebra Foundation in Mathematics: 7 Signs It Needs Work

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Word problems

Word Problems in WASSCE Maths: 7 Ways to Understand the Question

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Word Problems in Mathematics: 7 Hidden Clues

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Practise

Algebra Practice for Students Who Struggle: 10 Tasks to Try

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Stuck on something?

If a lesson doesn’t fully clear things up, send me your question and tell me where you got stuck.

The algebra mistakes examiners see most

MistakeFix
−2² written as 4(−2)² = 4, but −2² = −4: use brackets
3(x + 4) written as 3x + 4Multiply every term inside the bracket
Unlike terms combined (2a + 3b = 5ab)Only like terms can be collected
A term moved across without changing its signDo the same operation to both sides
Changing the subject by guessingUndo the operations in reverse order

Questions learners often ask

How do I change the subject of a formula?

List the operations done to the letter you want, then undo them in reverse order, doing the same to both sides each time.

How do I solve simultaneous equations?

Make the coefficients of one letter equal, then add or subtract the equations to eliminate it. Solve for the other letter and substitute back.

This clinic is part of How to Pass WASSCE and NOVDEC Core Maths.

Sources and further reading

The mistakes and topics in these lessons come from what WAEC examiners report year after year, matched to Ghana’s SHS curriculum. You can read the original sources here:

Dickson Sarpong, SHS Mathematics teacher and founder of The Maths Clinic
Written by Dickson Sarpong

NTC-certified SHS Mathematics teacher in Ghana with WAEC marking experience, and author of The Bridge Series textbooks. Every lesson here is built around the mistakes WAEC examiners keep reporting.

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