Pre-IB Mathematics Tuition
Year 3 & Year 4

Year 3 Foundation Programme

Small group online sessions that build the core mathematical fluency every pre-IB student needs — starting with indices and the laws of exponents, then algebraic expansion and factorisation, radicals and surds, and Pythagoras’ theorem. Your child learns to set out full, annotated working from day one — the ‘state the rule, then apply it’ habit that A-Worthy’s own solution manuals are built around, where every line carries a short ‘Why:’ explaining the move. By the end of Year 3, the foundations for logarithms, trigonometry and calculus are firmly in place.

• Indices and the laws of exponents
• Sets and Venn diagrams
• Algebraic expansion and factorisation
• Radicals and surds (including rationalising the denominator)
• Pythagoras’ theorem and its applications

SGD 280 / month

Year 4 Advanced Programme

Rigorous preparation across the toughest pre-IB topics, taught the way IB examiners reward: full analytical working with the reasoning shown at every step. Your child masters logarithms and exponential functions, trigonometry, and an introduction to calculus — differentiation from first principles, the differentiation rules, tangents and stationary points, and an introduction to integration and areas. Each topic is drilled through A-Worthy’s own annotated practice sets — including a 120-question Introduction to Calculus set with full, line-by-line model solutions — so the habits that earn method marks become automatic.

• Functions, graphs, and transformations
• Logarithms and exponential functions (laws of logs, change of base)
• Trigonometry and its applications
• Introduction to calculus: differentiation from first principles
• Differentiation rules, tangents, and stationary points
• Introduction to integration and areas under curves

SGD 320 / month

Individual Coaching

Fully customised to the student’s specific gaps — whether it’s surds, logarithms, trigonometry, or differentiation from first principles. Individual online sessions via Zoom, scheduled at your convenience.

SGD 120 / session

Number, Algebra & Functions

• Indices and the laws of exponents
• Sets and Venn diagrams
• Algebraic expansion and factorisation
• Radicals and surds (rationalising the denominator)
• Logarithms and exponential functions
• Functions, graphs, and transformations

Geometry, Trigonometry & Calculus

• Pythagoras’ theorem and its applications
• Coordinate geometry (gradient, midpoint, equation of line)
• Trigonometry and its applications
• Introduction to calculus: differentiation from first principles
• Differentiation rules, tangents, and stationary points
• Introduction to integration and areas under curves

See

Most students lose marks before they write a single line of working — because they misread what the question is actually asking. In the See step, your child learns to decode every question the way a lawyer reads a contract: what is the command word (solve, simplify, factorise, differentiate, show that)? Is this a first-principles question or one to be done by the rules? Which topic — indices, surds, logarithms, trigonometry, calculus — is really being tested? For differentiation, this means recognising whether the limit definition is required or a standard rule applies. For surds, it means seeing the conjugate that will rationalise the denominator. By the time your child picks up the pen, they already know exactly which method to deploy.

Hit

Once the question type is clear, your child reaches for the right tool — and states the rule before applying it. This isn’t vague advice like ‘show your working’; it’s a specific, named procedure for each topic: the limit definition for differentiation from first principles, the power rule for standard differentiation, the laws of logarithms for log equations, the conjugate method for surds, and the ‘reverse the power rule, never drop the + C’ routine for integration. Writing the rule down first — exactly as our annotated manuals do — is what turns a guess into a method an examiner can award marks for.

Apply

This is where the method becomes actual working — line by line, nothing skipped. Your child constructs the solution under guided conditions with live tutor intervention, not by passively watching. For differentiation from first principles, that means substituting x + h everywhere, expanding, and cancelling the h in the denominator before letting h tend to zero — the move the whole method hinges on. For integration, it means carrying the + C every time. Jeremy provides real-time feedback on screen-shared workings, flagging missing steps and careless slips as they happen. With a maximum of 6 students, every child gets at least three individual feedback touches per session.

Refine & Practise

The steps that turn good students into excellent ones. Your child self-checks every solution against a topic-specific checklist drawn straight from our ‘Watch:’ callouts: did you let h tend to zero rather than substitute h = 0 too early? Did the + C survive? Do logs only ever take positive arguments? Then comes retrieval practice — the most underrated study technique in education. Your child reworks key problems from memory until the procedure is automatic. This is how technique transfers from the classroom to the exam hall: not through last-minute cramming, but through spaced, deliberate repetition — the kind our 120-question calculus drill set is built for.

Differentiation from First Principles

First principles is where most students panic — and where careless ones throw away easy marks. The method is fixed, so we drill it as a fixed routine. State the limit definition: f′(x) = lim_h→0 [f(x + h) − f(x)] / h. Substitute x + h for every x in the function. Expand and simplify the numerator. Cancel the h in the denominator — the single move the whole method hinges on — and only then let h tend to zero. The classic error is substituting h = 0 too early, which gives 0/0 and zero marks. Our annotated drill set walks through this on every question, so the discipline becomes second nature.

Differentiation by Rules

Once first principles is understood, speed comes from the rules — applied cleanly, one term at a time. State the rule before using it: d/dx(xⁿ) = n·xⁿ⁻¹. Differentiate term by term, bringing the power down and reducing it by one. Keep constants and coefficients explicit, and rewrite roots and reciprocals as powers first so the rule applies directly. We train your child to write the rule at the top of the working — examiners reward the stated method, and it eliminates the silent slips that cost marks under time pressure.

Tangents & Stationary Points

Gradient questions reward a clear procedure, not guesswork. For a tangent: find dy/dx, evaluate it at the given point for the gradient, then use y − y₁ = m(x − x₁). For stationary points: set dy/dx = 0, solve for x, and substitute back for y. Then classify — second-derivative test or a sign check either side — to decide maximum, minimum, or point of inflexion. Each step is stated with its reason, so partial credit is never lost even if the final arithmetic slips.

Integration & Areas

Integration is differentiation in reverse, with two non-negotiable disciplines. Reverse the power rule: add one to the power and divide by the new power. For an indefinite integral, never drop the + C — the constant of integration, found from a known point. For a definite integral, substitute the upper limit, substitute the lower limit, and subtract — in that order. To find an area under a curve, integrate between the limits. These are exactly the two slips our ‘Watch:’ callouts flag most often, so we drill them until they disappear.

Indices & Surds

Indices and surds underpin everything that follows, so we make the laws automatic. For indices: identify which law applies — product, quotient, power-of-a-power, negative, or fractional — and apply one law per line so each step is checkable. For surds: simplify by extracting square factors, and rationalise a denominator by multiplying top and bottom by the conjugate. The reasoning sits beside every line, so your child understands why each move is the natural one — not just that it works.

Logarithms & Exponentials

Logarithms intimidate students who treat them as a new kind of arithmetic rather than the inverse of exponentials. We anchor them to one idea: a logarithm is an exponent. Convert fluently between exponential and logarithmic form, then apply the laws — product, quotient, power, and change of base — one at a time. Solve equations by isolating the logarithm or the exponential first, and always check the domain, because a logarithm only ever takes a positive argument. Stated laws, line-by-line working, and a domain check turn logs from a feared topic into a reliable source of marks.