A-Math — Functions support that helps you work it out
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.
9 tracked MOE/SEAB skills, from quadratic functions, discriminant and inequalities to trigonometric identities and r-formula. The tutor asks focused questions, you test the next step, and the understanding stays yours.
What an a-math — functions tutor covers
Each skill is tracked separately so strong chapters never mask a shaky prerequisite.
- 1
Quadratic functions, discriminant and inequalities
Foundation skillFind maximum/minimum values by completing the square, apply b² − 4ac for real roots and line–curve intersection, and solve quadratic inequalities.
Perform operations on surds, rationalise denominators and solve equations involving surds.
- 3
Polynomials and partial fractions
Builds on Quadratic functions, discriminant and inequalitiesApply the remainder and factor theorems, factorise cubics, and decompose proper algebraic fractions as partial fractions.
- 4
Binomial expansion
Builds on Polynomials and partial fractionsUse the Binomial Theorem for positive integer n and apply the general term (n choose r) aⁿ⁻ʳ bʳ to find specific coefficients.
- 5
Exponential and logarithmic functions
Builds on SurdsSimplify expressions and solve equations using laws of logarithms, change of base, eˣ and ln x, and sketch their graphs.
- 6
Coordinate geometry and circles
Builds on Quadratic functions, discriminant and inequalitiesSolve problems on parallel/perpendicular lines, area of rectilinear figures, and equations of circles in (x − a)² + (y − b)² = r² and general form.
- 7
Linear law
Builds on Coordinate geometry and circlesTransform non-linear relations into the linear form Y = mX + c and determine unknown constants from straight-line graphs.
- 8
Trigonometric functions, graphs and equations
Foundation skillUse the six trigonometric functions in degrees and radians, exact values for 30°, 45°, 60°, principal values and graphs of a sin(bx) + c and a cos(bx) + c.
- 9
Trigonometric identities and R-formula
Builds on Trigonometric functions, graphs and equationsProve identities and solve equations using sin²A + cos²A = 1, addition and double-angle formulae, and a cos θ ± b sin θ = R cos(θ ∓ α).
How an a-math — functions session unfolds
The student starts by asking for the answer—and ends up solving the key step themselves.
- Student
Just tell me the range of k so that x² + kx + 9 = 2x has no real roots.
- Tutor
Let’s get it into standard quadratic form ax² + bx + c = 0 before touching the discriminant. Bring the 2x across and group the x terms — what are a, b and c in terms of k?
- Student
x² + (k − 2)x + 9 = 0, so a = 1, b = k − 2 and c = 9.
- Tutor
Spot on. Now, for a quadratic equation to have no real roots (so the curve lies entirely above or below the x-axis), what condition must the discriminant b² − 4ac satisfy?
- Student
b² − 4ac < 0. So (k − 2)² − 4(1)(9) < 0, which gives (k − 2)² − 36 < 0, or (k − 8)(k + 4) < 0, so −4 < k < 8.
- Tutor
You factored and solved the quadratic inequality yourself. Now test it: pick any k inside your interval and work out the discriminant. Is it negative?
About this illustrative example
This walkthrough is an illustrative script written to show how the five-level hint progression works in A-Math — Functions, not a transcript from a real student account.
Have an a-math — functions 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 — functions, that means 9 separate skill bars — quadratic functions, discriminant and inequalities, surds, polynomials and partial fractions, 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 — Functions FAQs
Common questions from students and parents about studying this subject on tutor.ai.
Will it show me the method when I am properly stuck?
It names the rule or first move, then asks you to write and carry out the step yourself. If you are still stuck after honest attempts, it works a parallel problem with different numbers and asks you to apply the same move to yours.
Trigonometric identities and the R-formula always catch me out.
That is the usual experience. The tutor will not hand you the identity — it asks which side looks more complicated and which compound-angle, double-angle or R-formula identity you can substitute.
Which A-Math Functions topics are covered?
Aligned to Singapore O-Level / SEC Additional Mathematics (4049). Nine skills, in syllabus order: Quadratic functions, discriminant and inequalities; Surds; Polynomials and partial fractions; Binomial expansion; Exponential and logarithmic functions; Coordinate geometry and circles; Linear law; Trigonometric functions, graphs and equations; and Trigonometric identities and R-formula.
Does it replace my class?
No. It is practice between classes. It also will not help with a graded test that is in progress — it offers to practise the same topic afterwards instead.
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 — Calculus
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.
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 — functions question
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