Set builder and interval notation

Union and intersection of intervals

Product rule of exponents

Quotients of expressions involving exponents

Power rule: Positive exponents

Power rule: Negative exponents

Product rule of exponents in a multivariate monomial

Simplifying a radical expression: Problem type 1

Simplifying a sum of radical expressions

Simplifying a product of radical expressions

Rationalizing the denominator of a radical expression

Rational exponents: Basic

Rational exponents: Negative exponents and fractional bases

Rational exponents: Powers of powers

Simplifying a polynomial expression

Multiplying monomials

Multiplying polynomials

Factoring a quadratic with leading coefficient 1

Factoring a quadratic with leading coefficient greater than 1

Factoring a product of a quadratic trinomial and a monomial

Factoring a difference of squares

Factoring with repeated use of the difference of squares formula

Factoring a sum or difference of two cubes

Factoring a multivariate polynomial by grouping: Problem type 1

Rationalizing the denominator of a radical expression using conjugates

Solving a linear equation with several occurrences of the variable: Problem type 2

Solving a linear equation with several occurrences of the variable: Problem type 3

Solving a linear equation with several occurrences of the variable: Problem type 4

Solving a linear equation with several occurrences of the variable: Problem type 5

Solving an equation involving absolute value: Basic

Solving a rational equation that simplifies to a linear equation: Problem type 1

Solving a rational equation that simplifies to a linear equation: Problem type 2

Solving a rational equation that simplifies to a linear equation: Problem type 3

Solving an equation with radicals: Problem type 1

Solving an equation with radicals: Problem type 3

Solving an equation with radicals: Problem type 4

Finding the roots of a quadratic equation with leading coefficient 1

Finding the roots of a quadratic equation with leading coefficient greater than 1

Completing the square

Solving a quadratic equation using the quadratic formula

Finding the discriminant of a quadratic equation

Solving equations written in factored form

Solving a quadratic equation needing simplification

Solving a word problem using a linear equation: Problem type 3

Solving a word problem using a linear equation: Problem type 1

Solving a word problem using a linear equation: Problem type 2

Solving a word problem using a linear equation: Problem type 4

Solving a word problem using a quadratic equation with rational roots

Solving a word problem using a quadratic equation with irrational roots

Solving a linear inequality: Problem type 2

Solving a linear inequality: Problem type 3

Solving a linear inequality: Problem type 4

Solving an inequality involving absolute value

Solving a quadratic inequality

Graphing a parabola: Problem type 1

Midpoint of a line segment in the plane

Distance between two points in the plane

Graphing a line given its equation in slope-intercept form

Graphing a vertical or horizontal line

Graphing a line given its equation in standard form

Writing the equation of a line given the slope and a point on the line

Graphing a line through a given point with a given slope

Finding the slope of a line given its equation

Determining the slope of a line given its graph

Writing the equation of the line through two given points

Writing the equations of vertical and horizontal lines through a given point

Slopes of parallel and perpendicular lines: Problem type 1

Slopes of parallel and perpendicular lines: Problem type 2

Writing equations and drawing graphs to fit a narrative

Graphing a linear inequality in the plane: Problem type 1

Graphing a linear inequality in the plane: Problem type 2

Introduction to functions: Notation and graphs

Domain and range: Problem type 1

Domain and range: Problem type 2

Vertical line test

Vertical translation of the graph of a function

Vertical and horizontal translations of the graph of a function

Graphing a parabola: Problem type 2

Graphing a parabola: Problem type 3

Solving a word problem by finding a local extremum of a polynomial function

Sum, difference, and product of two functions

Quotient of two functions

Composition of two functions: Domain and range

Composition of two functions: Basic

Horizontal line test

Inverse functions: Basic

Inverse functions: Advanced

Simplifying a ratio of polynomials: Problem type 1 (

Inferring properties of a polynomial function from its graph

Solving a word problem involving a polynomial of degree 3 (

Polynomial long division: Linear divisor

Polynomial long division: Quadratic divisor

Synthetic division

Finding a polynomial of a given degree with given zeros

Using a given zero to write a polynomial as a product of linear factors

Adding and subtracting complex numbers

Multiplying complex numbers

Dividing complex numbers

Solving a quadratic equation with imaginary roots

N zeros theorem and conjugate zeros theorem

Using the conjugate zeros theorem to find all zeros of a polynomial

Sketching the graph of a rational function: Problem type 1

Choosing the form of a rational function given its graph

Sketching the graph of an exponential function: Basic

Sketching the graph of an exponential function: Advanced

Exponential and logarithmic equations

Evaluating a logarithmic expression

Sketching the graph of a logarithmic function

Translating the graph of a logarithmic or exponential function (

Basic properties of logarithms

Change of base for logarithms

Solving a logarithmic equation: Problem type 1

Solving a logarithmic equation: Problem type 2

Solving an exponential equation: Problem type 1

Solving an exponential equation: Problem type 2

Solving a word problem using an exponential equation: Problem type 1

Solving a word problem using an exponential equation: Problem type 2

Solving a word problem using an exponential equation: Problem type 3

Common Angles and Trig Functions (This is also in Sec 6.3)

Finding values of trigonometric functions given information about an angle: Problem type 1 (This is also in Sec 6.3)

Finding values of trigonometric functions given information about an angle: Problem type 2 (This is also in Sec 6.3)

Finding values of trigonometric functions given information about an angle: Problem type 3 (This is also in Sec 6.3)

Sketching the graph of a sine or cosine function: Problem type 1

Sketching the graph of a sine or cosine function: Problem type 2

Sketching the graph of a sine or cosine function: Problem type 3

Sketching the graph of a secant or cosecant function

Sketching the graph of a tangent or cotangent function: Problem type 1

Sketching the graph of a tangent or cotangent function: Problem type 2

Converting between degree and radian measure

Coterminal angles

Arc length and central angle measure

Sketching an angle in standard position

Special right triangles

Sine, cosine, and tangent ratios

Using a trigonometric ratio to find a side length in a right triangle

Using a trigonometric ratio to find an angle measure in a right triangle

Finding trigonometric ratios given a right triangle

Common Angles and Trig Functions (This is also in Sec 5.2)

Finding values of trigonometric functions given information about an angle: Problem type 1 (This is also in Sec 5.2)

Finding values of trigonometric functions given information about an angle: Problem type 2 (This is also in Sec 5.2)

Finding values of trigonometric functions given information about an angle: Problem type 3 (This is also in Sec 5.2)

Solving a triangle with the law of sines: Problem type 1

Solving a triangle with the law of sines: Problem type 2

Solving a triangle with the law of cosines

Cofunction identities

Verifying a trigonometric identity

Proving a trigonometric identity: Problem type 1

Proving trigonometric identities: Problem type 2

Proving trigonometric identities: Problem type 3

Sum and difference identities

Proving trigonometric identities: Problem type 4

Product-to-sum and sum-to-product identities

Double-angle identities

Values of Inverse Trigonometric Functions

Composition of a trigonometric function and an inverse trigonometric function: Problem type 1

Composition of a trigonometric function and an inverse trigonometric function: Problem type 2

Composition of a trigonometric function and an inverse trigonometric function: Problem type 3

Solving a basic trigonometric equation involving sine or cosine

Solving a basic trigonometric equation involving tangent, cotangent, secant, or cosecant

Solving a trigonometric equation involving a squared function

Solving a trigonometric equation involving more than one function

Solving a trigonometric equation involving an angle multiplied by a constant

Solving a trigonometric equation using sum and difference identities

Solving a trigonometric equation using double-angle identities

Solving a trigonometric equation using half-angle identities

Solving a trigonometric inequality (This is not covered in detail in the book)

Plotting a point in polar coordinates

Converting rectangular coordinates to polar coordinates

Converting polar coordinates to rectangular coordinates

Converting an equation written in rectangular coordinates to one written in polar form

Converting an equation written in polar form to one written in rectangular coordinates

Writing a complex number in trigonometric form

De Moivre's theorem

Finding the nth roots of a number

Last updated September 5, 2007 by William P. Clement.

© William P. Clement 2007