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Gauth Blog: Math Study Guides and Homework Tips

Longer pieces, reviewed by working teachers, on how to actually get better at this.

AI and academic integritySee where learning with AI ends and submitting work that is not yours begins. What integrity policies say, plus a four question self test.Studying for math testsStudy for a math test with retrieval practice, spaced repetition, and an error log. Why rereading notes feels productive and still fails.Common algebra mistakesTwelve algebra mistakes that show up in marked work. Each one is shown wrong, then right, with the misconception named and corrected.Showing your workSee how method marks are awarded, why a bare correct answer scores badly, and what a full credit solution looks like line by line.Checking your workSix ways to check a math answer: substitution, estimation, units, symmetry, limiting cases, and reverse operations, shown on real errors.Reading word problemsA five step method for reading word problems without panic, with a phrase to operator table and worked examples that get harder.Solving quadraticsFour ways to solve a quadratic, a way to choose between them, and a derivation of the quadratic formula by completing the square.Choosing an integration methodChoose an integration technique with a decision tree, a worked example on every branch, and the dead ends worth leaving early.Calculus prerequisitesThe algebra and trigonometry calculus assumes you already know, with a check that maps each gap to the guide that closes it.Math anxietyWhat research says about math anxiety, why it feels like a lack of talent, and a practical routine that reduces it.Function transformationsShifts, stretches, and reflections from one principle, so you do not have to memorise the table. Includes why f(x minus 3) moves right.Best AI math solversThe same ten problems through Gauth, Photomath, Symbolab, Mathway, Wolfram Alpha, ChatGPT, and Socratic, scored on correctness and working.

What we write about

Three kinds of thing. Method pieces that work a technique end to end, like solving any quadratic or choosing an integration technique. Study pieces grounded in research rather than folklore — retrieval practice and spaced repetition genuinely work, and re-reading your notes genuinely does not, however productive it feels. And honest pieces about using AI for schoolwork, including where the line sits.

A note on the hardest one to write: math anxiety is treated here as a working-memory problem with evidence behind the interventions, not a pep talk. If maths has felt impossible since a specific bad year, that piece is probably the most useful thing on this site for you, and it is worth reading before any of the method guides.

Everything is written by a mathematician and reviewed by a practising secondary teacher who marks exams, which is why the pieces on showing your work talk about how method marks are actually allocated rather than how people assume they are.

Start somewhere

Concept guidesShorter, method-focused explanations.Subject solversGet your own problem worked out.Academic integrityWhere we think the line sits.How accurate is it?An honest account of the limits.

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