학원 STARPREP® · Grades 6–12 · Premium School Math 1:1 Program

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STARPREP® · Grades 6–12 · Premium School Math 1:1

Premium School Math 1:1 Program — Grades 6–12 학교 수학 내신 1등 · 조기 선행 · AP & AIME/USAMO까지 연결되는 프리미엄 개인수업

In School, Math Must Be the #1 Subject · 학교에서 수학만큼은 반드시 압도적 1등

EN) STARPREP’s Premium School Math 1:1 Program is a long‑horizon pathway from Grade 6 to 12 that turns math into your child’s signature academic strength — the subject where they compete for undisputed #1 at school, while building a runway to AP Calculus, AP Statistics, Digital SAT Math, AMC/AIME, and USAMO.
KR) 단순 점수 향상이 아니라 “수학만큼은 최소한 압도적 1등”을 목표로 내신·선행·AP·DSAT·AIME/USAMO를 한 번에 연결하는 장기 전략 코스입니다.

Core Philosophy · 핵심 철학

• 매 학년 최소한 수학만큼은 절대 1등을 노리는 과목으로 설정합니다.
• 조기·여유 선행(6–8학년)으로 고등(9–12학년)에는 AP·경시·STEM 준비에 집중합니다.
• 선생님이 떠올리는 학생상: “수학에서 진짜 강한 학생”.

Grades 6–12 · School Math 1:1

Early Acceleration · Pre‑Algebra → AP Calc/Stats

Outcome‑Engineered · Error Taxonomy · Timed Calm

AP · DSAT · AMC · AIME · USAMO

1 · Core Vision — Math as Non‑Negotiable #1

In School, Math Must Be the Clear #1 Subject

Math is the gatekeeper for advanced science courses, CS, engineering, and quantitative majors. It also concentrates key evaluations — school grades, AP, DSAT Math, AMC/AIME/USAMO. 그래서 STARPREP는 “수학 1등 전제”를 명확히 둡니다.

2 · Early, Calm Acceleration — Why We Start in Grades 6–8

9–10학년에 급가속하면 스트레스·피상 이해·불안정 결과가 발생하기 쉽습니다. 우리는 6–8학년부터 여유 있게 선행을 분산해 깊이·안정을 확보합니다.

G5–6: Pre‑Algebra 엔진 완성
G6–7: Pre‑Algebra + Algebra 1 초기
G7–8: Algebra 1 심화 + Geometry 프리뷰
G8–9: Geometry + Algebra 2 코어
G9–10: Algebra 2 + Trig + AP‑level Precalculus
G10–11: AP Calc/Stats, AMC 10/12 & AIME
G11–12: AIME/USAMO 파이프라인, 대학수학 브리지

3 · Three Phases: Foundation · Acceleration · Distinction

Phase 1 · Foundation (≈ G5–7)

Fractions/ratios/percent mastery
Equation & inequality language
Early graphing & functions

KR) 프리알지브라 엔진 완성 단계

Phase 2 · Acceleration (≈ G7–10)

Alg1 · Geo · Alg2 · Trig · Precalculus
고등 과정 조기·심화 완료

KR) 고등 전범위 선행

Phase 3 · Distinction (≈ G10–12)

AP Calc/Stats, DSAT, AMC/AIME
Proof & University bridge

KR) 성과 기반 차별화

4 · Why STARPREP Is Structurally Superior

Outcome‑first 설계: 학교등수·AP·DSAT·AMC/AIME/USAMO 목표에서 역설계
인지부하 고려 수업: 작은 노트, 정제된 예제, 개념/스피드 분리
Error Taxonomy & Fix‑Rules: 오류유형→1줄 규칙→평행 문제 재테스트
Timed Calm & Exam Habit: 플래그‑앤‑리턴, 노‑선크코스트, 단위/부호/규모 체크
School‑Aligned & Global: 지역 커리큘럼 매칭 + AP/DSAT/AMC 사고 연결
Integrity First: 지름길/과장 없음. 설명과 습관으로 증명

5 · Grade‑by‑Grade Roadmap (Early Acceleration)

고등 수학을 일찍·깊게·안정적으로 완성한 뒤, AP·DSAT·경시로 차별화합니다.

Grade 6 · Pre‑Algebra Mastery + Early Algebra

Fractions/ratios/percent in multi‑step contexts
Word problems → equations/inequalities
Linear thinking & simple graphs

Grade 7 · Full Algebra 1 (Early)

Linear, systems, functions, factoring, quadratics
Real‑world models & multi‑step problems
Light AMC 8/10‑style entry

Grade 8 · Geometry + Algebra 2 Preview

Lines/angles/triangles/proofs/circles/area/volume
Quadratics review; complex numbers & exponentials

Grade 9 · Algebra 2 + Core Trigonometry

Polynomials/complex; rational/exp/log functions
Right‑triangle trig · unit circle · basic graphs

Grade 10 · AP‑Level Precalculus

Function families/transform/inverse/compose/model
Advanced trig · identities · equations · periodic models

Grade 11 · AP Calculus AB/BC, AP Statistics, AIME Track

AP Calculus AB/BC (FRQ justification)
AP Statistics (data→inference)
AMC 10/12 → AIME problem solving

Grade 12 · USAMO‑Level Depth & University Bridge

AIME refinement → USAMO‑style taste (when appropriate)
Linear Algebra / Multivariable / Discrete bridges

6 · AMC & AIME — English Overview

AMC (American Mathematics Competitions)

Levels: AMC 8 (middle school), AMC 10 (≤Grade 10), AMC 12 (≤Grade 12)
Format: Multiple‑choice; AMC 8 is short & fast‑paced, AMC 10/12 are longer and more advanced
Domains: Algebra, geometry, number theory, counting & probability, logical reasoning
Outcome: Strong AMC 10/12 scores may lead to an AIME invitation

AIME (American Invitational Mathematics Examination)

Eligibility: Invitation‑only for top AMC 10/12 performers (annual cutoff)
Format: 15 problems, extended time, each answer is a three‑digit integer 000–999
Role: AMC + AIME results are used to determine invitations to higher‑level Olympiad stages

Note: Dates, cutoffs, and policies are set annually by the organizers; check the latest announcements when planning.

7 · Who Is This Program For?

Core Excellence: 학교 페이스 대비 여유 확보, 수학 상위권 고정
Honors/AP Track: 고등 수학 조기완료 + 여러 AP 5
Elite STEM/Contest: AP/DSAT 상위, AMC/AIME/USAMO 실적

8 · What Parents Will Notice

몇 주: 노트/풀이 정리, 퀴즈·단원 성적 개선
한 학기: 자신감/참여도 상승, 수업 체감 난도 완화
1–3년: 생활기록부에서 수학이 확실한 1등 과목으로 자리

Course Map 커리큘럼 안내

Course	Key Topics (aligned to school pacing)
Pre‑Algebra Register	Integers/fractions/decimals operations & order Factors/multiples/ratios/proportions/percent Basic equations/inequalities; exponents & roots Coordinate plane; simple graphs; word‑modeling
Algebra 1 Register	Linear equations/inequalities; slopes & graphs Systems (substitution/elimination) Functions; polynomials & factoring Exponent laws; exponential & quadratic models
Geometry Register	Lines/angles/proofs; triangles (congruence/similarity) Quadrilaterals/polygons; circles (arcs/chords/tangents) Coordinate geometry; surface area/volume; 3D figures Intro trig ratios & applications
Algebra 2 Register	Advanced linear/quadratic; complex; polynomials Rational/exponential/logarithmic functions Sequences/series; intro probability/statistics Conics; advanced trigonometry
Trigonometry Register	Unit circle & radians; graphs & identities Trig equations; laws of sines/cosines Triangle applications; periodic modeling
AP Precalculus Register	Families/transform/inverse/compose; modeling & rates Poly/rational/exp/log models; domain/range/asymptotes Trig + polar/parametric; real‑context applications Sequences (finite); binomial; difference quotient
AP Calculus AB Register	Limits/continuity; derivatives (incl. implicit); MVT/IVT/EVT Motion/related rates/optimization; curve analysis Integrals: Riemann/FTC/u‑sub; accumulation; avg value Diff eq; area/volumes; FRQ justification & units
AP Calculus BC Register	Parametric/polar calc; arc length/area IBP/partials/improper; logistic; Euler’s Series tests; power/Taylor; error bounds FRQ craft: conditions/convergence/index shifts
AP Statistics Register	Exploring/collecting data; regression & residuals Sampling/experiments/bias/random assignment Probability & RVs; binomial/geometric; Normal models Inference: z/t, chi‑square, regression inference
AMC 8 Register	Number sense/ratios/percent; intro number theory Counting/probability; contest‑style geometry & logic 25‑item MC pacing; careful reading & elimination
AMC 10 Register	Algebra/Geometry/Counting/Number Theory (HS entry) Heuristics: working backward/invariants/extreme cases Penalty scoring aware selection; AIME score planning
AMC 12 Register	Algebra2/Adv. Geo/Trig/Inequalities/Sequences Elegant paths vs brute‑force; standard forms Refined pacing & triage; AIME index positioning
AIME Register	Algebra/Combinatorics/Number Theory/Geometry (integer response 000–999) Multi‑step reasoning; clean casework; bounding & substitutions Bridge toward proof‑flavored thinking and USAMO readiness

※ 지역별 스코프·교과서가 달라집니다. 교재/시험일정에 맞춰 시퀀스를 조정합니다.

Detailed Curriculum Map 상세 커리큘럼

Course	Concepts · Pitfalls · Habits (school‑aligned)
Pre‑Algebra	Concepts: int/frac/dec ops; ratios/proportions/percent; eq/ineq; exponents/roots; graphing. Pitfalls: sign/decimal slips; unit drift. Habits: ratio tables; unit sanity checks; bar models.
Algebra 1	Concepts: linear families; systems; functions; factoring; quadratics; exp laws; exp models. Pitfalls: distributing negatives; slope sign; vertex vs intercept. Habits: form→feature; intercept checks; sketch first.
Geometry	Concepts: proofs; similarity; circles; solids; right‑triangle trig. Pitfalls: not‑to‑scale traps; ratio misuse; 3D units. Habits: annotate givens; ratio ladders; “units first”.
Algebra 2	Concepts: poly division; complex; rational/exp/log; sequences/series; conics; advanced trig. Pitfalls: holes vs asymptotes; log laws; inverse mishandling. Habits: behavior tables; inverse compose test.
Trigonometry	Concepts: unit circle; graphs; identities; equations; periodic models. Pitfalls: deg↔rad drift; SSA ambiguity. Habits: reference triangles; general solutions; label amp/period/phase.
AP Precalculus	Concepts: families/transform; inverse/compose; modeling; trig/polar/parametric; finite sequences; binomial; diff quotient. Pitfalls: inverse domain traps; asymptote myths; polar conventions. Habits: graph skeletons; domain/range first; convert forms.
AP Calculus AB	Concepts: limits/continuity; derivatives; theorems; motion; related rates; optimization; Riemann/FTC; u‑sub; accumulation; diff eq; areas/volumes. Pitfalls: missing conditions; +C; units/bounds. Habits: state hypotheses; label units; justify words+math.
AP Calculus BC	Concepts: parametric/polar; IBP/partials/improper; logistic; Euler’s; series tests; power/Taylor; error. Pitfalls: wrong test; conditional vs absolute; index shifts. Habits: name the test+reason; interval/radius; param/polar first.
AP Statistics	Concepts: exploring/collecting data; probability & RVs; inference (z/t, chi‑square, regression). Pitfalls: correlation≠causation; conditions; parameter mix‑ups; p‑value misuse. Habits: state parameter/conditions; interpret with units; name tests + justify.
AMC 8	Concepts: arithmetic/ratios/counting/NT/contest geometry. Pitfalls: easy‑look traps; multi‑step misreads. Habits: diagram first; test small numbers; sanity before bubble.
AMC 10	Concepts: algebra/geo/counting/NT; inequalities; functional thinking. Pitfalls: over‑algebra; single‑problem time sink; penalty 무시. Habits: classify problems into easy/medium/hard; protect the baseline score; use bounding and estimation.
AMC 12	Concepts: full HS contest syllabus (Alg2/Adv Geo/Trig/Seq/Complex). Pitfalls: brute‑force approaches; missing symmetry; mishandling edge cases. Habits: substitution/symmetry/invariants; clean coordinate setups; AIME index management.
AIME	Concepts: olympiad‑flavored algebra/comb/NT/geometry (0–999 integer). Pitfalls: algebra blow‑ups; unstructured casework; careless arithmetic. Habits: line‑by‑line organization; check alternative approaches; leverage the integer‑answer structure.