A-Math — Calculus support that helps you work it out
MOE/SEAB Additional Mathematics (4049 / SEC K341) Calculus and Plane Geometry Proofs strands: differentiation rules, trig/exponential/ln derivatives, tangents and normals, connected rates of change, stationary points, integration, area under curves and kinematics.
9 tracked MOE/SEAB skills, from differentiation rules (chain, product and quotient) to proofs in plane geometry. The tutor asks focused questions, you test the next step, and the understanding stays yours.
What an a-math — calculus tutor covers
Each skill is tracked separately so strong chapters never mask a shaky prerequisite.
- 1
Differentiation rules (chain, product and quotient)
Foundation skillDifferentiate power functions and composite products and quotients using the chain, product and quotient rules.
- 2
Derivatives of trigonometric, exponential and ln functions
Builds on Differentiation rules (chain, product and quotient)Differentiate sin x, cos x, tan x, eˣ and ln x combined with the chain, product and quotient rules.
- 3
Tangents, normals and increasing/decreasing functions
Builds on Differentiation rules (chain, product and quotient)Find equations of tangents and normals to curves, and use dy/dx to test whether a function is increasing or decreasing.
- 4
Connected rates of change
Builds on Differentiation rules (chain, product and quotient)Apply the chain rule dy/dt = (dy/dx) × (dx/dt) to relate rates of change in geometric and physical contexts.
- 5
Stationary points, maxima and minima
Builds on Tangents, normals and increasing/decreasing functionsFind stationary points, determine their nature using the first and second derivative tests, and solve maxima/minima problems.
- 6
Integration as the reverse of differentiation
Builds on Differentiation rules (chain, product and quotient)Integrate (ax + b)ⁿ, sin(ax + b), cos(ax + b), sec²(ax + b), eᵃˣ⁺ᵇ and 1/(ax + b), and evaluate constants of integration.
- 7
Definite integrals and area bounded by curves
Builds on Integration as the reverse of differentiationEvaluate definite integrals and calculate the area of regions bounded by a curve and lines parallel to the coordinate axes.
- 8
Kinematics — displacement, velocity and acceleration
Builds on Definite integrals and area bounded by curvesApply differentiation and integration to motion in a straight line (v = ds/dt, a = dv/dt, instantaneous rest and total distance travelled).
- 9
Proofs in plane geometry
Foundation skillProve properties of triangles, quadrilaterals and circles using congruence, similarity, the midpoint theorem and the tangent-chord theorem.
How an a-math — calculus session unfolds
The student starts by asking for the answer—and ends up solving the key step themselves.
- Student
Can you differentiate y = (2x − 1)³ for me and find the gradient at x = 1? I’ll copy the steps.
- Tutor
I won’t write the finished derivative for you, but the chain rule will do the heavy lifting. Look at (2x − 1)³ as an outer cube power around an inner bracket (2x − 1). Differentiate the outer power first, then state the derivative of the inner bracket.
- Student
Outer power gives 3(2x − 1)², and the derivative of 2x − 1 is 2.
- Tutor
Good — that inner factor of 2 is the one students forget under exam pressure. Multiply them together to write dy/dx in simplified form.
- Student
dy/dx = 6(2x − 1)². At x = 1, 2(1) − 1 = 1, so dy/dx = 6(1)² = 6.
- Tutor
You derived and evaluated it yourself. Now check where this curve has its stationary point by setting your dy/dx expression equal to 0.
About this illustrative example
This walkthrough is an illustrative script written to show how the five-level hint progression works in A-Math — Calculus, not a transcript from a real student account.
Have an a-math — calculus question right now?
Bring your own school worksheet problem or test our interactive whiteboard with zero login required.
How skill progress is recorded
Sessions build a clear skill record for the student and a calm, read-only summary for linked parents.
One bar per skill
Mastery is tracked skill by skill, not as a single subject percentage, so a strong topic cannot hide a weak one.
The hint level counts
Getting something right with one small hint moves the bar more than getting it right after five. The number we show you reflects how much help you needed.
Built from an event log
Every attempt, hint and explanation is recorded as an event, and the bars are calculated from that history. It can be replayed, which means the numbers are reproducible rather than asserted.
A parent sees the same numbers
A linked parent gets the same skill bars, the last judgement and its line of evidence behind each level, the recent session summaries and the flag counts — read-only, and nothing that is not also on your own pages.
9 skill bars, tracked independently
In a-math — calculus, that means 9 separate skill bars — differentiation rules (chain, product and quotient), derivatives of trigonometric, exponential and ln functions, tangents, normals and increasing/decreasing functions, and the rest — each updating based on verified problem steps. Linked parents see the same topic bars and session takeaways in read-only mode.
A-Math — Calculus FAQs
Common questions from students and parents about studying this subject on tutor.ai.
Will it check my working?
Yes. Bring your steps and it confirms what is sound and says exactly which step breaks, without repairing it for you.
Can it just do the derivative or integral?
No. It asks which rule applies (chain, product, quotient or reverse chain rule) and why that one. Producing a finished solution with your numbers is the one thing it is built never to do.
Which A-Math Calculus topics are covered?
Aligned to Singapore O-Level / SEC Additional Mathematics (4049). Nine skills, in syllabus order: Differentiation rules (chain, product and quotient); Derivatives of trigonometric, exponential and ln functions; Tangents, normals and increasing/decreasing functions; Connected rates of change; Stationary points, maxima and minima; Integration as the reverse of differentiation; Definite integrals and area bounded by curves; Kinematics — displacement, velocity and acceleration; and Proofs in plane geometry.
Does it know my exam board’s notation?
It uses standard Singapore O-Level / SEC A-Math notation (dy/dx, d²y/dx², radians for trigonometric calculus) and asks when anything in your question is ambiguous.
More Sec 3–4 (O-Level / SEC) subjects
Switch between subjects at the same school level or open the full catalogue.
E-Math — Algebra
MOE/SEAB Elementary Mathematics (4052 / SEC K310) Number and Algebra strand: algebraic manipulation, linear and fractional equations, simultaneous linear equations, quadratic factorisation and equations, indices, standard form and graphs of functions.
E-Math — Geometry
MOE/SEAB Elementary Mathematics (4052 / SEC K310) Geometry and Measurement strand: angle properties, congruence and similarity, Pythagoras’ theorem, trigonometry (sine and cosine rules, bearings), mensuration in degrees and radians, circle properties, coordinate geometry and 2D vectors.
A-Math — Functions
MOE/SEAB Additional Mathematics (4049 / SEC K341) Algebra and Geometry & Trigonometry strands: quadratic functions and discriminant, surds, polynomials and partial fractions, binomial expansion, exponential and logarithmic functions, coordinate geometry (including circles), linear law and trigonometry.
Biology
MOE/SEAB Pure Biology (6093 / SEC K325): cell structure, movement of substances, biological molecules and enzymes, human and plant nutrition, transport and respiration, excretion and homeostasis, molecular genetics, inheritance and ecology.
Bring your a-math — calculus question
Free during testing, with no credit card required.