Algebra Tutorials!
Friday 12th of July  
Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Angles and Degree Measure
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In many engineering calculations you will come across the symbol ! which you may not have met before in mathematics classes. This is known as a factorial. The factorial is a symbol which is used when we wish to multiply consecutive whole numbers together, as you will see below.

1. Factorials

The number 5×4×3×2×1 is written as 5!, which is read as "five factorial". If you actually perform the multiplication you will find that 5! = 120. Similarly 7! = 7×6×5×4×3×2×1 which equals 5040. A rather special case is 0!. This is defined to equal 1 and this might seem somewhat strange. Just learn this!

You will not be required to find factorials of negative numbers or fractions. Factorials are used in combination notation which arises frequently in probability theory. The notation stands for . For example


1. Without using a calculator evaluate 2!, 3! and 4!.

2. Show that equals 20.

3. Explain why n! = n×(n - 1)! for any positive whole number n.

4. Explain why for any positive whole number n

5. Evaluate


1. 2! = 2. 3! = 6 and 4! = 24. Note that 3! = 3×2!, and that 4! = 4×3!.

5. a) 84, b) 10, c) 6.

2. Using a calculator to find factorials

Your scientific calculator will be pre-programmed to find factorials. Look for a button marked !, or consult your calculator manual. Check that you can use your calculator to find factorials by verifying that 10! = 3628800.

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