Math
Interactive Math — Secondary 1 through 4, plus tools and puzzles.
S1 Math Notes
S1 C1 — Primes, HCF and LCM
Breaking a number into its prime factors and writing the result in index form, then using that one skill for everything else: square and cube roots without a calculator, the highest common factor, the lowest common multiple, and the word problems about tiles, gift packs and recurring events that quietly ask for them.
- Prime factorisation
- Index notation
- HCF & LCM
- Roots by factorising
S1 C2 — Integers, Rational & Real Numbers
Numbers below zero and how to order, add, subtract, multiply and divide them — with the sign rules explained rather than chanted. Then the bigger picture: fractions and decimals as rational numbers, roots that refuse to be fractions, and where every number lives on the real number line.
- Negative numbers
- The four operations
- Number line
- Rational vs real
S1 C3 — Approximation & Estimation
Rounding to decimal places and to significant figures — and the difference between the two — then estimation as a skill of its own: rough answers before exact ones, and the habit of asking whether a calculator answer can possibly be right.
- Decimal places
- Significant figures
- Estimation
- Sense-checking answers
S1 C4 — Basic Algebra & Algebraic Manipulation
Letters standing for numbers: what 3x and x² actually mean, collecting like terms, expanding brackets, and taking out a common factor — the four moves every later algebra chapter is built from, plus evaluating an expression once the letter gets a value.
- Algebraic notation
- Like terms
- Expanding brackets
- Common factors
S1 C5 — Linear Equations
Solving equations by doing the same thing to both sides — the balance idea — including equations with brackets and fractional coefficients. Ends where the marks are: turning a sentence about ages, money or lengths into an equation of your own.
- Balancing both sides
- Brackets & fractions
- Checking solutions
- Forming equations
S1 C6 — Linear Functions & Graphs
The Cartesian plane and how a rule like y = 2x + 1 becomes a straight line on it. Plotting from a table of values, reading the gradient as rise over run — positive and negative — and what the numbers in y = ax + b each control.
- Coordinates
- Tables of values
- Straight-line graphs
- Gradient
S1 C7 — Number Patterns
Sequences and the two ways to describe them: the rule from one term to the next, and the general term that jumps straight to the 50th without listing 49. Includes the figure patterns made of dots and matchsticks that the exam likes to grow.
- Sequences
- Term-to-term rules
- The general term
- Figure patterns
S1 C8 — Percentage
Switching between fractions, decimals and percentages, finding a percentage of a quantity, and percentage change in both directions — including the reverse problem, where the answer is known and the original is not. Discounts and GST get their own worked treatment.
- Conversions
- Percentage of a quantity
- Percentage change
- Discount & GST
S1 C9 — Ratio & Rate
Simplifying ratios, sharing a quantity in a given ratio, and the map scales that are really ratios in disguise. Then rates: price per unit and the best-buy comparison, and speed as the rate everyone already knows.
- Simplifying ratios
- Sharing in a ratio
- Rates & best buys
- Speed
S1 C10 — Basic Geometry
The angle facts everything later leans on: angles at a point, on a straight line, and vertically opposite — then two parallel lines cut by a transversal, and the corresponding, alternate and interior angles that come with them, each with its reason named the way the marker wants it.
- Angle facts
- Vertically opposite
- Parallel lines
- Naming reasons
S1 C11 — Polygons & Geometrical Constructions
Angle properties of triangles and quadrilaterals, then the angle sums of any polygon — interior and exterior — and finally real ruler-and-compasses work: bisecting angles, perpendicular bisectors, and constructing triangles and quadrilaterals to specification.
- Triangles & quadrilaterals
- Polygon angle sums
- Bisectors
- Constructions
S1 C12 — Perimeter & Area of Plane Figures
Where the area formulae for the parallelogram and trapezium come from — cut, slide and rearrange — not just what they say. Composite figures built from pieces, and the unit conversion that catches everyone: 1 m² is 10 000 cm², not 100.
- Parallelogram & trapezium
- Where formulae come from
- Composite figures
- Unit conversion
S1 C13 — Volume & Surface Area: Prisms & Cylinders
What makes a solid a prism, why volume is base area times height, and surface area from the net. Cylinders as the limiting case that is not quite a prism, composite solids, and the cubic-unit conversions — including litres — done properly.
- Prisms & nets
- Volume = base × height
- Cylinders
- Composite solids
S1 C14 — Statistical Data Handling
Collecting and tabulating data, then the four displays the syllabus names — pictograms, bar graphs, pie charts and line graphs — when each is the right choice, and how a truncated axis or a scaled picture makes an honest chart lie.
- Collecting & tallying
- The four charts
- Choosing a display
- Misleading graphs
S1 Math Interactives
S1 - StarMath Village (Maths Town RPG)
Run Auntie Sharon's fruit stall in a cozy Stardew-style town — every sale, discount and GST line at the till is real S1 maths, one question per concept, with the whole village cheering you on.
- Ch 8 Percentage
- GST & discounts
- Town RPG
S1 C1 - Primes, HCF, and LCM
Sort primes against the clock, grow factor trees and run the ladder method, then watch HCF and LCM come alive — runners lapping a track, gift packs, buses, tiles and flashing lanterns with pause-anywhere animations.
- Prime factorisation
- HCF & LCM
- 5 animated stories
S1 C2 - Integers, Rational & Real Numbers
Put negative numbers on a number line, then build every sign rule yourself with number discs — zero pairs for adding, a flip of the disc for taking the negative. Finish with fractions, decimals, and where each number sits inside the real numbers.
- Number line & integers
- Sign rules with discs
- Rational & real numbers
S1 C3 - Approximation & Estimation
See exactly where a number sits between its two neighbours before you round it, with the midpoint marked. Work through the five significant-figure rules digit by digit, then estimate in real situations — buses, lift loads, currency — where a sensible range beats one exact number.
- Rounding off
- Significant figures
- Real-world estimation
S1 C4 - Basic Algebra & Algebraic Manipulation
Find out for yourself why 2n is not 2 + n, then take the number discs from Chapter 2 and give them letters. Group like terms, expand a bracket by making groups, flip the discs for a negative multiplier, and run the whole thing backwards to factorise.
- Notation & expressions
- Like terms with discs
- Expand & factorise
S1 C5 - Linear Equations (Balance Scale)
Build an equation on a balance scale, then keep it balanced — add, subtract, divide or group both sides until x stands alone.
- Linear equations
- Balance method
- Solve for x
S1 C6 - Flappy Animals (Coordinates)
The arcade dodger with maths mode on — switch on the axes and read your bird's position as coordinates while dodging pipes and answering questions.
- Linear functions
- Coordinates
- Quiz mode
S1 C7 - Number Patterns
Say what governs a sequence, then hunt its general term with differences, common ratios and guess-and-check. Step a figure sequence up one at a time — the new pieces light up, and every count is taken off the drawing — then meet the bee family tree, Fibonacci squares and the Golden Ratio.
- Sequences & rules
- General term T(n)
- Figures & Fibonacci
S1 C8 - Percentage
Move between a percentage, a fraction and a decimal and watch all three stay in step. Find out why 25% of one thing and 25% of another are different sizes, why a 10% rise then a 10% fall leaves you short, and how a restaurant bill really adds up — discount, service charge and GST each charged on something different.
- Fraction, decimal, percent
- Percentage change
- Profit, discount & GST
S1 C9 - Ratio & Rate
Compare quantities with a ratio, and see why the units have to match before you simplify anything. Share an amount in a given ratio on a bar model, meet the Golden Ratio, then work with rates — best buys, interest, exchange rates and tax — and finish with speed, where the average is never the average of the speeds.
- Ratio & sharing
- Rate & best buy
- Speed & average speed
S1 C10 - Basic Geometry
Measure angles on a 360° protractor and name every type, then explore complementary, supplementary, intersecting-line and parallel-line angle properties — with a quiz to test yourself.
- Types of angles
- Angle properties
- Parallel lines
S1 C11 - Polygons & Constructions
Reshape triangles and special quadrilaterals, discover the angle-sum rules by splitting polygons into triangles, then pick up a virtual ruler, protractor, set square and compasses to construct figures step by step.
- Triangles & quadrilaterals
- Angle sums
- Constructions
S1 C12 - Perimeter & Area
Stretch six different shapes on a centimetre grid and count the unit squares inside, then build each area formula yourself — cut and slide a parallelogram into a rectangle, rotate a trapezium into a parallelogram, and unroll a circle into sectors to reach πr². Finish with m² ↔ cm² conversion and a quick-check quiz.
- Perimeter & area
- Formula derivations
- m² ↔ cm²
S1 C13 - Volume & Surface Area
Extrude a base into a prism and watch the volume build from its cross-section, then unfold nets to total the surface area. Discover that all twelve formulas are really just two — V = A h and TSA = P h + 2A — and test yourself with flip cards and a printable summary sheet.
- Prisms & cylinders
- Nets & surface area
- Formula recall
S1 C14 - Statistical Data Handling
Tally a survey as the answers arrive, then show the same data five ways. Drag a bar graph's axis off zero and watch it start to lie, lay pie sectors down with a protractor, and take apart six real misleading graphs — a cut axis, a 3-D pie, a rigged poll.
- Tally & frequency
- Bar, pie & line graphs
- Spotting a lie
S2 Math Notes
S2 C1 — Linear Graphs & Simultaneous Equations
Graphs of ax + by = k and the horizontal and vertical lines students forget, then two equations solved together three ways: reading the crossing point off a graph, elimination, and substitution — ending with the word problems that supply the two equations.
- Graphs of ax + by = k
- Graphical method
- Elimination & substitution
- Word problems
S2 C2 — Linear Inequalities
What stays true when you add to, subtract from, multiply or divide both sides of an inequality — and the one move that flips the sign. Solutions drawn on the number line with the open and filled circles used correctly, then problems that ask for the smallest integer that works.
- Properties of inequality
- Solving inequalities
- Number-line answers
- Smallest & greatest values
S2 C3 — Expansion & Factorisation
Expanding the product of two linear expressions, then reversing it: factorising ax² + bx + c by the cross method, and — for G3 — factorisation by grouping, the four-term trick that makes later chapters possible.
- Expanding products
- The cross method
- Factorising quadratics
- Grouping (G3)
S2 C4 — Special Algebraic Identities
The three identities worth memorising — (a + b)², (a − b)² and a² − b² — used in both directions: expanding without grinding through brackets, factorising on sight, and the mental-arithmetic party tricks like 199² they make possible.
- The three identities
- Expanding on sight
- Factorising on sight
- Clever arithmetic
S2 C5 — Quadratic Equations & Graphs
One small idea carries the chapter: if two things multiply to give zero, one of them is zero. Solving quadratics by factorising, then the graph of y = ax² + bx + c — the parabola, its symmetry, and what the sign of a does — and quadratics as models of real situations.
- Zero-product idea
- Solving by factorising
- The parabola
- Quadratic models
S2 C6 — Algebraic Fractions & Formulae
Simplifying algebraic fractions and multiplying and dividing them, then the G3 extensions: adding and subtracting with unlike denominators, fractional equations that reduce to linear ones, and changing the subject of a formula — the skill science lessons quietly assume.
- Simplifying fractions
- Multiply & divide
- Fractional equations
- Change of subject (G3)
S2 C7 — Direct & Inverse Proportions
Two quantities growing together, or one shrinking as the other grows — recognising each from a table, writing the equation, and reading the graphs. Map scales complete the picture: distance scales, and the area scales that square the ratio.
- Direct proportion
- Inverse proportion
- Their graphs
- Map scales
S2 C8 — Congruence & Similarity
Figures that are exactly the same and figures that are the same shape: what congruence statements promise letter by letter, what similarity does to lengths, and — for G3 — enlargement with a scale factor and the centre it radiates from.
- Congruent figures
- Similar figures
- Matching statements
- Enlargement (G3)
S2 C9 — Pythagoras' Theorem
The one theorem everyone remembers, taught with its converse: the square on the hypotenuse for finding sides, and the check that tells you whether an angle really is 90°. Ladders, diagonals and every right triangle the exam can dress up.
- The theorem
- Finding sides
- The converse
- Real applications
S2 C10 — Trigonometric Ratios
Sine, cosine and tangent of an acute angle as ratios of sides — TOA CAH SOH earned, not just recited — used to find missing sides and missing angles in right-angled triangles, then heights and distances measured without climbing anything.
- The three ratios
- Finding sides
- Finding angles
- Heights & distances
S2 C11 — Pyramids, Cones & Spheres
Volume and surface area for the three curved-and-pointed solids, with the formula-sheet split made explicit: the cone and sphere formulae are printed on the eventual national paper, pyramid volume is not. Composite solids finish the job.
- Pyramids
- Cones
- Spheres
- What the sheet gives
S2 C12 — Probability of Single Events
Chance made countable: listing a sample space, probability as favourable over possible, the 0-to-1 scale, and the complement rule that answers “at least one” questions the short way — grounded in dice, cards, spinners and real experiments.
- Sample space
- P(event)
- The 0–1 scale
- Complement rule
S2 C13 — Statistical Diagrams
The Sec 2 additions to the chart toolkit: dot diagrams and stem-and-leaf plots, which keep every data value visible while still showing the shape — how to draw them, read them, and say which display fits which data.
- Dot diagrams
- Stem-and-leaf
- Reading distributions
- Choosing a display
S2 C14 — Averages of Statistical Data
Mean, median and mode — how to find each from raw data and from a frequency table, including the Σfx/Σf formula the national paper prints — and the judgement call the marks are really for: which average honestly represents the data, and which one an outlier has dragged.
- Mean, median, mode
- Frequency tables
- Σfx/Σf
- Choosing the average
S2 Math
More coming soon
Secondary 2 Math interactives are on the way.
Watch this spaceUpper Sec EM
EM C1 — Indices & Standard Form
The five laws of indices, what a zero, negative or fractional index actually means, and standard form for numbers too big or too small to write out. Ends with compound interest — the one formula here the paper prints for you.
- Laws of indices
- Zero & negative indices
- Rational indices
- Standard form
EM C2 — Quadratic Equations & Graphs
Three ways to solve a quadratic — completing the square, the formula, and reading the roots off a graph — plus fractional equations that turn into quadratics, and sketching the curve from its factorised or completed-square form.
- Completing the square
- Quadratic formula
- Fractional equations
- Sketching graphs
EM C3 — Linear Inequalities
Solving inequalities and showing the answer on a number line, including the rule every paper punishes: multiplying or dividing by a negative reverses the sign. Then simultaneous inequalities, and the integer values they pin down.
- Solving and reversing the sign
- Simultaneous inequalities
- Greatest and least integers
- Modelling with inequalities
EM C4 — Graphs of Functions
What each power of x looks like, from x⁻² up to x³, plus reciprocal and exponential curves and their asymptotes — then finding the gradient of a curve by drawing a tangent, on distance–time and speed–time graphs.
- Cubic & power graphs
- Reciprocal graphs & asymptotes
- Exponential graphs
- Gradient of a curve
EM C5 — Sets
The twelve symbols the syllabus names, Venn diagrams and the universal set, union and intersection, shading a region from its notation — and the counting problems that hide an unknown in the overlap.
- Set notation
- Venn diagrams & complement
- Union & intersection
- Real-world counting problems
EM C6 — Matrices
Reading information out of a matrix, adding and scaling them, and multiplying — where the inner dimensions must match, the order of the answer comes from the outer ones, and AB is not BA.
- Order & interpretation
- Adding & scaling
- Multiplication & conformability
- Matrices as data models
EM C7 — Congruence & Similarity
When two triangles are forced to be identical — SSS, SAS, AAS, RHS, and never SSA — and when they are merely the same shape. Then the chain that follows: multiply every length by k and areas grow by k², volumes by k³.
- Bisectors & scale drawings
- SSS, SAS, AAS, RHS — never SSA
- Similarity tests
- Area & volume ratios
EM C8 — Properties of Circles
Nine properties of chords, tangents and angles — the angle at the centre, the angle in a semicircle, angles in the same segment, cyclic quadrilaterals — and the angle chases that string them together, where naming the reason is the working.
- Chords & symmetry
- Tangents
- Angle at the centre
- Cyclic quadrilaterals
EM C9 — Trigonometry
Sine and cosine of obtuse angles, the area of a triangle as ½ab sin C, and the sine and cosine rules for triangles with no right angle. Then angles of elevation and depression, bearings, and lengths and angles inside a solid.
- Sine & cosine rules
- Area = ½ab sin C
- Bearings
- 3-D problems
EM C10 — Arc, Sector & Radian Measure
Arc length, sector area and the area of a segment — first in degrees, then again in radians. What a radian actually is, how to convert between the two, and which of these formulae the paper gives you.
- Arc length & perimeter
- Sector area
- Area of a segment
- Radian measure
EM C11 — Coordinate Geometry
Three tools that turn geometry into arithmetic: the distance between two points, the gradient of a line, and the equation y = mx + c. Then using all three on a shape — to prove it, to complete it, or to find its area.
- Distance formula
- Gradient of a line
- y = mx + c
- Geometric problems
EM C12 — Vectors in Two Dimensions
Column vectors and their magnitude, adding and subtracting by the triangle and parallelogram laws, scalar multiples and what makes two vectors parallel, position vectors — and the geometric proofs that all of it makes short work of.
- Column vectors & magnitude
- Adding, subtracting, scaling
- Position vectors
- Geometric problems
EM C13 — Statistical Data Analysis
Cumulative frequency curves and reading the median, quartiles and percentiles off them; box-and-whisker plots; and standard deviation for grouped and ungrouped data — then using an average and a spread together to compare two sets.
- Cumulative frequency curves
- Quartiles, percentiles & IQR
- Box-and-whisker plots
- Standard deviation
EM C14 — Probability of Combined Events
Possibility diagrams and tree diagrams, the Addition Law for mutually exclusive events and the Multiplication Law for independent ones — and the distinction that decides most of the marks: whether what you took out goes back in.
- Possibility diagrams
- Addition Law & mutually exclusive
- Multiplication Law & independence
- With & without replacement
EM C15 — Problems in Real-World Contexts
The last question of Paper 2, which never tells you which topic it is. Running costs and life-cycle comparisons, packing and layout, timetables and networks, games of chance, and reading a decision out of a table of data.
- Money & cost decisions
- Design & measurement
- Data & chance
- Justifying a decision
S3 C9-10 - Similar & Congruent Lab
Find out how much you must be told before a triangle is forced — SSS, SAS, AAS and RHS lock it, SSA does not, and you can drag out both triangles that fit. Then build proofs with the vertices in the right order, and watch one slider drive length, area and volume together.
- Congruence tests
- Similarity tests
- Area & volume ratios
More coming soon
More Upper Sec Elementary Math interactives are on the way.
Watch this spaceUpper Sec AM
AM C1 — Quadratic Functions
Additional Maths, K341. The three forms of a quadratic and what each one gives away, completing the square to find a maximum or minimum, the conditions for a curve to stay wholly above or below the axis, and quadratics used as models.
- The three forms
- Completing the square
- Always positive or negative
- Quadratic models
AM C2 — Equations and Inequalities
Solving a quadratic by completing the square and by the formula, and what the discriminant says about how many roots there are before you find them. Then a line meeting a curve as a pair of simultaneous equations, and quadratic inequalities read off a sketch.
- Completing the square
- The discriminant
- Line meets curve
- Quadratic inequalities
AM C3 — Surds
Roots that will not simplify to a fraction, and the rules for adding, multiplying and rationalising them — clearing a surd from a denominator with its conjugate. Ends with equations whose answers are surds, and the check that catches an answer that is not really one.
- Simplifying surds
- Rationalising the denominator
- Conjugates
- Equations with surds
AM C4 — Polynomials, Cubic Equations and Partial Fractions
Dividing one polynomial by another, and the two theorems that shortcut it: the remainder theorem and the factor theorem. Then factorising cubics, the sum and difference of two cubes, and splitting a fraction into partial fractions — with a denominator that is linear, repeated, or a quadratic that will not factorise.
- Polynomial division
- Remainder & factor theorems
- Cubic equations
- Partial fractions
AM C5 — Binomial Theorem
Expanding (a + b)n without multiplying it out n times: the binomial coefficients, Pascal’s triangle, and the general term that lets you pick out one coefficient — or the term with no x at all — without writing the rest.
- n! and nCr
- Expanding (a + b)n
- The general term
- Finding a particular term
AM C6 — Exponential and Logarithmic Functions
What a logarithm is — an index in disguise — and the three laws with change of base, then equations in which the unknown is an index. The graphs of y = ax and y = loga x, mirror images in the line y = x, and the growth and decay they model.
- Exponential equations
- Logarithms and their laws
- Change of base
- Graphs and models
AM C7 — Coordinate Geometry
Gradient, midpoint and the condition for two lines to be parallel or perpendicular, then the area of any polygon from its vertices by the shoelace method. The second half is the circle: its two equation forms, finding centre and radius, and the tangent that meets the radius at right angles.
- Parallel & perpendicular
- Midpoint
- Area of a polygon
- Equation of a circle
AM C8 — Linear Law
Turning a curve you cannot read constants off into a straight line you can: y = axn and y = kbx become Y = mX + c once you take logs, and the gradient and intercept hand back the unknowns. Which variables to plot is the whole skill.
- Why straighten a curve
- y = axn and y = kbx
- Choosing X and Y
- Reading constants back
AM C9 — Trigonometric Functions and Graphs
The six trig functions for angles of any size, in degrees and radians, with the quadrant rule that fixes their signs. Exact values for 30°, 45° and 60°, principal values for the inverse functions, and the graphs of a sin bx + c and its relatives — amplitude, period and shift.
- Angles of any magnitude
- Exact values
- Principal values
- Amplitude, period & graphs
AM C10 — Trigonometric Equations and Identities
Solving trig equations across a whole interval without dropping a solution, and the identities the paper prints: Pythagorean, compound-angle, double-angle. Then the one it does not — the R-formula, which turns a cos θ + b sin θ into a single wave whose maximum and minimum you can read off.
- Trig equations
- Proving identities
- Compound & double angles
- The R-formula
AM C11 — Gradients, Derivatives and Differentiation Techniques
What a derivative is — the gradient of the tangent, caught as the limit of a family of chords — and the machinery for finding one: the power rule for any rational index, then the chain, product and quotient rules. Ends with higher derivatives, and reading where a function rises or falls from the sign of dy/dx.
- First principles, once
- The power rule
- Chain, product & quotient
- Increasing & decreasing
AM C12 — Applications of Differentiation
The derivative put to work: tangents and normals at a point, rates of change chained together — how fast the volume grows while the radius grows — and stationary points classified by sign table or second derivative. Ends with the maximisation problems the whole topic exists for.
- Tangents & normals
- Connected rates of change
- Stationary points
- Maximum & minimum problems
AM C13 — Differentiation of Trigonometric, Exponential and Logarithmic Functions
The derivatives the formula sheet does not print: sin, cos and tan — true only in radians — then ex, the function that is its own derivative, and ln x. The chain rule carries each into composites, and the applications of the last two chapters run again with the new functions.
- The trig derivatives
- Radians only
- ex and ln x
- Chain-rule composites
AM C14 — Integration
Differentiation run backwards: the power rule with the new power on the bottom, the + c every indefinite integral must carry, and the linear-inside rule for (ax + b)n. Every answer checked by differentiating it back — and the one power the rule cannot touch, n = −1.
- Anti-differentiation
- The + c
- (ax + b)n
- Trig, ex and 1/x
AM C15 — Applications of Integration
The definite integral as the area under a curve: evaluate F(b) − F(a) and the + c cancels itself. Then the questions that need a picture first — regions below the axis coming out negative, areas split at a root and added as magnitudes, and regions closed off by a line.
- Definite integrals
- Area under a curve
- Below the axis
- Curve-and-line regions
AM C16 — Kinematics
A particle on a straight line, run entirely on calculus: differentiate displacement for velocity and acceleration, integrate back with the constants fixed by initial conditions. At rest means v = 0 — and total distance is not displacement, so split the motion where the particle turns.
- s, v and a
- Instantaneous rest
- Initial conditions
- Distance vs displacement
AM C17 — Proofs in Plane Geometry
Writing a proof the marker can follow: statement by statement, each line carrying its named reason. The congruence tests and similarity, what a special quadrilateral lets you assume and what it makes you prove, the midpoint theorem — and the tangent-chord angle, equal to the angle in the alternate segment.
- Writing a proof
- Congruent & similar triangles
- Special quadrilaterals
- Tangent-chord theorem
More coming soon
Upper Sec Additional Math interactives are on the way.
Watch this spaceMath — Others
Math Driller (S1–S4 + A Maths)
Endless generated drill questions with instant marking — type answers in a proper math editor — plus printable worksheets with answer keys for teachers, tiered to the textbook exercises.
- 369 skills, S1–S4 + AM
- Auto-marked practice
- Printable worksheets
Math-Rover
Drive a rover with typed commands — distances, angles and coordinates — through challenges from thin ropes to drawing a whole house.
- Coordinates
- Angles
- Coding commands
Happy / Sad Numbers
Pick a number, square its digits, sum them, repeat — does it reach 1 (happy) or fall into a loop (sad)? Trace the sequence step by step.
- Happy numbers
- Iteration
- Cycles & loops
CM-97SG X Calculator
A full scientific calculator in your browser — natural display, fractions, trig, logs, memory and S⇔D, laid out like the approved exam model.
- Natural display
- Fractions
- Trig & logs
- Memory
Math Gallery
Interactive 3D exhibits of beautiful mathematics in six rooms — surprises like Monty Hall and the birthday problem, impossible shapes like the Gömböc and Möbius strip, emergent patterns, higher dimensions, networks and proofs you can see — each with a “What's the maths?” panel and a Sec 1–4 syllabus note.
- Probability & statistics
- Geometry & topology
- Patterns & chaos
- Proofs you can see