Competition mathematics · Live instruction
Build fluency with primes, divisibility, modular reasoning, counting, and proof-minded problem solving through a structured AoPS-based pathway.
A focused use case
AMC 10 number theory tutoring is guided instruction for students learning to recognize and solve competition problems involving integers, primes, divisibility, remainders, parity, ratios, powers, and counting. The goal is not simply to remember a rule; it is to understand why a method works, choose an efficient approach, and explain the reasoning clearly. ACE Academy connects this work to Honors Math and Competition Math courses built around AoPS materials, international competition strategies, worked examples, independent practice, and teacher feedback.
Students may enter through a placement evaluation and follow a level-appropriate pathway that includes Pre-Algebra, Algebra I, Geometry, or competition-focused instruction. Families exploring the broader subject can also review this number theory competition guide or compare a structured AMC 10 tutoring pathway with their current study plan.
Inside the learning experience
The strongest AMC 10 preparation connects foundational arithmetic to flexible competition reasoning. These examples show the type of thinking the curriculum is designed to develop.
One practice problem considers unordered two-digit pairs that add to 88. There are 35 total pairs and three favorable prime pairs: (17, 71), (29, 59), and (41, 47). The resulting probability is 3/35, but the deeper lesson is how to define the sample space before testing prime conditions.
For any three consecutive integers n, n + 1, and n + 2, exactly one is divisible by 3. Students can prove this by checking the three possible remainders of n modulo 3. The same reasoning shows that exactly one of three consecutive odd integers, or three consecutive even integers, is divisible by 3.
In a problem where A + B = C and A + C = D for four different primes, C and D must be odd, forcing A to be 2. Then B, C, and D are consecutive odd primes. Divisibility by 3 identifies 3, 5, and 7, producing the answer 31 for A × C + B × D.
AMC preparation is not isolated to one chapter. Pre-Algebra includes arithmetic, fractions, prime factorization, LCM, GCD, counting, probability, and pattern recognition, while Algebra I and Geometry strengthen the modeling and spatial reasoning needed for multi-step competition questions.
A complete topic map
The instruction emphasizes strategy selection, accuracy, and mathematical communication. It also places number theory inside a broader competition pathway, so students can connect discrete reasoning with algebra, geometry, ratios, and probability.
From foundations to competition
Lessons combine explanation, worked examples, independent practice, and feedback. Approximately 39% of classroom time is allocated to student output, including problem solving and mathematical explanation.
How the pathway works
Students complete placement testing before enrollment so the recommended course reflects current knowledge, strengths, and gaps.
What the student sees: A timed diagnostic with clear level guidance.
A typical Honors lesson uses a warm-up, core instruction, tiered practice, advanced work, and review in a 90-minute live class.
What the student sees: Worked examples followed by increasingly independent problems.
Students use homework, teacher explanations, testing, and error analysis to improve flexibility rather than memorize isolated formulas.
What the student sees: Feedback that connects errors to a next strategy.
Curriculum architecture
Placement assessment before enrollment
Pre-class preparation and live instruction
Worked examples and independent practice
Homework, review, and testing
AMC, MathCounts, and competition problem practice
AoPS-based curriculum positioning
Structured 18-lesson semester format
Six to twelve students in standard Honors classes
100% English instruction and materials
Teacher feedback and error analysis
Pre-Algebra number theory foundations
Algebra I modeling and equations
Geometry and spatial reasoning
AMC 8 to AMC 10 progression
Online classes and learning centers
A worked use case
Consider four different primes A, B, C, and D where A + B = C and A + C = D. At first glance, the problem appears to invite trial and error. A competition student can instead use structure:
C and D are odd primes because each is a sum involving primes.
Therefore A must be the only even prime, so A = 2.
The relationships become C = B + 2 and D = C + 2.
Three consecutive odd primes must be 3, 5, and 7, giving 31.
A × C + B × D = 2 × 5 + 3 × 7 = 10 + 21 = 31
This is the kind of use case where tutoring focuses on noticing parity and divisibility before calculating. Students who want a broader transition can explore an AMC 8 to AMC 10 pathway or review AMC 10 preparation planning.
Evidence and perspective
Reported stronger logic after eight lessons in a site survey.
Reported better learning habits in a site survey.
Reported increased confidence in a site survey.
Of families gave five-star ratings according to site figures.
“I love teaching at ACE Academy because I get to work with students of all personalities, and my experience helps me connect with each of them in meaningful ways.”
“The curriculum is also thoughtfully designed, using engaging characters that make lessons more enjoyable and easier to understand for both students and teachers.”
“Join thousands of families who have transformed their children's academic journey with ACE Academy.”
“Expert teachers. Engaging learning. Real results.”
Choose the right format
| Decision factor | ACE Academy | Self-directed study | General private tutoring |
|---|---|---|---|
| Starting level | Placement testing before enrollment | Student or family determines level | Depends on tutor and intake process |
| Curriculum | AoPS-based competition curriculum | Materials selected independently | May be tutor-selected |
| Live instruction | Weekly 90-minute live classes | Not inherent to the format | Usually depends on arrangement |
| Peer setting | Small groups of 6–12 in standard Honors format | Usually individual study | Often individual, depending on provider |
| Competition practice | AMC, MathCounts, and related problem practice | Requires independent selection | Depends on tutor experience and materials |
Credentials and key stats
Years of combined mathematics education and talent-development experience in the research and teaching team
Of North American instructors cited as having mathematics or related STEM backgrounds
Years of teaching experience cited for North American instructors
Lessons in the standard Honors semester format
The teaching and curriculum information includes university professors, competition experts, and instructors with backgrounds connected to Columbia University, Caltech, Rutgers University–Newark, Tulane University, Stanford University, and the Mathematical Association of America.
Questions families ask
The most appropriate starting point depends on the student’s current knowledge and goals. ACE Academy uses placement testing before enrollment to identify strengths, weaknesses, and a recommended course level. Number theory preparation may be connected to Pre-Algebra, Algebra I, Honors Math, or Competition Math. Students preparing for AMC 10 may need different amounts of support in arithmetic, algebra, geometry, counting, and proof-minded reasoning. A placement result gives families a clearer basis for choosing a pathway rather than relying only on the student’s grade level.
Relevant topics include prime and composite numbers, prime factorization, divisibility rules, common multiples, common divisors, LCM, and GCD. Students also work with modular reasoning, remainders, parity, consecutive integers, fractions, ratios, powers, and square roots. Counting, probability, casework, pattern recognition, and working backward are included because AMC problems often combine several ideas. Pre-Algebra A emphasizes multiples, primes, factorization, fractions, and AMC 8 practice. Pre-Algebra B extends into counting, restrictions, probability, patterns, worst-case scenarios, and additional competition practice.
A standard Honors course is described as 18 lessons per semester, with one 90-minute lesson each week. The class structure includes a five-minute mathematics game or warm-up, 45 minutes of core instruction and tiered practice, a short break or activity, 30 minutes of advanced instruction and practice, and a final review. Students receive explanations, work through examples, solve independently, and receive feedback. Approximately 39% of classroom time is allocated to student output, including problem solving and mathematical explanation. This structure is intended to make the student’s reasoning visible instead of limiting the lesson to lecture and memorization.
ACE Academy offers live online classes as well as in-person learning centers. The listed learning-center locations include San Jose, Great Neck, Scarsdale, Melbourne, and Singapore. Availability, schedule, and course options can vary by location and program. Online instruction allows students to follow the live class format from a different region. Families can contact the team to ask which option is available for their student’s subject, level, and location.
New students complete placement testing before enrollment. The Honors Pre-Algebra test has 16 questions and a 40-minute time limit, with a 60% threshold and approximately 10 to 11 correct answers needed to pass. The Honors Algebra I A test has 17 questions, a 40-minute limit, and an 85% threshold requiring 14 correct answers. The Honors Algebra I B test has 16 questions and a 60% threshold, while the AMC 8 Basics A test has 16 questions, 40 minutes, and a 60% threshold. These results are used to identify current knowledge and recommend a course level, not to replace ongoing teacher feedback.
The provided math pricing examples show a 36-lesson package at $999 and a 72-lesson package at $1,819. These figures are examples listed in the available source information and may not represent every course or current enrollment option. The final recommendation depends on the student’s placement result, selected program, lesson package, and scheduling needs. A family should confirm current pricing and availability directly with ACE Academy before enrolling. A free trial and placement conversation can help clarify the appropriate program before making a longer commitment.
Start with a placement conversation, then build the prime, divisibility, modular, counting, and problem-solving foundations that competition mathematics demands.