The Complete High School and College Mathematics
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Welcome to The Complete High School and College Mathematics!
We take you through everything you need to know about high school and college mathematics in this course. This course covers Number bases, Indices, Logarithms, Calculus, Statistics, Probability and much more in details, with loads of examples and work through exercises. This course is designed to make you a standout mathematician and set you on the path to becoming an A student in Mathematics.
If you need a crash course to set your mathematics foundation right, then this is the course for you. Everything you need to know about high school and college mathematics in one place: there are hundreds of examples in this course, work through solutions using past questions from different exams, exam tips for success, and practical advice to get you flying in mathematics. The Complete High School and College Mathematics is the course for any student who wants to be a top mathematics student.
If you are looking at starting a STEM-based career, a sound understanding of mathematics concepts, application, and use will help you achieve your dream. In addition to excellent teaching, there are soft copies of summary notes for each topic. This is provided to aid your revision process and accelerate your learning process.
Also, our teaching assistants are ready to take your questions in the comment section, so you are never left in the dark with regards to any high school or college mathematical problem.
See you in the course.
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2
ObjectivesAt the end of this lesson, students should be able to:
1. Convert numbers from base ten to other bases
2. Convert numbers from other bases to base ten
3. Add, subtract, multiply and divide in different bases
4. Solve different equations involving number bases
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3
Introduction to number base system
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4
Binary system A
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5
Binary system B
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6
Application of number bases
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7
Objectives
At the end of the lesson, you should be able to:
1. Write and express numbers in standard form
2. Use the laws of indices to evaluates problems in indices
3. Evaluate problems involving indicial equations
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8
Multiplication law
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9
Division power law
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10
Zero and negative power laws
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11
Composite power laws
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12
Fractional power laws
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13
Examples on application of indices
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19
Objectives
At the end of this lesson, learners should be able to:
I. Define sequence and series
II. Explain Arithmetical progression
III. Explain Geometrical progression
IV. Solve questions involving A.P and G.P
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20
Definition of sequence and series
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21
Arithmetic progression
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22
questions in AP
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23
Sum of arithmetic progression
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24
Geometric progression
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25
Questions in GP
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26
Objectives
At the end of this lesson, you should be able to;
1.Interpret the meaning of Set, write and describe set in various ways in terms of their elements or members
2.Identify and distinguish between the different types of set
3.Draw Venn diagrams to illustrate sets
4.Find the union, intersection and complement of set
5. solve standard Examination questions on set
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27
Meaning of set
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28
Types of set
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29
Set operations
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30
Sample questions
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31
Objectives
At the end of this lesson candidates should be able to:
1 Define logic
2 Identify and form open and closed simple statements
3 Deduce the truth or otherwise of simple statements
4 Form a negation of a simple statement
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32
Definition of logical reasoning and statement
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33
Negation of a simple statement
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34
Truth table
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35
Compound statement
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36
Connectives
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37
Bi-conditional statements
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38
Tautology
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39
Objectives
At the end of this topic, learners should be able to:
I. Define and represent a number in surd form;
II. Identify the basic laws of surds;
III. Convert a number from its surd form to its basic form;
IV. Add, subtract and multiply numbers in surd form;
V. Rationalize denominators of surds.
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40
Definition of surd
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Basic operations in surd
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Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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Example 6
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48
Sample questions
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57
Objectives
At the end of the lesson, you should be able to:
1. Define ratios and percentages
2. Explain the various types of proportions
3. Explain the concept of percentages
4. Solve problems involving ratios, proportions and percentages
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58
Introduction
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59
Examples on ratios
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60
Proportions
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61
Percentages
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62
Objectives
At the end of this lesson, learners should be able to:
1.) Calculate the simple and compound interest on a given principal, at a given rate, over a given period of time
2.) Use the compound interest formula;
A = P(1 + r/100)n , to calculate the amount A,
if a principal P is invested for n years at r% per annum
3.) Calculate discount, cash worth, commission, profit and loss
4.) Solve standard Examination questions on financial arithmetic
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63
Simple interest
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Compound interest
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Commission
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66
Profit and loss
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67
Objectives
At the end of the lesson, you should be able to:
1. Define the term ‘variation’
2. explain the various types of variation
3. solve mathematical problem involving the various types of variation
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68
definition of variation
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69
Direct variation
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70
Inverse variation
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Joint variation
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Partial variation
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73
Practice questions
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74
Objectives
At the end of this lesson, students should be able to:
1. Define Linear Equation
2. Solve Simultaneous Linear Equation Using the three Methods
3. Solve Standard Examination Questions On Simultaneous Linear Equations
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75
Defintion and methods of simultaneous linear equations
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Substitution method
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77
Elimination method
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78
Graphical solution A
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79
Graphical solution B
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80
World problem leading to S.L.E (part1)
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81
World problem leading to S.L.E (part2)
