Curriculum
IDEA MATH provides an extensive curriculum. Our courses are intended for able students who wish to expand their mathematics knowledge beyond regular classroom settings. We emphasize study skills (such as taking notes, oral and written presentations, listening, observing, organization, etc). We believe in studying math via problem solving as a medium to develop students' learning interests and critical thinking abilities. Courses offered by IDEA MATH are categorized into six different series:
Extra-Curricular (EC) Series
(PC0, PCA, PC1, PC2, PCX, UC1, UC2, UC3)
Accelerated Championship (XC) Series
(XC7, XC9, XC10)
Contest Edge (CE) Series
(CE1-CE10)
School Enrichment (SE) Series
(Algebra 1, Geometry, Algebra 2)
Math Olympiad (MO) Series
(MO1, MO2, MO3)
Winter Contest (CW) Prep Series
(CW0-CW10)
Full courses are offered for the SE, EC, XC, and MO Series. Please see the following course flow chart for relations between these courses.
Contest Edge (CE) Series and the Winter Contest Prep (CW) Series can be considered as a supplement to any of the SE/EC/XC/MO series. Each course in the CE and Winter program provides additional practice for contests such as MATHCOUNTS school/chapter/state/national, AMC8/10/12, AIME, ARML, HMMT, USAJMO, USAMO, etc. Please see the following course flow chart for relations between the CE series/Winter program and the SE/EC/XC/MO series.
Courses in School Enrichment (SE) Series build students' understanding of the concepts they are likely to encounter in general school curriculum with extra depth and breadth. SE Series courses are Algebra 1 (ALG1), Geometry (GEO), Algebra 2 (ALG2).
| Algebra 1 | |
|---|---|
| School Extension Component: |
Algebra 1 based, problem-solving oriented (to register, please visit the home page) |
| Intended For: | Able and interested 6th and 7th graders |
| Sample Lectures: | ALG1 Sample Syllabus ALG1 Sample Lecture 1 ALG1 Sample Lecture 2 |
| Geometry | |
|---|---|
| School Extension Component: |
Geometry based course, problem-solving oriented (to register, please visit the home page) |
| Intended For: | Able and interested 7th and 8th graders |
| Sample Lectures: | Geometry Sample Syllabus Geometry Sample Lecture 1 Geometry Sample Lecture 2 |
| Algebra 2 | |
|---|---|
| School Extension Component: |
Algebra 2 (to register, please visit the home page) |
| Intended For: | Able and interested 7th, 8th, and 9th graders who have completed IDEA MATH PCX or UC1 or equivalent |
| Sample Lectures: | ALG2 Sample Syllabus ALG2 Sample Lecture 1 ALG2 Sample Lecture 2 |
Courses in Extra Curricular (EC) Series are designed for students pursuing extra curricular mathematics far beyond general school curriculum and provides extensive preparation for contests such as MATHCOUNTS, AMC8/10/12, and AIME etc. EC Series courses are PC0, PCA, PC1, PC2, PCX, UC1, UC2, UC3.
| PCA/Pre-Algebra 2 | |
|---|---|
| School Enrichment Component: |
Pre-Algebra 2 (to register, please visit the home page) |
| Extra-curricular Component: |
More on arithmetic techniques, number sense, patterns recognition, and word problems; getting familiar with shapes and figures, counting basics. Contest reference: CML, Intro AMC8. |
| Intended For: | Able and interested 4th, 5th, and 6th graders |
| Sample Lectures: | Sample Syllabus and Lectures |
| PC1 (covering IM1 and MC1) | |
|---|---|
| School Enrichment Component: |
Integrated Math 1 (IM1): Algebra 1 based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 1 (MC1). Contest reference: Intro to medium level AMC8 and school rounds of MATHCOUNTS |
| Intended For: | Able and interested 6th and 7th graders who have an excellent command of Pre-Algebra (some familiarity with Algebra 1 is welcome) and some experience with extracurricular activities such as AMC8 and MATHCOUNTS or equivalent. (For example, students who have completed IDEA MATH's PC0 course or equivalent.) |
| Sample lectures: | Math Challenges 1 Algebra Sample Lecture Math Challenges 1 Counting Sample Lecture Math Challenges 1 Geometry Sample Lecture Math Challenges 1 Number Sample Lecture Integrated Math 1 Sample Lecture |
| PC2(covering IM2 and MC2) | |
|---|---|
| School Enrichment Component: |
Integrated Math 2 (IM2): Algebra 1 based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 2 (MC2).
Contest reference: Medium level AMC8, intro level AMC10, school and chapter rounds of MATHCOUNTS |
| Intended For: | Able and interested 6th, 7th graders who have good command on Algebra and experience with extracurricular activities such as AMC8 and MATHCOUNTS or equivalent.
(For example, students who have completed IDEA MATH's PC1 course or equivalent.) |
| sample lectures: | Math Challenges 2 Algebra Sample Lecture Math Challenges 2 Counting Sample Lecture Math Challenges 2 Geometry Sample Lecture Math Challenges 2 Number Sample Lecture Integrated Math 2 Sample Lecture |
| PCX (covering IM3 and MC3) | |
|---|---|
| School Enrichment Component: |
Integrated Math 3 (IM3): Advanced Algebra 1 and Geometry based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 3 (MC3).
Contest reference: Advanced level AMC8, intro to medium level AMC 10, chapter and state rounds of MATHCOUNTS |
| Intended For: | Students who have completed IDEA MATH PC2 course or equivalent.
(As a general reference, students shall have an AMC10 score close to 90.) |
Sample lectures: | Integrated Math 3 Algebra Sample Lecture Integrated Math 3 Geometry Sample Lecture Math Challenges 3 Algebra Sample Lecture Math Challenges 3 Counting Sample Lecture Math Challenges 3 Geometry Sample Lecture Math Challenges 3 Number Sense Sample Lecture |
| UC1 (covering IM4 and MC4) | |
|---|---|
| School Enrichment Component: |
Integrated Math 4 (IM4): Advanced Algebra 1 and Geometry based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 4 (MC4).
Contest reference: Medium level AMC 10, intro level AMC12 and AIME, state and national rounds of MATHCOUNTS |
| Intended For: | Students who have completed IDEA MATH's PCX course or equivalent.
(As a general reference, students should have an AMC10 score close to 105.) |
| sample lectures: | Integrated Math 4 Algebra Sample Lecture Integrated Math 4 Geometry Sample Lecture Math Challenges 4 Algebra Sample Lecture Math Challenges 4 Counting Sample Lecture Math Challenges 4 Geometry Sample Lecture Math Challenges 4 Number Sense Sample Lecture |
| UC2 (covering IM5 and MC5) | |
|---|---|
| School Enrichment Component: |
Integrated Math 5 (IM5): Advanced Algebra 2 and Geometry and Trigonometry based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 5 (MC5).
Contest reference: Medium to advanced level AMC 10, medium level AMC12, intro to medium level AIME, state and national rounds of MATHCOUNTS, intro to medium level HMNT |
| Intended For: | Students who have completed IDEA MATH's UC1 course or equivalent.
(As a general reference, students should have an AMC10 score close to 120.) |
| Sample lectures: | Integrated Math 5 Algebra Sample Lecture Integrated Math 5 Geometry Sample Lecture Math Challenges 5 Algebra Sample Lecture Math Challenges 5 Counting Sample Lecture Math Challenges 5 Geometry Sample Lecture Math Challenges 5 Number Sense Sample Lecture |
| UC3 (covering IM6 and MC6) | |
|---|---|
| School Enrichment Component: |
Integrated Math 6 (IM6): Advanced Algebra 2 and Geometry and Trigonometry based (to register, please visit the home page) |
| Extra-curricular Component: |
Math Challenges 6 (MC6).
Contest reference: Advanced level AMC 10, medium level AMC12 and AIME, state and national rounds of MATHCOUNTS, medium level HMNT |
| Intended For: | Students who have completed IDEA MATH's UC2 course or equivalent.
(As a general reference, students shall have an AIME score close to 6.) |
| Sample lectures: | Integrated Math 6 Algebra Sample Lecture Integrated Math 6 Geometry Sample Lecture Math Challenges 6 Algebra Sample Lecture Math Challenges 6 Counting Sample Lecture Math Challenges 6 Geometry Sample Lecture Math Challenges 6 Number Sense Sample Lecture |
Courses in Accelerated Championship (XC) Series intend to improve top level young students' command of the core knowledge leading to higher studies in mathematics.
XC Series courses are
XC7,
XC9,
XC10.
From 2000 to 2022, the Phillips Exeter Academy Red Lion (PEARL) math club/team, under the supervision of IDEA MATH academic director Dr. Zuming Feng (joined by
IDEA MATH staff member Ivan Borsenco more recently), has become a dominant force in US high school math contests. Students from PEARL have diverse backgrounds, skillsets,
and personalities. What do they have in common? Well, almost all of them have studied PEA Math Transition 3X (or 31X-40X-41X) and PEA Math 431-511-521. The materials in the
XC Series build upon materials that Zuming has used for these PEA courses. Courses in the XC series are designed to improve students' command of the core knowledge, leading to
higher studies in mathematics. Students will be surprised to discover that the school curriculum could be as challenging and as useful for preparing for higher-level contests
(such as AMC 12/AIME/ARML/HMMT/USAJMO/USAMO), if the right problems are posed, and more importantly, the school curriculum could and should be far more important,
if learned with good depth and breadth. While math contests are not the main focus for these courses, these courses cultivate young talented math students' vision on the
flow of mathematics and the ability to reason and argue mathematically and rigorously. Therefore, students' achievements in math contests tends to follow as a natural result.
| XC7 | |
|---|---|
| Course content: | XC7 Part 1/2/3 (parametric equations, vector operations, 3-D geometry, advanced trigonometry; advanced 3-D geometry, matrices and vector operations; introduction to Calculus with an emphasis on proofs/math reasoning; and all the related contest extensions. |
| Prerequisites and general student body: | (1) Passing UC3 (or above) with good marks; or
(2) with a USAJMO/USAMO index close to (or above) the official USAJMO/USAMO cutoff, and solid work on the T4 placement test; This course is for 7th, 8th and 9th graders in general. |
| Sample lectures: |
XC7 part1 Sample Lecture XC7 part2 Sample Lecture XC7 part3 Sample Lecture |
| XC9 | |
|---|---|
| Course content: | Calculus AB with an emphasis on proofs and extensions to (college level) math contests |
| Prerequisites and general student body: | (a) For younger students: passing XC7 and MO1 with good marks; or
(b) for 9th, 10th, and 11th graders: with a USAJMO/USAMO index close to (or above) the official USAJMO/USAMO cutoff, and excellent work in the T4 placement. This course is for 8th, 9th, and 10th graders in general. |
| Sample lectures: |
XC9 Sample Lecture |
| XC10 | |
|---|---|
| Course content: | Calculus BC with an emphasis on proofs and extensions to (college level) math contests |
| Prerequisites and general student body: | Passing XC9 with good marks;
This course is for 9th, 10th, and 11th graders in general |
| Sample lectures: |
XC10 Sample Lecture |
Courses in the Math Olympiad (MO) Series focus on systematic development on math reasoning skills to prepare for math olympiads. The MO Series courses are
MO1,
MO2,
MO3,
MO4, and MO5.
From 2000 to 2022, the Phillips Exeter Academy Red Lion (PEARL) math club/team, under the supervision of IDEA MATH academic director Dr. Zuming Feng
(joined by IDEA MATH staff member Ivan Borsenco more recently), has become a dominant force in US high school math contests. In this period, students from PEARL
have been USAMO winners more than 45 times and have won 27 IMO gold medals, 11 silver medals, and 8 bronze medals. The materials in the Math Olympiad (MO)
Series build upon materials that Zuming and Ivan have used for PEARL math club activities and the US Math Olympiad Summer Program (MOSP) entry level courses.
| MO1 | |
|---|---|
| Course Content | Math Olympiads 1:
Contest reference: Advanced level AMC10 and AMC12, medium to advanced level AIME and HMNT, intro level HMMT |
| Intended For: | Students who have completed IDEA MATH's XC7 course or equivalent.
As a general reference, students shuold have an USAJMO/USAMO index close to (or above) the official USAJMO/USAMO cutoff. If a student has not completed XC7 but has placed in the top 75% on the USAJMO, please contact info@ideamath.org for special permission---likely, the student will be required to take a T4 placement test. |
Sample lectures: |
Math Olympiads 1 Algebra Sample Lecture Math Olympiads 1 Combinatorics Sample Lecture Math Olympiads 1 Geometry Sample Lecture Math Olympiads 1 Number Theory Sample Lecture |
| MO2 | |
|---|---|
| Course Content | Math Olympiads 2:
Contest reference: Advanced level AMC10 and AMC12, medium to advanced level AIME and HMNT, medium level HMMT -- optional |
| Intended For: | Students who have completed IDEA MATH XC9 and MO1 courses or equivalent.
As a general reference, students should have a solid performance (i.e., making the top 50%) on the |
Sample lectures: |
Math Olympiads 2 Algebra Sample Lecture Math Olympiads 2 Combinatorics Sample Lecture Math Olympiads 2 Geometry Sample Lecture Math Olympiads 2 Number Theory Sample Lecture |
| MO3 | |
|---|---|
| Course Content | Math Olympiads 3:
Contest reference: Advanced level AMC10 and AMC12, advanced level AIME and HMNT, medium level HMMT -- optional |
| Intended For: | Students who have completed IDEA MATH XC9, XC10, and MO2 courses or equivalent.
As a general reference, students should have a solid performance (i.e., making the top 50%) on the USAMO. |
Sample lectures: |
Math Olympiads 3 Algebra Sample Lecture Math Olympiads 3 Combinatorics Sample Lecture Math Olympiads 3 Geometry Sample Lecture Math Olympiads 3 Number Theory Sample Lecture |
Courses in the Contest Edge (CE) Series are intended to be supplementary courses to courses in the SE, EC, XC, and MO series. These courses provide additional preparation opportunities for various math contests such as MATHCOUNTS (School, Chapter, State, National rounds) and American Math Competitions (AMC 8/10/12, AIME, USA(J)MO). Materials in these courses are oriented by subject and topic. The CE Series courses are CE1 to CE10.
| CE1 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the PC1 and Algebra 1 courses. |
| Intended For: | Goal: A pleasant start on AMC8 and MATHCOUNTS school/chapter round;
General scoring reference: AMC8 score 10 or above; Recommended companion course: CE1 is a good supplementary course for PC1 (Extra-Curricular series) or Algebra 1 (School Enrichment series). |
Sample lectures: | Coming Soon |
| CE2 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the PC2 and Geometry courses. |
| Intended For: | Goal: A solid job on AMC8 and MATHCOUNTS school/chapter round;
General scoring reference: AMC8 score 16 or above; Recommended companion course: CE2 is a good supplementary course for PC2 (Extra-Curricular series). |
Sample lectures: | Coming Soon |
| CE3 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the PCX and Geometry courses. |
| Intended For: | Goal: A pleasant start on AMC10 and a solid job on MATHCOUNTS chapter/state round;
General scoring reference: AMC8 score 20 or above and/or AMC10 score around 90; Recommended companion course: CE3 is a good supplementary course for PCX (Extra-Curricular series) or Geometry (School Enrichment series). |
Sample lectures: | Coming Soon |
| CE4 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the UC1 and Algebra 2 courses. |
| Intended For: | Goal: A solid job on AMC10, a pleasant start on AIME, an excellent job on MATHCOUNTS chapter/state round.
General scoring reference: AMC10 around 100; Recommended companion course: CE4 is a good supplementary course for UC1 (Extra-Curricular series) or Algebra 2 (School Enrichment series). |
Sample lectures: | Coming Soon |
| CE5 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the UC2, UC3, XC7 and Algebra 2 courses. |
| Intended For: | Goal: A solid job on AMC10/12, a solid job on AIME, an excellent job on MATHCOUNTS state round.
General scoring reference: AMC10 score around 110 and AIME score around 6; Recommended companion course: CE5 is a good supplementary course for UC2 (Extra-Curricular series). |
Sample lectures: | Coming Soon |
| CE6 | |
|---|---|
| Course Content | This course provides additional contest practice. It is also a great supplementary course for the UC3 and XC7 courses. |
| Intended For: | Goal: An excellent job on AMC10/12 and AIME;
General scoring reference: USAJMO/USAMO index (AMC10/12 score + 10* AIME score) are consistently above 190; Recommended companion course: CE6 is a good supplementary course for UC3 (Extra-Curricular series). |
Sample lectures: | Coming Soon |
Courses in the Winter Contest (CW) Prep Series are intended to be supplementary courses to courses in the SE, EC, XC, and MO series. In each course, materials for the CW Series are different from year to year. Courses in the 2022 CW Series will focus upon Contest Review 2022: selected high-quality problems from US math competitions (such as AMC 8/10/12, AIME, USAJMO/USAMO, MATHCOUNTS chapter, ARML, HMNT, HMMT) and around the world from 2012, 2002, and 1992. These courses also feature about 16 new (original) practice sets (covering all different levels) written by our academic team.