# Math Acceleration and Problem Solving for High Schools

With a good math background, our students are ready to excel in the most challenging high school math and science classes by completing their math and science graduation requirements in 11th grade. While most high school students are busy prepping for SAT and AP exams, Ardent students will have time to build an attractive profiles for applying to elite colleges.

## Overview

Our curriculum is designed to align problem solving training, math and science competitions with preparation for PSAT, SAT and AP exams to achieve good grades, excellent test scores, and stellar academic competition results to maximize admission chances to elite colleges. We mentor our students in brainstorming math/science related research projects, searching for scholarships and summer opportunities with universities and businesses, applying strengths or passions in leadership and community service activities, and exploring careers. By the time our students start their college application process in 11^{th} grade , they have all the key ingredients to present their unique portfolio—GPA, test scores, awards/scholarships, research projects, intern/work experience, leadership, community services, essay topics, career plan, and interview skills. The goals for this group are:

- Achieve top scores in PSAT, SAT I/II and AP exams
- Develop leadership skills in math and/or science clubs
- Shine in math and science competitions (AMC, ARML, USA Math Olympiad, USA Physics Olympiad, USA Chemistry Olympiad, USA Biology Olympiad and USA Informatics Olympiad)
- Enhance admission opportunities to elite colleges

## M109 - Honors Algebra II Problem Solving

This course assumes you will concurrently enroll in an Algebra II class either at your school, at a local community college, or via distance learning programs such as CTY, EPGY or Ardent Academy. You can also purchase a self-study web-based multimedia Algebra II course from Ardent Academy. The multimedia course covers college level algebra and offers many of the topics in greater depth than a typical high school curriculum.

The purpose of this course is to teach problem solving strategies and techniques related to Algebra II and prepare the students to take SAT II Mathematics Level 1 exam or participate in AMC 10 math competition.

If you have just completed Algebra II, this course will fill in the gaps and add depth to your Algebra knowledge and give you a solid problem solving foundation for Honors Precalculus.

### Problem solving topics include:

**Algebra II**(45%): Linear equations, quadratic equations, radical equations, inequalities, absolute value, equations of lines and circles, graphing functions, transformation (shift, stretch, symmetry and reflection), long division, synthetic division, the remainder theorem, the factor theorem, the rational roots theorem, zeroes of polynomial functions, exponential and logarithmic functions, systems of equations, parapolas, ellipses, and hyperbolas.**Art of Problem Solving**(40%): Exponents and logarithms, complex numbers, linear equations, proportions, divisibility, number bases, modular arithmetic, primes, quadratic equations, angles, triangles, quadrilaterals, polygons, angle chasing, areas, the power of coordinates, power of a point, 3-D geometry, inequalities, sequence & series, counting & probabilities, statistics, and sets.**Test Skills**(15%): AMC 10, ARML, and other math contest problems will be used to cover additional problem solving topics and techniques. These skills will enable you to do well on similar problems found on SAT II Mathematics Level 1 exam and AMC 10/12 math competitions.

Prerequisite: | E130, E230, or Concurrent Enrollment in Algebra II. |

Grades: | 9^{th} or 10^{th} Grade honor students |

Total Time: | 45 Hours (30 meetings at 1.5 hour per meeting) |

Next Course: | M110 - Honor Pre-Calculus Problem Solving |

## M110 - Honors Pre-Calculus Problem Solving

This course assumes you will concurrently enroll in a precalculus or trigonometry class either at your school, at a local community college, or via distance learning programs such as CTY, EPGY or Ardent Academy. You can also purchase a self-study web-based multimedia precalculus course from Ardent Academy. The multimedia course covers college level precalculus and offers many of the topics in greater depth than a typical high school curriculum.

The purpose of this course is to teach problem solving strategies and techniques related to Precalculus and prepare the students to take SAT II Mathematics Level 2 exam or participate in AMC 12 math competition.

If you have just completed Precalculus, this course will fill in the gaps and add depth to your Algebra and Trigonometry knowledge and give you a solid problem solving foundation for AP Calculus.

### Problem solving topics include:

**Advanced Algebra**(25%): Relations and functions, domain and range, graphing equations, linear and quadratic equations, manipulating graphics, composite functions, polynomial functions, long divisions, synthetical division, finding zeroes of polynomial functions, exponent and logrithmic functions, linear system of equations, and introduction to linear algebra.- Trigonometry (30%): Angles and radian measures, right angle trigonometry, trigonometric functions, graph of trigonometric functions, inverse trigonometric functions, trigonomitric identities, solving trigonometric equations, the law of sins, the law of cosines, vectors, complex numbers in trigonometric forms, polar coordinates, and powers and roots of complex numbers.
**Art of Problem Solving**(30%): Trigonometric functions, triangle laws, cyclic quadrilaterals, conics, polar cordinates, polynomials, functions and inverse functions, complex numbers, vectors and matrics, cross products and determinants, analytic geometry, inequalities, combinatorics, sequence & series, advanced counting and probabilities, collinearity and concurrency, number theory, diophantine equations, and graph theory.**Test Skills**(15%): AMC 10, ARML, and other math contest problems will be used to cover additional problem solving topics and techniques. These skills will enable you to do well on similar problems found on SAT II Mathematics Level 2 exam and AMC 12 math competitions.

Prerequisite: | G110 or Concurrent Enrollment in Precalculus. |

Grades: | 9^{th} - 11^{th} Grade honor students |

Total Time: | 45 Hours (30 meetings at 1.5 hour per meeting) |

## M111 - AP Calclus

This class follows the College Board AP Calculus AB/BC requirements and prepares you to take the AP Calculus AB exam. A score of 4 or higher will enable you to earn college credits at some colleges. The course is a combination of self-study distance learning and seminar-based problem solving sessions.

Prerequisite: | Ardent Academy Placement Test |

Grades: | 9^{th} - 11^{th} Grade honor students |

Total Time: | 45 Hours (30 meetings at 1.5 hour per meeting) |