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Curriculum & Standards · Pre-Calculus

Pre-Calculus — the bridge to university, calibrated to IB AA HL + Cambridge A2 + Singapore JC2 + Japan Math III + Korea Calculus.

From advanced functions and asymptotic analysis with limit notation, to 2D / 3D vectors with dot and cross product, to parametric and polar curves, to complex numbers in polar / Euler form with DeMoivre's theorem and n-th roots of unity, to intuitive limits and continuity (with the Intermediate Value Theorem and L'Hôpital's rule intro), sequences and series with telescoping and partial sums, the four-step mathematical induction proof, the intuitive derivative as a limit of the secant slope, and the intuitive integral as the limit of a Riemann sum — all aligned to the union of CCSS HS Functions / Number-CN, IB Mathematics AA HL, Cambridge International A2 9709 (Pure 3 + Mechanics), Singapore JC2 H2 9758, Japan MEXT Math II / III and Korea KICE 2022 Revised Calculus.

66

Skills

11

Modules (hex)

14

Official standards benchmarked

16–18

Age coverage

Why Pre-Calculus is the make-or-break program before STEM university

Pre-Calculus is where a student stops being a high-school math user and becomes a university math user: limits and continuity replace ad-hoc plotting, induction replaces example-based proof, and the derivative + integral show up as concepts before they show up as rules. Singapore JC2, Japan Math III, Korea Math II / Calculus and IB AA HL all teach this material before any formal calculus — and TIMSS Advanced 2015 shows the cohort with these foundations dominating STEM admissions. Rodybee tracks the union of CCSS HS, IB AA HL, Cambridge A2, Singapore JC2 H2, Japan SHS and Korea KICE 2022 Revised.

#CountryTIMSS Advanced score
1🇸🇬Singapur605
2🇹🇼Chinese Taipei597
3🇰🇷Corea596
4🇯🇵Japón595

Source: TIMSS Advanced 2015 Final Year Math ↗

Find your child's level

Pick an age and see exactly what we teach at that point — and what the most demanding standards in the world expect at the same age. There's no marketing fluff: each topic links to the official curriculum document.

Your child's age

Rodybee for your child · 7 años

What we teach at this age

No skills calibrated for this exact age yet — try an adjacent year.

Highest international bar at this age · G11 / Sec 4 / JC2 Y1

🇸🇬Singapur

Advanced functions (composition, decomposition, formal inverse with domain restriction, advanced piecewise including floor function, function modeling), transformations chained on multiple families, end-behavior with limit notation (lim x→∞), complete asymptotic analysis (vertical/horizontal/oblique + holes), graphing unknown polynomials and combined function families, advanced trig identities (half-angle, product-to-sum, sum-to-product, rigorous identity proof).

Grade-by-grade benchmark

Full table of what each major standard expects per grade. Every cell is sourced from the official ministry, board or framework document.

G11 / Sec 4 / JC2 Y1

First third — advanced functions + asymptotic analysis + advanced trig identities (~16–17 años)

Highest bar · 🇸🇬 Singapur

Advanced functions (composition, decomposition, formal inverse with domain restriction, advanced piecewise including floor function, function modeling), transformations chained on multiple families, end-behavior with limit notation (lim x→∞), complete asymptotic analysis (vertical/horizontal/oblique + holes), graphing unknown polynomials and combined function families, advanced trig identities (half-angle, product-to-sum, sum-to-product, rigorous identity proof).

CountryExpected topicsOfficial source
🇸🇬SingapurJC2 H2 9758: Functions (composite + inverse formal con domain restriction), graphs of rational/polynomial functions y asymptotic analysis completa, trigonometry (R-form, identities completas).Singapore JC2 H2 Mathematics 9758 (SEAB) ↗
🇺🇸Estados UnidosHSF-BF.4 (inverse functions formal). HSF-IF.7 (analyze graphs incl. asymptotes). HSF-TF.8/9 (Pythagorean identity + sum/diff/half-angle).CCSS-M HS Functions ↗
🌐Cambridge A2 9709Pure 3: functions (modulus, composite, inverse), advanced graphs and asymptotes, advanced trigonometry (incl. R cos(θ ± α), proof of identities).Cambridge International A Level Mathematics 9709 (Pure 3 + Mechanics) ↗
🌐IB AA HLTopic 2 (Functions): inverse formal, composite, transformations chained. Topic 3 (Trigonometry): identities including double/half-angle and product/sum.IB Diploma Mathematics: Analysis and Approaches HL ↗

Rodybee skills at this grade

Function composition (f ∘ g) · Decompose a function into f ∘ g · Formal inverse function · Inverse with domain restriction · Piecewise functions — continuity at boundaries · Greatest integer (floor) function ⌊x⌋ · Choose the right function family for data · Chained transformations a · f(b(x − c)) + d · End behavior with lim notation · Complete asymptotic analysis (V/H/oblique + holes) · Sketch an unknown polynomial function · Graph combined function families (e^x · sin x …) · Half-angle identities sin(θ/2), cos(θ/2) · Product-to-sum identities · Sum-to-product identities · Rigorously prove a trig identity

G11–G12 / JC2 Y2 / Y13

Second third — vectors 2D+3D + parametric + polar + complex polar/DeMoivre (~16–17 años)

Highest bar · 🇯🇵 Japón

2D and 3D vectors (notation, magnitude, addition, scalar multiplication), dot product with angle and orthogonality/parallelism tests, vector physics applications (work), 3D cross product (anti-commutative, perpendicular), parametric curves with elimination, classics (line, ellipse, cycloid) and projectile motion, polar coordinates with conversion, classic polar graphs (cardioid, rose, spiral, conic with focus at origin), complex numbers in polar form (modulus + argument + cis), Euler's formula e^(iθ), polar multiplication/division, DeMoivre's theorem for powers, n-th roots of unity as regular n-gons.

CountryExpected topicsOfficial source
🇸🇬SingapurJC2 H2: vectors 3D completos (dot product + cross product + ecuación de línea/plano). Complex numbers en forma polar + DeMoivre + raíces n-ésimas.Singapore JC2 H2 Mathematics 9758 (SEAB) ↗
🇯🇵JapónMath II/III: vectors 2D y 3D incluyendo dot/cross product, complex numbers en forma polar (極形式), DeMoivre's theorem (ド・モアブルの定理), polar coordinates (極座標).MEXT Senior High School Math II / III (Japan) ↗
🇺🇸Estados UnidosHSN-VM.1-11 (Vector & Matrix Quantities incl. 3D, dot/cross). HSN-CN.4-6 (complex polar form, DeMoivre). HSG-GPE.3 (parametric/polar implícito).CCSS-M HS Number — Complex Numbers + Vectors/Matrices ↗
🌐Cambridge A2 9709Pure 3: vectors 3D completos, complex numbers en polar form + DeMoivre. Mechanics: parametric motion (proyectil).Cambridge International A Level Mathematics 9709 (Pure 3 + Mechanics) ↗
🌐IB AA HLTopic 1: complex polar/Euler/DeMoivre + roots. Topic 3: vectors 3D + dot + cross + line/plane. Topic 5: parametric curves.IB Diploma Mathematics: Analysis and Approaches HL ↗

Rodybee skills at this grade

Vector notation and magnitude |v| · Vector addition and subtraction · Scalar multiplication of vectors · 3D vectors (i, j, k) · Dot product u · v · Angle between vectors via dot product · Orthogonal vs parallel vectors · Physics applications (work, velocity) · 3D cross product u × v · Parametric representation (x(t), y(t)) · Eliminate the parameter t · Classic parametric curves (line, ellipse, cycloid) · Parametric motion (projectile, circular) · Polar coordinates (r, θ) · Polar ↔ rectangular conversion · Classic polar graphs (cardioid, rose, spiral) · Polar conic with focus at origin · Polar rate of change (intuitive) · Complex — polar form full (r cis θ) · Complex — Euler form e^(iθ) · Complex — multiply/divide in polar form · DeMoivre's theorem · Complex n-th roots (regular n-gon)

G12 / JC2 Y2 / Y13

Final third — limits + continuity + sequences/series + induction + derivada + integral intuitiva (~17–18 años)

Highest bar · 🇰🇷 Corea

Intuitive limits (definition, algebraic substitution, factoring/rationalizing, one-sided, at infinity, indeterminate forms), formal continuity with classification of discontinuities, Intermediate Value Theorem, L'Hôpital's rule intro, sequences (recursive vs explicit, convergence), series (telescoping, partial sums), mathematical induction (4-step proof, sum formula, divisibility), derivative as limit (average rate of change → secant → tangent → instantaneous → derivative + tangent line equation + instantaneous velocity), integral as Riemann sum limit (rectangle approximation → formal Riemann sum → integral as signed area → simple geometric integrals).

CountryExpected topicsOfficial source
🇰🇷CoreaMath II / Calculus 2022 Revised: limits y continuity (극한, 연속), derivative as limit (미분계수 + 도함수), integral via Riemann sum (정적분), induction (수학적 귀납법) — todo intuitivo, no épsilon-delta.KICE 2022 Revised Curriculum — Mathematics II / Calculus ↗
🇯🇵JapónMath III: limits (極限), continuity (連続), derivative (微分) intuitivo, integral (積分) como Riemann sum, sequences and series (数列), induction (数学的帰納法).MEXT Senior High School Math II / III (Japan) ↗
🇸🇬SingapurJC2 H2: sequences and series con sigma + telescoping + partial sums + induction completa, intro a differentiation (chain, product, quotient — formal derivative concept).Singapore JC2 H2 Mathematics 9758 (SEAB) ↗
🇺🇸Estados UnidosPre-Calculus extends HSF-IF / HSA-SSE: limit notation, continuity intuitiva, average vs instantaneous rate como puente a Calculus AB. CCSS deja calculus para AP.CCSS-M HS Functions ↗
🌐Cambridge A2 9709Pure 3: numerical methods (incl. Newton-Raphson) que dependen de IVT y derivada. Differentiation introducida formalmente (incl. tangent line, instantaneous rate).Cambridge International A Level Mathematics 9709 (Pure 3 + Mechanics) ↗
🌐IB AA HLTopic 5: limits intuitivo + continuity + induction + derivative as limit + integral como Riemann sum (HL only — SL salta directo a reglas).IB Diploma Mathematics: Analysis and Approaches HL ↗

Rodybee skills at this grade

Intuitive definition of a limit · Limit by algebraic substitution · Limit by factoring or rationalizing · One-sided limits (left/right) · Limit at infinity · Indeterminate forms (0/0, ∞/∞ …) · Formal continuity at a point · Types of discontinuity (hole, jump, infinite) · Intermediate Value Theorem (IVT) · L'Hôpital's rule (intro) · Recursive vs explicit sequences · Convergence of a sequence (intuitive) · Telescoping series · Series and partial sums · 4-step mathematical induction · Induction — sum formula · Induction — divisibility · Formal average rate of change · Secant line vs tangent line · Instantaneous rate of change concept · Derivative as a limit · Tangent line equation · Instantaneous velocity (s'(t)) · Area by rectangle approximation · Formal Riemann sum · Integral as a limit (concept) · Simple geometric integrals

Full research document

Methodology, gap analysis, recommendations and the complete list of sources are in the underlying research markdown.

Read the full benchmark document →
Pre-Calculus Curriculum & Standards — Rodybee