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.
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?
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?
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?
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?
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?
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?
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?