Number, Algebra & Trigonometry - In 24 Minutes Books 1 - 24 of the In A Minute Series

721 Pages·2015·19.49 MB·English

by  Paul Carson

Contents
Name/Copyright
Series Contents
Proverb
Introduction to Multiplication
What Multiplication Is
New Method for Times Tables
What Brackets Mean
2 x 2 Digit Numbers
3 x 3 Digit Numbers
Bigger Numbers
What Multiplication Is For
What Is Division
What Is Division - Part 2
Three Types of Division
Less-Straightforward Division
The Third Rule of Maths
So-Called Long Division
Introduction To Fractions
Addition Of Fractions
Subtraction of Fractions
Multiplication of Fractions
Dividing Fractions
"Mixed Numbers"
Division of Mixed Numbers
Addition of Mixed Numbers
Ultra-Fast Ways of Adding and Subtracting Fractions
Decimals
Key Change Effect
Reverse Situation - taking the Key Change Effect further
Division of Decimals
Percentages - In A Minute
Finding a Percentage of Any Number
Calculate Percentages Mentally
Useful percentages
Calculating Discounts
Real Life example - using the Multiplier in reality
Reverse Percentage
Compound Interest
The Flip Side
Fast calculation of compound interest
Depreciation - the reverse of Compound Interest
Writing A Division As A Percentage
Introduction to Negative Numbers
Everyday life
Multiplying Negative Numbers
Division of Negative Numbers
Final Problem
Introduction to Squaring & Area
Squaring is called ‘Squaring'
The Squaring System
Calculation of Areas
A New Angle
Introduction to Cubing
How Engines Work
Use of Letters
Volumes of Other Shapes
Introduction to Indices
Indices - In A Minute
Second Rule
Third Rule
Fourth Rule
Fifth Rule of Indices
The Sixth Rule
Rule 7 of Indices
Algebraic Indices
Surds
Rationalising The Denominator
Introduction to Standard Form
Standard Form - The Short Way of Writing Large Numbers
Standard Form for Small Numbers
Multiplying Numbers In Standard Form
Dividing Numbers In Standard Form
Typical Example Question
Further Examples of use of Standard Form in Science
Introduction to Logarithms
What Are Logarithms?
Touch Base
Logarithms in everyday life
The Rules of Logarithms
Introduction & Puzzles
Hints
Solutions
Introduction to Sequences
Sequences - In A Minute
Non-linear Sequences
A Man Called Al
Child, 12, Amazes Teacher
Example Questions
Introduction to Gradient
What Is Gradient?
The Equation of A Straight Line
Calculating the Gradient and ‘Cut
Other Straight Line Graphs
Introduction to Simultaneous Equations
Simultaneous Equations
Type 2 Algebra
Type 3 Algebra
What We’re Doing This For
Real-Life Example of Simultaneous Equations
Simultaneous Equations - School Style
Introduction to Quadratic Equations
Multiplying Brackets
Factorising
Multiplying - In A Minute
What We’re Doing This For
Solving A Quadratic
Non-factorisable Quadratics
Any Type of Quadratic
Another Example
Completing the Square
A Closer Look At The Quadratic Formula
What Multiplying Two Expressions Together Will Give
Why Is it Called ‘Completing The Square'?
Simultaneous Equations - Extended
Epilogue
Introduction to Inequalities
Three Types of Algebra for Inequalities
Type 2 Algebra
Type 3 Algebra
When the Inequality Sign Flips
Inequalities of Quadratics
Quadratics and Straight Lines
Introduction to Changing The Subject
Using BIDMAS to Change the Subject
Examples
How We've Used This Before
Exceptions To The Rule
Famous Science Formulae Rearranged
Introduction to Cubics
Multiplying Three Brackets
Factorising a Cubic
Factorising a Cubic 2
Remains of The Day
Finding the maximum or minimum values
Introduction to Advanced Mental Multiplication
The Times Tables
How to Multiply Two Digit Numbers In Your Head
Squaring Large Numbers
Finding Square Roots from Square Numbers
The Christmas Party Where I Was Called A Wizard
How To Check Multiplications Are Correct - In Seconds
The Christmas Party Magic Trick
Algebra Behind the Multiplication Method
Algebra Behind The Squaring System
Algebra Behind Advanced Multiplication Using Squares
Introduction to Gradient/Tangent
Concept Connected To Gradient
Putting Our Values To Use
Secondary Solutions
Introduction to Sine & Cosine
Normalising the Hypotenuse
Putting Our Values To Use 1
Secondary Solutions
Using Sine To Find the Area of A Triangle
The Other Two Sides of The Triangle
Putting Our Values To Use 2
The Relationship Between Sine, Cosine, Tangent, Gradient
Reverse of Sine
A New Angle
Pythagoras’ theorem
Special Situation
Reverse Situation
The Pythagorean Theorem Is Not Just For Triangles Once
Introduction to Sine & Cosine Rules
The Sine Rule
Right-Angled Triangles
One Situation Remains - The Cosine Rule
Derivation of Cosine Rule
THE END
Name/Copyright
Number, Algebra & Trigonometry
In
24 Minutes
© Paul Carson 2014
Dedication
To Edyta, for inspiring me to start writing again.
Blog
http://mathsinaminute.blogspot.com
Website
http://www.paulcarsonmaths.co.uk
Twitter
@In_A_Min
Email
[email protected]
YouTube
Channel Containing Instructional Videos
http://www.youtube.com/user/InAMinMaths
Series Contents
Series of books and titles
Naked Numbers: The 3 Rules To Make Your Life Add Up, Hodder Education,
the Michel Thomas Method (2010)
Maths in a Minute Series
Contents and numbering 2nd September 2013
1. Multiplication
2. Division
3. Fractions
4. Decimals
5. Percentages
6. Negative Numbers
7. Squaring & Area
8. Cubing & Volume
9. Indices
10. Standard Form
11. Logarithms
12. Sequences
13. Gradient/Equation of A Straight Line
14. Simultaneous Equations
15. Quadratics
16. Inequalities
17. Changing the Subject
18. Cubics
19. Algebraic Fractions
20. Algebra of Arithmetic
21. Angles and Radians
22. Gradient/Tangent
23. Sine and Cosine
24. Sine and Cosine Rules
25. Pythagoras’ Theorem
26. Gradient/Differentiation 1
27. Integration 1
28. Polynomials
29. Types of Functions
30. Co-ordinate Geometry
31. Differentiation 2
32. Integration 2
33. Binomial Theorem
34. Trigonometry
35. Numerical Methods
36. Differential Equations
37. Mechanics
38. Vectors
39. Engineering Fundamentals
40. Coding Fundamentals
41. Statistics
42. Matrices
43. The Slide Rule
44. Richard Feynman
45. The Current Mathematics Teaching System
46. How the MinAMin Method Works
47. Complex Numbers
48. Partial Differentiation
49. Series
50. Integration 3
51. Multiple Integrals
52. Differential Equations
53. Fourier Series
54. Partial Differential Equations
55. Vector Calculus