Analytical Geometry: Midpoints, Gradients and Lines
Master the four core formulas — distance, midpoint, gradient and the line equation — and use gradients to prove shapes and angles.
High School
Short, exam-focused revision you can do on your phone.
Revision MicroQuests for learners in Grades 10 to 12, written around the CAPS curriculum: English First Additional Language skills, Mathematics Paper 1 and Paper 2, and Grade 12 Geography — climate, geomorphology and mapwork.
Each one explains a single topic, checks you understood it and ends with an exam-style challenge. Every shelf starts with free MicroQuests, so you can see how it works before you pay for anything.
Analytical geometry, circles and tangents, Euclidean geometry and proofs, trigonometry — identities, equations, graphs and the sine and area rules — and statistics, from grouped data to regression.
Master the four core formulas — distance, midpoint, gradient and the line equation — and use gradients to prove shapes and angles.
Read a circle's centre and radius from its equation, complete the square when it is not in standard form, and find the tangent at any point.
Learn the circle theorems that carry the marks, and write proofs the way they are marked — a statement with a reason on every single line.
Estimate a mean from grouped data, build and read an ogive, and draw a box-and-whisker plot that shows skewness and outliers.
Describe a scatter plot properly, interpret the correlation coefficient, use the least squares line to predict, and know when a prediction is worthless.
Prove triangles similar, use the proportion theorem correctly, and set up ratios that give the right answer every time.
Choose between the sine rule, cosine rule and area rule with confidence, and handle 2D and 3D problems without losing your way.
Solve trig equations with the general solution, and read amplitude, period and shifts off a sine, cosine or tangent graph.
Prove identities with a reliable method, reduce any angle to an acute one, and know which quadrant makes each ratio positive.
Climate and weather, geomorphology and mapwork for Grade 12 Geography: pressure cells, cyclones, berg winds, local climates, drainage basins, river profiles and hydrographs, map calculations and GIS, plus the exam verbs that tell you what a question wants.
Learn what common Geography instruction verbs are actually asking you to do, so your answer matches the task instead of losing marks you already knew.
Build a mapwork checklist covering scale, bearings, coordinates, contours and orthophotos, plus the GIS ideas that go with them.
Understand how berg winds warm and dry the coast, why cities build their own heat island, and how a valley inversion traps the air we breathe.
Learn to recognise dendritic, trellis, radial and rectangular drainage patterns, and read what drainage density tells you about the rock and soil beneath.
Learn how Highs and Lows differ in pressure, vertical air movement and surface circulation, and why each brings the weather it does.
Practise reading evidence off a map — climate, river stage, economic activity and settlement — instead of answering from memory.
Understand why opposite slopes heat differently, how cold air collects on a valley floor, and how anabatic and katabatic winds develop.
Learn the four mapwork calculations, the formula for each, and how to check an answer is sensible before you write it down.
Separate mid-latitude cyclones from tropical cyclones by where they form, how they are built and the weather each one brings.
Learn what a hydrograph shows, how to read discharge, flood peak, time lag and the receding limb, and what makes the shape steep or gentle.
Learn to read river profiles, explain how a meander erodes and deposits, and recognise the features left behind by river capture.
Reading, writing, listening and speaking skills for English FAL: reading strategies, skimming and scanning, summarising, inference and tone, paragraphs, opinions, transactional writing and prepared speeches.
Turn reading into a three-step routine. Learn how to prepare before you start, read closely for meaning, and make sense of a text after you finish.
Learn three reading speeds and when to use each one. Stop reading every text in exactly the same way, and stop running out of time in comprehension.
Find the main idea, keep what matters and rewrite it briefly in your own words — without losing the meaning or blowing the word count.
Turn loose sentences into a focused paragraph using a topic sentence, supporting detail and clear links between the ideas.
Plan, organise, practise and deliver a speech with a clear purpose, a real audience and a structure your listeners can follow in real time.
Move from "I think" to a clear viewpoint backed by reasons and evidence, and learn to answer an opposing argument without attacking the person.
Build a simple listening process — prepare, listen with a purpose, take useful notes and respond afterwards using what was actually said.
Learn how writers reveal meaning through clues, word choice and tone, even when they never say it directly — and how to prove it from the text.
Learn what makes practical texts work — a clear purpose, the right audience, the correct format, and every detail the reader needs to act on it.
Stop treating the first draft as the final answer. Plan, draft, revise, edit, proofread and present — doing the big thinking before the small corrections.
Algebra, equations and inequalities, number patterns, sequences and series, functions and inverses, the hyperbola, financial maths, calculus and probability — the Paper 1 topics, one MicroQuest each.
Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
Tell arithmetic patterns from quadratic ones using differences, build the general term for each, and read sigma notation without panic.
Use the first and second derivatives to analyse a cubic graph, locate turning and inflection points, and build the equation of a tangent.
Differentiate from first principles when asked, apply the power rule everywhere else, and know what a derivative actually tells you about a graph.
Choose the right financial formula, handle monthly compounding correctly, and work out loan repayments and outstanding balances without guessing.
Read a parabola or exponential graph properly — intercepts, turning point, asymptotes, domain and range — and find an inverse without guessing.
Work with the common ratio, find any term or sum, and know exactly when an infinite series converges and when it does not.
Turn a word problem into one equation, differentiate it to find the maximum or minimum, and interpret rates of change in real units.
Apply the addition rule, tell independent from mutually exclusive, read a Venn or tree diagram, and count arrangements without listing them.
Solve linear and non-linear systems by substitution, keep your ordered pairs matched, and handle the exponent-law questions that look harder than they are.
Read a hyperbola from its equation — both asymptotes, the shape, the axes of symmetry and its domain and range — and sketch it with confidence.
For employers, schools and training providers
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