Video Lessons
37 free maths videos from the Danemathics YouTube channel, organised by type and grade. Each lesson page adds notes on what it covers, extra worked examples and exercises to try.
37 videos
Adding & Subtracting Common Fractions
How to add and subtract fractions with different denominators by finding a common denominator first. A core skill that shows up everywhere, from algebra to financial maths.
Improve Your Fractions in 5 Minutes
Equations where x sits in the denominator, solved with one simple trick: write the other side as a fraction over 1, then swap the denominator with the number across the equal sign. Three worked examples, ending with a two-term denominator.
Ratio – Introduction & Examples
What a ratio means — 'for every 1 sweet John has, Stacy has 3' — how to simplify a ratio by writing it as a fraction, and how to share an amount in a ratio with one formula: your part over the parts added, times the total.
Simplifying Algebraic Expressions
Multiplying out brackets with the distributive property — the term outside times every term inside, adding the exponents of the same letter — and then collecting like terms.
Exponential Expressions Examples
Worked examples applying the exponent laws to simplify expressions — multiplying, dividing and raising powers to powers.
Factorisation: Grouping
How to factorise an expression with four terms by grouping them in pairs — an essential technique for Grade 10 algebra.
Simple Interest
Simple interest with the formula SI = (P × R × T) ÷ 100: take P, R and T out of the sentence, multiply, then divide by 100 — for loans and for investments — and answer only what the question asks.
Compound Interest
Compound interest — interest on the interest — with the formula A = P(1 + i)ⁿ, the rate going in over 100 (15% is 15 over 100): finding the future value and the interest earned, and working backwards to the amount first borrowed.
Hire Purchase
How hire purchase works: paying a deposit and then monthly instalments (with interest) until an item is paid off — a real-life application of simple interest.
Geometry of 2D Shapes – Part 1
Part 1 of a Grade 9 worksheet on 2D shapes: six questions on parallelograms, a rhombus and triangles — alternate and co-interior angles, the exterior angle of a triangle, vertically opposite angles and isosceles triangles — each step with its reason.
Geometry of 2D Shapes – Part 2
Part 2 of a Grade 9 worksheet on 2D shapes: the properties of triangles and quadrilaterals — an isosceles triangle, a rectangle, a square with a kite, and a trapezium — used to find unknown angles and sides, with a reason for every step.
Solving Angles in a Triangle
How to find unknown angles in a triangle using the fact that the three interior angles always add up to 180°.
Triangle Properties: Exterior Angle
One Grade 8 exam question worked in full: use the exterior angle of a triangle to set up an equation with only one unknown, solve it, then use a straight line for the second unknown and classify the triangle.
Solving x as an Exponent
How to solve exponential equations where the unknown is in the power, by writing both sides with the same base.
Exponential Equations
More advanced exponential equations, including using factorising and substitution when the bases can't be matched directly.
Equations with Rational Exponents (Advanced)
Grade 11 equations with rational exponents, all solved with the substitution (k) method: put k in place of the smaller power, factorise the trinomial, then resubstitute and square, cube or raise both sides to the right power.
Adding & Subtracting Algebraic Fractions
Adding and subtracting algebraic fractions the long way, with every step shown: factorise the denominators, build the LCD, write one big fraction, multiply in with brackets, then factorise the top and cancel.
Simplifying Algebraic Fractions using Factorisation
Simplifying algebraic fractions by factorising the top and the bottom first — and the cancelling rule behind it: only a whole bracket, or an identical top and bottom, may cancel.
Mathematics Grade 8 Term 1 Prep Test
A whole Grade 8 Term 1 prep test worked through: multiple choice, whole numbers (primes, HCF and LCM from factor trees, ratio, simple interest, speed), integers and common fractions — and when the calculator is allowed versus when every step must be shown.
Maths Grade 9 Prep Test
A Grade 9 prep test worked through: kinds of numbers, HCF, ratio, time from speed, hire purchase with the months turned into years, the exponent laws, an integer word problem and algebraic fractions.
Grade 9 Mathematics Term 1 Practice Test
A Grade 9 Term 1 practice test worked in full: fractions and decimals, squares and roots, scientific notation, a square root by prime factors, the HCF of three numbers, percentages, ratio, a rate problem, the exponent laws, compound interest, and buying a car with VAT, a trade-in and interest.
Grade 9 Mathematics June Exam Prep
The Gauteng 2023 Grade 9 June control test (75 marks, 1½ hours) worked through: number properties, LCM, ratio and indirect proportion, simple versus compound interest, integers, exponents and roots, patterns, flow diagrams, algebraic expressions, factorising and equations.
Class Test: Exponents and Surds
A Grade 11 class test on exponents and surds, answered step by step: exponential equations by a common factor and by the k-method, expanding a surd bracket properly, simplifying with a common factor, and why you cannot take the root of each term separately.
Mathematics Paper 1 November 2025
Grade 10 Mathematics Paper 1, November 2025 (Nelson Mandela Metro, Eastern Cape) worked through in full: surds and recurring decimals, factorising and simplifying, equations and inequalities, simultaneous equations, number patterns, finance and exchange rates, functions and graphs, and probability.
Taxation Test – Grade 12 Math Literacy
A 30-mark Grade 12 Maths Literacy test on taxation worked through: reading a salary advice, gross, basic and net salary, pension as a percentage, annual taxable income, tax rebates and the tax threshold, income tax from the tax table with medical tax credits, and a progressive tax formula.
Graad 8 Wiskunde Vraestel 2 Nov 2023
The Afrikaans recording of Grade 8 Mathematics Paper 2, November 2023 (Eastern Cape): geometry of straight lines, triangles and congruency, the Theorem of Pythagoras and quadrilaterals. The extra examples below are written in English.
Grade 8 Mathematics Paper 2 November 2023
Grade 8 Mathematics Paper 2, November 2023 (Eastern Cape) worked through: geometry terms, angle pairs on parallel lines, triangles and congruency, the Theorem of Pythagoras and quadrilaterals — with a reason for every step.
Grade 8 Mathematics Paper 1 – Term 4 Prep
Grade 8 Mathematics Paper 1, November 2023 (Eastern Cape) worked through: number sense, integers with powers and roots, exponents and scientific notation, ratio, percentages, speed, number patterns and the general term, and algebra — expressions, substitution and equations.
Grade 8 Term 3 2025 Maths Test Preparation
A Grade 8 Term 3 test worked through: simplifying algebraic expressions, solving equations (one with the unknown in the exponent), angles on straight lines and parallel lines, and the properties of triangles.
Grade 8 Geometry Test Questions – Part 1
Five Grade 8 geometry questions on parallel lines and triangles: vertically opposite, corresponding, alternate and co-interior angles, the angles of a triangle, and equations built from angle facts — with the reason that earns each mark.
Grade 8 Algebra Test Questions
Grade 8 algebra test questions worked through: collecting like terms, expanding brackets with the distributive property — signs included — and solving equations, including one with fractions.
What to Expect for Maths in Grade 8
The Grade 8 maths year term by term, as CAPS sets it out: whole numbers, integers, fractions, decimals and patterns in Term 1; exponents, algebra, functions and graphs in Term 2; data handling, the geometry of straight lines, 2D shapes, congruence and similarity in Term 3; the Theorem of Pythagoras, transformations, area, surface area and volume in Term 4 — and why no topic may be left half-understood.
Grade 9 Mathematics Topics for 2026
The Grade 9 maths year term by term, as CAPS sets it out: whole numbers, integers, exponents, patterns and algebraic language in Term 1 (new in finance: commission, rentals and compound interest); expressions, equations, graphs and the geometry of straight lines in Term 2; 2D shapes, area and perimeter, data and probability in Term 3; 3D objects, surface area, volume and transformations in Term 4. Much of it revises Grade 8 — so go back and master what you got wrong.
Top 10 Secret Maths Tips
Ten study habits for maths, counted down: no excuses, master the previous grade's work, aim to understand 80–90%, ask the 'stupid' question, use resources and past papers, keep notes tailored to your own mistakes, practise daily, the Feynman technique, a study group, and the Annual Teaching Plan (ATP).
Minute Math Challenge: Integer Edition
A one-minute challenge of quick integer sums: check how fast you can calculate with positive and negative numbers. Then time yourself on the ten sums below.
Try to Beat Me: Integers
Five timed integer questions — brackets, two minus signs side by side, roots and powers — then the full working for each, with no calculator. Pause the video and try to beat the teacher.
ChatGPT Challenges Me with 3 Tough Maths Questions
ChatGPT sets three tough questions: a quadratic equation solved with the quadratic formula and again with the X method, two simultaneous equations solved by elimination, and an equation with x both in an exponent and outside it — found by inspection, then solved graphically, a challenge beyond CAPS.