SAT/ACT STUDY GUIDE

 

The math review contains many examples.  Some of them have been designed to test your understanding while others serve as an introduction to new concepts.   Some sections include typical test questions at the end.

 

Part I Number

 

Section 1:  Numbers

Section 2:  Sequences

Section 3:  More Definitions and Basic Properties of Numbers

 

The first part of this review focuses on the idea of number.  We'll answer questions such as:

 

What is a number?

What is an integer? 

What is a digit?

What is the difference between a counting number and a real number?

What do we need to know about computation with positive and negative numbers?

What is the absolute value of a number?

What is the one crucial fact to know about inequalities?

What are prime numbers?

What patterns do even and odd numbers present?

What are sequences?

How can we use patterns to find mathematical solutions?

How can we compute the greatest common factor and the least common multiple of two numbers?

 

Part II Basic Arithmetic

 

Section 1:  Handy Math Facts to Know

Section 2:  Common Terms and Examples Used in Arithmetic

Section 3:  Properties of Arithmetic

Section 4:  Compensating or Balancing Techniques

 

The second part of this review provides terms and techniques that simplify understanding and computation.  We'll answer questions such as:

 

What computational facts beyond the basic addition and multiplication facts are helpful to know?

What arithmetic operations are indicated by words like "product" and "factor"?

How can using properties of arithmetic save time on computation?

How can problems be "reorganized" to simplify computation?

 

Part III Fractions, Decimals, Percents, Ratio and Proportion

 

Section 1:  Fractions

Section 2:  Divisibility Rules

Section 3:  Prime Factorization

Section 4:  Operations with Fractions

Section 5:  Ratio and Proportion

Section 6:  Common Fraction/Decimal/Percent Equivalent Relationships

Section 7:  Percent Problems

 

Part III provides a basic review of fractions and highlights the relationships among fractions, decimals, and percents.  There is also an emphasis on problem solving using ratios and proportions.  We'll answer questions such as:

 

How is a mixed number converted to an improper fraction?

How do divisibility rules help to simplify fractions?

Are there computational shortcuts for fractions?

How are ratios and proportions used to solve problems?

What is direct and inverse variation?

How can we remember the important decimal/fraction/percent facts?

How are percent increases and decreases computed?

 

Part IV Other Topics

 

Section 1:  Exponents and Radicals

Section 2:  Statistics

Section 3:  Probability

Section 4:  Very Unusual Symbols

 

This part of the review includes a survey of exponents and square roots,  basic statistics and probability, as well as how to answer test questions that define new symbols and operations.  We'll answer questions such as:

 

When should exponents be added and when should they be multiplied?

What are the common traps to avoid when working with exponents?

What are negative and fractional exponents?

How do we find the mean, the median, and the mode of a set of numbers?

How are basic probabilities computed?

Can we answer test questions that use symbols we have never seen before?

 

Part V Algebra

 

Section 1:  Linear Equations

Section 2:  Polynomials

Section 3:  Problem Solving in Algebra

 

This section provides a review of how to solve basic algebraic equations and what to do with expressions that contain more than one term.  We'll answer questions such as:

 

How do we solve linear equations?

What do we when there are two equations and two variables?

What is the FOIL Method of algebraic multiplication?

How do we solve equations with polynomials?

How are rate problems, mixture problems, and work problems alike?

 

Part VI Geometry

 

Section 1:  Plane Geometry

Section 2:  The Pythagorean Theorem

Section 3:  Coordinate Geometry

 

Plane geometry has to do with measurement and relationships among lines, angles, circles, and polygons.  Coordinate geometry refers to the real number line and the coordinate plane.  A special section is devoted to the Pythagorean Theorem. We'll answer questions such as:

 

How are angles measured?

What is the relationship between corresponding sides of similar triangles?

What is the relationship between linear and area measurement?

How can we find the perimeters and areas of geometric figures?

When is the Pythagorean Theorem useful for solving problems?

What is the slope of a line? 

Is there an easy way to find the distance between two points?

 

Part VII Advanced Topics

 

Section 1:  Conic Sections

Section 2:  Logarithms

Section 3:  Trigonometry

 

The final part of the math review includes parabolas, circles, ellipses , and hyperbolas, as well as logarithms and the basic trigonometric functions.  We'll answer questions such as:

 

What do the graphs of parabolas, circles, ellipses, and hyperbolas look like?

What kinds of equations describe parabolas, circles, ellipses, and hyperbolas?

How are the "roots" of an equation found?

How are logarithms and exponents related?

What do "sine," "cosine," and "tangent" mean?

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