Maths Made Simple
Past papers, memos, worksheets and video lessons — all free, all in one place.
Free Maths Lessons
Plain-language lessons for Grades 8–12, written by a South African maths teacher. Every lesson explains a topic, works through exam-style examples step by step, and ends with a worksheet you can try — answers included. Tap a grade to jump straight to it.
Equivalent Fractions & Simplifying
What the top and bottom of a fraction actually mean, how to build equivalent fractions, and how to simplify to lowest terms using the HCF — with a bar diagram, worked examples, a worksheet with memo and a quiz.
Read the lessonAdding & Subtracting Fractions
Adding and subtracting fractions with the same denominator, with different denominators using the LCD, and with mixed numbers — shown with a bar diagram, exam-style worked examples, a worksheet with memo and a quiz.
Read the lessonMultiplying & Dividing Fractions
Multiplying straight across, the reciprocal, and why dividing by a fraction means multiplying by its flip — including mixed numbers and dividing whole numbers by fractions, with worked examples, a worksheet with memo and a quiz.
Read the lessonSquares, Cubes & Roots of Fractions
Squaring and cubing fractions, and finding square roots and cube roots of fractions — the rule is simply 'do it to the top and to the bottom', with worked examples, a worksheet with memo and a quiz.
Read the lessonFractions of Quantities, Grouping & Sharing
Finding a fraction of an amount, working backwards from a fraction to the whole, and the grouping and sharing word problems that carry the marks in exams — worked examples, a worksheet with memo and a quiz.
Read the lessonDecimals: Place Value, Ordering & Rounding
What each digit after the decimal comma is worth, how to compare and order decimals correctly, and how to round off to a given number of decimal places — with a place-value chart, worked examples, a worksheet with memo and a quiz.
Read the lessonAdding & Subtracting Decimals
The one rule that makes decimal addition and subtraction reliable — line up the decimal commas — plus filling gaps with zeros and money problems, with worked examples, a worksheet with memo and a quiz.
Read the lessonMultiplying & Dividing Decimals
Counting decimal places when multiplying, the shift trick for dividing by a decimal, multiplying and dividing by 10, 100 and 1 000, and estimating the answer first — worked examples, a worksheet with memo and a quiz.
Read the lessonSquares, Cubes & Roots of Decimals
Squaring and cubing decimals, and finding square and cube roots of decimals, using the decimal-place count or by converting to fractions — with worked examples, a worksheet with memo and a quiz.
Read the lessonAdding and Subtracting Integers
Ordering integers on a number line, then the two adding rules and the 'add the opposite' trick for subtracting — with a number-line diagram, exam-style worked examples, a worksheet with memo and a quick quiz.
Read the lessonMultiplying and Dividing Integers
The one sign rule that covers both × and ÷ — same signs give a positive, different signs give a negative — shown as a grid, with exam-style worked examples, a worksheet with memo and a quick quiz.
Read the lessonIntegers: Squares, Cubes, Roots & Mixed Operations
Squares, cubes, square roots and cube roots of integers, the crucial difference between (−3)2 and −32, and how to run BODMAS through a calculation containing negatives — worked examples, worksheet with memo and a quiz.
Read the lessonProperties of Integers & Inverses
The commutative, associative and distributive properties applied to integers, plus additive and multiplicative inverses — what they are, how exams ask for them, with worked examples, a worksheet with memo and a quiz.
Read the lessonExtending Numeric & Geometric Patterns
Spotting what a pattern is doing — a constant difference, a constant ratio, or something else entirely — and extending it, including patterns given as diagrams or tables, with worked examples, a worksheet with memo and a quiz.
Read the lessonPattern Rules: In Words and in Algebra
Turning a pattern into a general rule — first described in words, then written algebraically as Tₙ = dn + c — and using that rule to find far-off terms or to work backwards, with worked examples, a worksheet with memo and a quiz.
Read the lessonProperties of Whole Numbers
The commutative, associative and distributive properties, the identity roles of 0 and 1, and why dividing by 0 is undefined — the rules that let you rearrange any calculation, with a diagram, worked examples and an exam-style worksheet with memo.
Read the lessonFactors, Multiples & Prime Factorisation
What factors and multiples really are (and how never to mix them up), what makes a number prime, and how to break any number into its prime factors with a factor tree — worked examples, a clear diagram and an exam-style worksheet with memo.
Read the lessonHCF and LCM (Highest Common Factor & Lowest Common Multiple)
Highest Common Factor and Lowest Common Multiple made simple by reading them straight off the prime factors — with a Venn-diagram picture, exam-style worked examples and word problems, plus a worksheet with memo.
Read the lessonSimple Interest & Budgets (Grade 8)
Working out simple interest on savings and loans, finding the total amount owed or saved, and drawing up a monthly budget that balances.
Read the lessonOrder of Operations: Getting BODMAS Right
Do calculations in the wrong order and you can get the wrong answer, even with perfect arithmetic. BODMAS is the rule that fixes that.
Read the lessonRatio and Rate: The Five Question Types
The five ratio and rate question types of Grade 8–9 — simplifying, sharing in a ratio, finding a missing part, equivalent ratios, increasing/decreasing in a ratio, and unit rates — each worked in full, with a worksheet.
Read the lessonPercentages: Discounts, VAT, Profit and Loss
The seven percentage question types of Grade 8–9 — finding a percentage, increase and decrease, one number as a percentage of another, percentage change, VAT, profit and loss, and reverse percentages — each worked in full, with a worksheet.
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Danemathics: Rise to Legend
A free CAPS-aligned Grade 8–12 maths game. 250+ question types, story zones, boss levels and a global leaderboard.
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