Straight, practical advice from Mr. Gan on choosing subjects, fixing the habits that cost marks, and turning borderline passes into distinctions.
Choosing subjects and understanding how the O-Level syllabus shapes your child's options.
A-Math is one of the hardest O-Level subjects in Singapore. Here is the exact approach that helps students go from borderline passes to A1 distinctions.
Read guide →Many families make this choice without fully understanding the difference. This guide covers what each subject actually tests and how the decision affects your child's future options.
Read guide →Struggling with maths in Singapore secondary school is more common than most parents realise. The root cause is almost never intelligence. Here is what is really going on.
Read guide →Exam-room tactics that protect the easy marks most students throw away under pressure.
Learn how to find mean, median, and mode from frequency tables — common mistakes and when to use each measure.
Read guide →Every 3D trig question reduces to one flat right-angled triangle hidden inside the solid. Learn the 3-step extract-and-redraw method with cuboid and pyramid worked examples.
Read guide →The 6 set symbols, the union formula, and the inside-out method for filling any 2-set or 3-set Venn diagram without double-counting, with fully worked examples.
Read guide →The wrong degree/radian setting silently wrecks every trig answer. Check your Casio fx-97SG in five seconds and run the 30-second pre-exam routine so it never happens again.
Read guide →A decision flowchart that picks the right rule on sight, three worked examples, and the obtuse-angle trap examiners love to set. Stop freezing on triangle questions.
Read guide →Turn ax² + bx + c into vertex form and read off the minimum point, line of symmetry, and surd-form solutions directly. Covers a≠1 and negative coefficients too.
Read guide →Isolate any target variable with inverse operations in reverse order, even when it's buried in a square root, appears twice, or sits in a denominator.
Read guide →Draw North at the right point, measure clockwise, and use back bearings and the cosine rule with confidence. The diagram is where marks are actually lost.
Read guide →The split-the-middle-term method replaces trial and error with a repeatable 4-step process that works even when a is not 1.
Read guide →Build the table against upper class boundaries, read off the median and quartiles precisely, and compare box plots the way examiners expect.
Read guide →All 8 O-Level circle properties grouped into 4 categories, with the exact mark-scheme abbreviation examiners expect for each.
Read guide →A two-question decision rule for choosing the faster method every time, four worked examples, and the bracket mistake that silently costs marks.
Read guide →The 4 congruence tests with diagrams, two full worked proofs, and the exact 3-line structure examiners want for full marks.
Read guide →The 3 similarity tests with diagrams, worked examples, and the length-area-volume scale-factor rule (k, k², k³) that trips students up.
Read guide →The frequency-table method, the exact calculator STAT-mode steps, and the 2-part structure examiners expect when comparing two data sets.
Read guide →Line, parabola, cubic, hyperbola, y=a/x² and exponential — the general shape of each family and the sign rule that flips it, plus a fast way to spot the family from any equation.
Read guide →I = PRT/100 gives simple interest, A = P(1 + r/100)ⁿ gives compound. Learn to convert r and n for half-yearly compounding and avoid the formula mix-up that costs marks.
Read guide →Find the original price or value before a percentage discount or increase, by writing the final value as a decimal multiplier and dividing back, not adding the percentage back on.
Read guide →Average speed is total distance divided by total time, not the simple average of two speeds. Two worked examples show the correct method, including why rest stops count towards the total time.
Read guide →Every volume and surface area formula for cones, spheres, cylinders, pyramids, prisms and cuboids, including which ones the O-Level formula sheet actually gives you and how to find slant height with Pythagoras.
Read guide →Length scale factor k gives an area scale factor of k squared and a volume scale factor of k cubed, the single most common mistake students make in similar figures questions. Two worked examples cover a similar-triangle area ratio and a similar-container volume ratio.
Read guide →Learn the two-step method for finding y = mx + c from any two coordinates: calculate the gradient, then substitute one point to solve for c. Covers parallel lines, horizontal/vertical lines, and the classic subtraction-order mistake.
Read guide →The distance formula is Pythagoras' theorem in disguise: draw the right triangle between two points and the hypotenuse is the distance. The midpoint is just the average of the coordinates, worked through two exam-style examples including finding a missing endpoint.
Read guide →Tree diagrams turn multi-stage probability into a repeatable multiply-along, add-across process, and this guide pins down the one detail that costs marks: with replacement the second-draw fractions stay the same, without replacement they shrink.
Read guide →Mutually exclusive events cannot happen together and add: P(A or B) = P(A) + P(B). Independent events do not affect each other and multiply: P(A and B) = P(A) x P(B). Two worked examples show exactly when to use each.
Read guide →Learn the two nth-term methods O-Level E-Math actually tests: dn + c for linear sequences (tied to the gradient of a straight line), and constant second differences for quadratic dot patterns.
Read guide →A column vector is a movement, not a position: vector AB is always B minus A, and its magnitude is just Pythagoras applied to the components. Two worked examples cover finding AB and its surd magnitude from coordinates, and solving for unknowns in a vector equation using scalar multiples.
Read guide →Try factorising first, use the quadratic formula when it always has to work (or the question asks for 2 decimal places), and complete the square only when the question asks for it or for a maximum/minimum value.
Read guide →Gradient means speed on a distance-time graph but acceleration on a speed-time graph, and only the speed-time graph's area gives you distance travelled. Two worked examples show how to read a two-stage journey and a speed-time trapezium without falling for the classic "flat means stopped" mistake.
Read guide →Every index law in one place: multiply by adding indices, divide by subtracting them, and turn negative or fractional indices into reciprocals and roots, with two fully worked exam-style examples.
Read guide →Converting numbers to and from standard form, multiplying and dividing with index laws, adding and subtracting by aligning powers first, and avoiding the classic A out of range mistake.
Read guide →Solve inequalities like equations, except one rule: flip the sign when you multiply or divide by a negative. Covers number lines and listing integer solutions.
Read guide →Label the triangle relative to the marked angle, pick the ratio that has what you know and what you want, then solve. Two worked examples: finding a side and finding an angle.
Read guide →When you have two sides of a triangle and the included angle but no height, ½ab sin C gives the area directly, and it works for obtuse angles too.
Read guide →Both angles are measured from the horizontal, and the depression angle from the top always equals the elevation angle from the bottom (alternate angles). Two worked examples show how to sketch first, mark the horizontal, and pick the right trig ratio.
Read guide →Arc length and sector area both come from the same fraction, theta over 360, but students still lose marks forgetting that sector perimeter needs the two radii added to the arc. Two worked examples cover exact-pi and 3sf answers plus a full perimeter question.
Read guide →Alternate angles are equal, corresponding angles are equal, co-interior angles sum to 180°: how to spot each pattern fast and name the reason examiners want.
Read guide →The exterior angles of any polygon always sum to 360°, which makes it the fastest route to finding the number of sides or a missing interior angle. Two worked examples cover the regular-polygon and irregular-polygon cases.
Read guide →Same-radius arcs from both ends of a segment, then join where they cross: that's the perpendicular bisector, and every point on it is equidistant from the two endpoints. This guide covers both classic O-Level constructions with worked examples and the marks-losing mistakes to avoid.
Read guide →HCF takes the lowest power of every common prime; LCM takes the highest power of every prime present. Two worked examples (360 and 300, plus a bells word problem) show how to translate exam-style word problems into the right operation.
Read guide →Decimal places count from the decimal point, significant figures count from the first non-zero digit, and mixing up the two rules is one of the most common ways O-Level students lose marks on small decimals.
Read guide →A one-test method (can it be written as an exact fraction) for sorting integers, decimals, surds and π into rational or irrational, with a recurring-decimal-to-fraction worked example.
Read guide →A step-by-step guide to the compatibility rule and row-by-column method for multiplying matrices, with worked examples showing why AB and BA are usually not equal.
Read guide →A step by step guide to turning each condition in a loci question into a locus you can draw, then shading only the region where every condition overlaps.
Read guide →A four-sided shape with all four corners on one circle follows one reliable rule: opposite angles always sum to 180°, and this guide shows how to apply it and prove it with worked examples.
Read guide →Divide a quantity in a given ratio, convert a map scale into a real distance, and see why the area scale factor is the length scale factor squared.
Read guide →A step-by-step method for proving three points are collinear using vectors: form two vectors from a shared point, show one is a scalar multiple of the other, then state the common point, with two fully worked O-Level examples including one with an unknown constant k.
Read guide →A step-by-step method for splitting composite solids (cone on cylinder, hemisphere on cube) into basic shapes and correctly combining their volumes and surface areas, including the hidden-join trap that costs the most marks.
Read guide →A comparison of two data sets needs two separate statements, one on the average and one on the spread, both written in context, and this guide gives the exact wording that earns full marks.
Read guide →A 3-step check (right angle, hypotenuse, add or subtract) that stops students misapplying Pythagoras' theorem before it breaks their SOH-CAH-TOA and 3D trigonometry working.
Read guide →A quick same-way test tells you from the numbers in a word problem whether direct or inverse proportion applies, so you set up the right equation the first time.
Read guide →Learn to recognise reciprocal graphs (y = k/x, two branches, two asymptotes) versus exponential graphs (y = k·aˣ, one curve, one asymptote) on sight, with worked examples and the sign rules for each.
Read guide →Learn how to find the gradient of a curve at any point by drawing an accurate tangent and applying the gradient formula to two points on it.
Read guide →Read solutions off a graph by finding where two curves or lines cross: the intersection point gives the x and y values that satisfy both equations at once.
Read guide →A step-by-step guide to reading conversion graphs accurately and building a real-life linear model (y = mx + c) from a word problem.
Read guide →Master the perimeter and area formulas for rectangles, triangles, composite shapes and circles, including circumference and area of a circle, with worked examples for O-Level E-Math.
Read guide →Learn to recognise square, cube, triangular, and Fibonacci-style number sequences on sight and build the correct nth term without guesswork.
Read guide →A step-by-step guide to finding P(A) from the sample space and using the complement rule 1 − P(A) for "not" and "at least one" O-Level probability questions.
Read guide →Learn the fixed order for collecting like terms and expanding brackets, plus the three identities (a+b)², (a-b)², and (a+b)(a-b) that turn slow expansion into instant recall.
Read guide →Factorise first, then simplify, add, subtract, multiply, divide and solve algebraic fractions with a repeatable method for O-Level E-Maths.
Read guide →A step-by-step method for solving linear equations with brackets and fractions, showing exactly the working examiners award marks for.
Read guide →A clear walkthrough of matrix addition, subtraction, scalar multiplication, and the zero and identity matrices, with a data-handling example, for O-Level E-Maths.
Read guide →A clear, repeatable method for rate questions and profit/loss questions: keep cost price and selling price straight, and always find percentage profit or loss against the cost price.
Read guide →Find a circle segment's area by taking sector area minus triangle area, with the ½r²(θ − sin θ) shortcut for radians.
Read guide →A property-table reference for classifying triangles by side and angle, matching each of the eight quadrilaterals to its parallel-side, equal-side, and diagonal properties, and reading off line and rotational symmetry.
Read guide →A step-by-step ruler-and-compasses method for constructing triangles from SSS, SAS or ASA data, extended to quadrilaterals by splitting the shape into two triangles along a shared diagonal.
Read guide →Sine stays positive but cosine and tangent turn negative for obtuse angles, and this guide shows how to use the sin(180° − θ) and cos(180° − θ) identities to find and solve with them correctly.
Read guide →A step-by-step method for reading and plotting coordinates on the Cartesian plane correctly, covering the x-before-y order, quadrant sign rules, and the careless mistakes that cost marks in O-Level E-Maths coordinate geometry.
Read guide →A quick powers-of-ten method for converting between metric prefixes from kilo down to nano, with the direction rule that trips most students up.
Read guide →How the number sets nest inside each other, from counting numbers up to the reals, with worked examples on classifying any number correctly.
Read guide →Rearranging the speed formula and converting between km/h and m/s without losing marks on mismatched units.
Read guide →The multiplier method that turns discount, commission and GST questions into a single step instead of three.
Read guide →Finding the exact point where two lines cross, and what the algebra tells you when the lines are parallel.
Read guide →One cross-section rule that generates every prism formula, plus the curved-versus-total surface area trap.
Read guide →Why volume uses vertical height and surface area uses slant height, and how Pythagoras converts between them.
Read guide →The vocabulary that makes the nth term make sense: terms, positions, and term-to-term versus position-to-term rules.
Read guide →Combining vectors in column form and reading journeys off a diagram, including the AB = b minus a rule.
Read guide →Proving a shape is a parallelogram and finding the position vector of a point that divides a line in a given ratio.
Read guide →Why a single extreme value ruins the range, and the exact phrasing that earns the comparison mark.
Read guide →Every diagram in the syllabus: pictograms, bar charts, pie charts, line graphs, dot diagrams, histograms and stem-and-leaf, plus the gap rule and pie chart angles.
Read guide →Percentiles are quartiles generalised, plus the top-versus-bottom conversion students get backwards.
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