Topics: geometry, arithmetic, algebra I, algebra II, statistics and data interpretation, counting and probability, miscellaneous topics.

Style: The class emphasizes sound reasoning with a focus on logic and observation. Students who follow the instructors' advice will see their scores improving considerably.

Geometry review: Lines, planes, points, parallel and perpendicular lines, angles, circle definition and elements, triangles, quadrilaterals, medians, midlines, angle bisector, altitude, area of parallelogram, triangle, circle, cube, box, volume of box, cube, similarity, special triangles, Pythagorean theorem and Pythagorean triples, symmetries.

Arithmetic review: Factors, multiples, writing integers in expanded form, even/odd numbers, place value, equivalent fractions, operations with fractions, decimals, ratios, proportions, percentages, factor trees, integer division with remainder, integer exponents, least common multiple, greatest common divisor/factor, averages, digit patterns, direct and inverse proportionality, rates.

Counting and probability: Definition of discrete and geometric probability, sum and product rules, notions of set theory, inclusion-exclusion principle, the Pigeonhole principle, triangular numbers, sequences, linear and circular permutations.

Algebra I and II: negative and positive expressions, perfect squares, algebraic identities, factoring, absolute values, functions: domain and range, functions transformations, inequalities, linear and quadratic functions and equations, equations with parameters, rational expressions, operations with exponents.

Statistics and Data Interpretation: statistic analysis of data sets, graphs, percent variation.

Other miscellaneous topics will be taught.

Homework will be assigned at each lesson and is expected to take 1 hour to complete. It is recommended that students open the homework immediately after the class instead of attempting it at the last moment. The emphasis is on independent reasoning. Answer verification is automatic and a report is emailed to parents.

Progress will be measured through performance on homework assignments, class quizzes and diagnostic tests. Three full diagnostic tests are included with the purchase of the entire package: before the course, midterm and final.

Materials used produce scores that are very close to scores on actual tests. We selectively use a very large base of problems and quizzes that do not repeat sooner than 2 years. Students who re-take this class will encounter different practice problems each time around.

Basics
The sentence Nouns Subjects Verbs Objects Predicates Prepositions Adverbs Articles Clauses
Easy
Subject-Verb Agreement Adverbs vd. Adjectives Parallelism Double negatives Tense consistency Pronoun consistency Possessives
Medium
Dangling modifiers Misplaced modifiers Sentence fragments Coordinating conjunctions Subordinating conjunctions Run-on sentences Comma splices Noun phrase appositives
Hard
Passive & active voice Commas Semi-colons Colons
Writing
Outlining Sentence variety Sentence combining Coherence Transitions Developing paragraphs

Vocabulary
Vocabulary Synonyms Antonyms

Figures of Speech
Metaphors Similes Allusion Personification

Common SAT critical reading question types
Tackling tone questions Techniques for sentence completions Uncovering a passage's main idea Strategies for comparative passages Short passage time management Long passage time management