Kit Library / Mathematics / STSE Exam Preparation
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💡 Key Idea
Master these 15 areas, master the paper.
STSE Maths rewards conceptual clarity + formula recall + application. The 15 suggested areas cluster into 5 families:
↳ Every STSE question maps to one of these 5 families — identify the family first, then pick the tool.
📖 Definition
One fraction decides everything.
↳ Recurring or terminating decimal ⇒ rational; non-recurring non-terminating ⇒ irrational.
➗ Formula
Three identities solve half the paper.
↳ Sign flips inside the cube identity are the #1 source of errors — write it slowly.
⚙️ Process
Pick the fastest method, not the first.
↳ If coefficients are 1, substitute; if they're integers, eliminate; if fractions, cross-multiply.
➗ Formula
One formula, all quadratics.
↳ Check $D$ first — it tells you the answer's shape before you compute.
➗ Formula
Two formulas unlock the plane.
↳ Distance = Pythagoras on coordinates; midpoint = simple average.
⭐ Important Fact
Three shortcuts prove similarity.
Similar triangles have equal angles but proportional sides — not equal sides.
↳ Similar ≠ congruent: same shape, different size.
⭐ Important Fact
Angles in circles follow strict rules.
↳ If you see a diameter, look for a right angle — it's almost always the key.
➗ Formula
Every 2D shape in one card.
↳ Always match units — convert cm to m before multiplying.
➗ Formula
Curved vs total — know the difference.
↳ Cone volume is exactly $\tfrac{1}{3}$ of cylinder with same base and height.
➗ Formula
Three words, six ratios.
↳ Memorise the $0°$–$90°$ table cold — it's used in every trig problem.
➗ Formula
Three averages, three uses.
↳ Median resists outliers; mean is pulled by them — pick the right average for the context.
➗ Formula
Favourable over total — that's it.
↳ Always check outcomes are equally likely before applying the formula.
➗ Formula
Constant difference, three formulas.
↳ If last term is given, use the $(a+l)$ form — it's faster.
⚠️ Common Mistake
Same numbers, wrong units, zero marks.
↳ Write units at every step — it forces consistency and catches errors early.
🎯 Exam Tip
The chart lies if you skim.
↳ Spend 20 seconds reading the chart's labels — it saves 2 minutes of wrong calculation.
🌍 Real World
Maths isn't abstract — it's everywhere.
↳ STSE loves word problems — translate the story into an equation before solving.
🧠 Memory Trick
Three syllables, six ratios.
Sin = Opp/Hyp · Cos = Adj/Hyp · Tan = Opp/Adj. Say it aloud three times before the exam.
↳ SOH-CAH-TOA is the fastest way to recall trig ratios under pressure.
Skip the loop, use the formula.
↳ Recognise AP patterns in sums — the formula is always faster than adding.
Four steps, every problem.
↳ A consistent 4-step routine beats random formula-hunting every time.
A high-yield tour of the 15 STSE Maths areas — from number systems and polynomials to trigonometry, statistics and real-life data interpretation. Each bite isolates one exam-critical insight, formula or trap so you can r…
Full explanation, worked examples & memory tricks in the app
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