SAT Math Curriculum
Our SAT students come to us with varied skills and unique goals. Because each of those students brings a unique set of strengths and weaknesses, our private SAT tutoring is highly personalized; we alter the specifics of our approach to cover the issues you need to learn. The following 20 SAT math lessons can represent a menu of choices for those needing to brush up on definite topics or a full lesson plan for those needing a more comprehensive review. Our private tutoring emphasizes the mastery of SAT-specific content and the development of intelligent strategies and effective analytical skills.
Lesson 1: Algebra Foundation I
Students are first taught the conventional algebra used on almost all SAT questions, such as basic linear equations for one, two, and three variables; equations with fractions; equations that express one variable in terms of other variables; equations that require maintaining the order of operations; basic equations involving exponents; and basic quadratic equations. Second, students are taught the basic algebra that is unique to the SAT. This includes solving for the addition or subtraction of multiple variables, handling simultaneous equation traps, and learning how to group equations with multiple variables.
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Lesson 2: SAT-Specific Word Problems
In this lesson, students learn intelligent strategies for recognizing, developing, and solving numerous common SAT word problems, including age and weight problems; consecutive integer problems; profit, cost, and loss problems; fraction word problems; and problems involving money, digits, and length. The skills gained in this lesson will continuously be reinforced throughout the lessons that follow.
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Lesson 3: Exponents and Radicals
This lesson covers all of the necessary rules of exponents and radicals. Students leave this lesson with a formal set of note cards and problem case studies. Most importantly, this lesson teaches students to recognize and solve the unique problems that the SAT typically presents. Some of these include simplifying exponents and exponent expressions, solving algebra and exponents, solving addition and subtraction with exponents, simplifying radicals,
and solving algebra with radicals.
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Lesson 4: Algebra Foundation II
In this lesson, students are taught more complex skills and strategies for working with algebra on the SAT, including quadratic equations, applied algebra, and advanced equation setup and solution. Students will learn which classic quadratic equations to memorize and how to apply them in specific situations.
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Lesson 5: Absolute Values and Inequalities
Inequalities are common on the SAT, and students often stumble over these problems or fall into classic answer traps. Here, we teach students all of the inequality rules necessary for the SAT, and, most importantly, we teach student how to handle the unique ways in which the SAT tests inequality knowledge. Absolute value problems present similar difficulties for students. We ensure that students know the rules of absolute values and provide the students with powerful strategies for handling these unique SAT problem types. Once both of these concepts are learned, we provide a variety of problems that include both inequalities and absolutes.
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Lesson 6: Polygons, Quadrilaterals, and Solid Geometry
Properties of the square, rectangle, parallelogram, rhombus, and trapezoid are covered in detail. These properties include area, perimeter, sum of interior angles, and sum of exterior angles. Next, students are instructed in issues concerning the three main three-dimensional shapes: the cylinder, cube, and rectangular solid. We cover the formulas for surface area, volume, and diagonal for the cube and rectangular solid and the formulas for surface area and volume of a cube. We also cover the other surface area and volume formulas for spheres, cones, and pyramids. Following the lesson, students are given more formulas and concepts to memorize.
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Lesson 7: Lines, Angles, and Triangles
In this lesson, students master skills on one of the SAT's favorite shapes – the triangle. Students begin by learning the properties of lines and angles, which include parallel lines, perpendicular lines, lines cut by a transversal, and the sum of angles. Then, these skills are applied to the study of triangles: isosceles triangles, equilateral triangles, and the special right triangles, including the 3-4-5 right triangle, 5-12-13 right triangle, and the 8-15-17 right triangle. Students will also learn all the important triangle computations: the Pythagorean theorem, triangle inequality theorem, exterior angle theorem, similar triangles, area of a triangle, perimeter of a triangle, and simplifying angles within a triangle. After this lesson, students will have a list of formulas and concepts to be memorized and mastered.
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Lesson 8: Circles and Multiple Figures
In this lesson students are first taught the basics of circles, including area, circumference, arcs, sectors, inscribed and central angles. Since circles are one of the most common shapes in multiple figure problems, students are then taught how to relate different shapes when they are inscribed in circles, such as triangles, squares, hexagons, etc. Finally students are shown other types of multiple figure problems, including squares inscribed in triangles, triangles inscribed in squares, and shaded regions. This lesson serves as an excellent review of the geometry learned in earlier lessons.
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Lesson 9: Coordinate Geometry
This lesson covers the important issues in coordinate geometry: the coordinate plane, points, lines, graphing lines, slope of a line, the point-slope formula, the slope-intercept equation, properties of vertical and horizontal lines, properties of parallel and perpendicular lines, geometrical shapes on the coordinate plane, the distance formula, the midpoint formula, and graphing inequalities. In addition, students will begin to build their knowledge of functions.
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Lesson 10: Functions
In this lesson, students learn the inner-working of functions. These include using functions with algebraic equations as well as being able to recognize and use commonly graphed functions. Additionally, students will learn how function graphs are shifted horizontally and vertically, as well as how they are widened and thinned.
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Lesson 11: Sequences
In this lesson, students learn how to set up and solve various sequences. This chapter will build off of skills already learned in the algebra lesson.
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Lesson 12: Ratios
Ratios are also common on the SAT, and students must have a strong knowledge of ratios in order to solve many geometry problems, as well as many word problems and probability problems. Students learn all of the important details of ratios, including what information a ratio does and does not convey, the ratio multiplier, multipart ratios, adding and subtracting to achieve a desired ratio. Finally, students learn to solve proportion problems as well as direct and inverse variation problems.
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Lesson 13: Overlapping Sets
In this lesson, we demystify set problems and provide students with a mechanical, yet flexible and adaptable, approach to solving overlapping set problems. We cover a wide-range of these problems, including sets with fractions, decimals, and percents and algebra within sets. Students are also taught to solve three-circle Venn diagrams.
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Lesson 14: Statistics
In this lesson, students learn to handle averages (arithmetic mean), weighted averages, median, mean, mode, range, and standard deviation.
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Lesson 15: Percents
This lesson teaches students to work confidently with percents and percent word problems. Students are taught how to convert percents and decimals and how to solve specific percent word problems, such as "percent of," "what percent," "percent less than," "percent greater than," and "percent change" problems. In addition, students are taught to comfortably work with percents in variable form.
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Lesson 16: Rate Problems
Rate Problems include Rate-Time-Distance and Rate-Time-Work problems. Students begin this lesson by learning how to convert units (measurement problems) since many rate problems require some change of units. Then students are taught how to attack the specific types of work and distance problems.
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Lesson 17: Probability
In this lesson, students will master basic probability concepts, including independent events, dependent events, the complement rule, and sample spaces.
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Lesson 18: Number Properties
In this lesson, students learn about positive/negative numbers, prime numbers, even/odd number remainder theory, divisibility, factors and multiples, powers of ten, absolute values, factorials, perfect squares, number patterns, consecutive integers, and other number properties that are common on the SAT. Since most high school students use calculators in math class, these concepts often appear foreign to SAT students. Following this lesson, students will have many concepts and formulas to memorize.
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Lesson 19: Graphs and Logic
In this lesson, students will get comfortable with the various ways in which graphing questions are presented, i.e. Bar graphs, line graphs, scatter graphs, and pie charts. Skills learned in previous sections, such as statistics, percents, ratios, and fraction questions, will be used to solve these graphing questions. Finally, students are shown various types of logic questions and how to apply a strategy that eliminates incorrect answer choices.
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Lesson 20: Combinatorics
Combinations and permutations are used to count the number of ways that certain tasks could be accomplished. Although these problems are not tested as frequently as others on the SAT, they are a must-know for the high level student.
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SAT Verbal Curriculum
Because each of our students brings a unique set of strengths and weaknesses, our private SAT tutoring is highly personalized; we alter the specifics of our approach to cover the issues you need to learn. The following SAT lessons can represent a menu of choices for those needing to brush up on definite topics or a full lesson plan for those needing a more comprehensive review. Our private tutoring emphasizes the mastery of SAT-specific content and the development of intelligent strategies,effective analytical skills, and the ability to recognize what issues are being treated in any specific question. In addition to this sequence of topics, students are expected to practice extensively, thus providing constant feedback to the tutor. The tutor and student will review any errors in detail. Additional lessons beyond the initial seven will consist of intensive review of the student's practice tests.
Lesson 1: Sentence Completion
The first lesson will introduce students to the sentence completion questions of the Critical Reading Section. The lesson will cover strategies in analyzing the logic of a sentence and in using the context of a sentence to determine the content of missing vocabulary items. Students will practice deciphering the cues for meaning that should direct their responses.
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Lesson 2: Sentence Structure
The primary skill necessary for success in the Writing portion of the verbal test is the ability to recognize an English sentence. This lesson will provide a precise description of simple, compound, and complex sentences. In addition, students will learn to recognize the different types of clauses out of which sentences are built: independent clauses, subordinate clauses, and relative clauses. Students will also learn to distinguish between adverb clauses, adjective clauses, and noun clauses. Students will learn how to avoid fragments and run-ons, two major errors that are a pervasive problem throughout the Writing section.
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Lesson 3: Noun Modifiers
A significant subset of the Sentence Improvement, Sentence Error, and Paragraph Improvement questions involves the recognition and accurate manipulation of the different linguistic structures that are capable of modifying nouns. Students will acquire a precise understanding of relative clauses, participial phrases, appositives, prepositional phrases, and infinitive phrases. Students will also learn principles that will help them choose which structures to use in differing contexts. Importantly, they will also learn the common mistakes in modifier usage that the test attempts to exploit.
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Lesson 4: Subject-Verb Agreement – Pronouns – Parallelism
Students will practice recognizing situations where subject and verb agreement problems are likely to appear. The lesson will also cover the importance of pronoun agreement in eliminating improper answers. Parallelism is a major sentence correction issue on the SAT. Students must be able to recognize contexts that require parallel grammatical structures: idioms of comparison and idioms of contrast, elements in a series, and elements joined by coordinating conjunctions. Students will get in-depth practice in identifying clues that trigger parallelism.
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Lesson 5: Diction and Idioms
This lesson covers idioms characteristically tested on the SAT, including idioms of comparison and contrast, verb plus preposition formations, and noun plus preposition formations. In addition, students will learn proper adverb and adjective usage. The discussion will also cover stylistic conventions such as conciseness, converting abstract nouns into active verbs, and avoiding redundancy.
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Lesson 6: Introduction to Reading Comprehension
Students will learn to identify the logical backbone of each passage, taking note of major divisions and using transition words to break the arguments down into manageable portions. Students will be taught to distinguish between what is being asserted in a given argument and what serves as support for those assertions. We will discuss "mapping" techniques that help the student find important elements of the argument when responding to questions.
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Lesson 7: Reading Comprehension Questions
Students will learn to develop a consistent approach to each of the different question types the SAT uses to measure students' ability to analyze college level texts. Students will learn to identify questions by type, for instance, main point, author's attitude, according to the passage, and the passage suggests questions. Students will then learn how to find good evidence for their responses in the passage.
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Lessons 8 +: Practice Tests and Review
Full-length practice tests will be assigned, and the results analyzed and reviewed with the student, both to uncover any new issues and suggest strategies for avoiding incorrect responses. Student may schedule as many of these sessions as are necessary.
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