WorldMathBook, Exercises English

Tom Pedersen. Company: WorldMathBook
cvr. 44731703
ISBN 978-87-975307-1-9

WorldMathBook, Exercises (problems and solutions)Summary

English

For high school and beyond - all subjects are included.

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An exercise book with problems and proposed solutions, well suited for study as well as for self study.

All subjects for high School are included – and more.

Thisexercise book is meant to be:

• Your math exercise companion for upper secondary school, high school, and the first semester(s) of study.
• Exercise book for high school or similar as well as the first semester(s) of study.
• Exercise book which should be supplemented by the accompanyingtextbook “WorldMathBook” as well as a formula collection.

The book is independent of which formula collection is used.You can use the book without a formula collection, but it will be harder.

The book is also independent of using a calculator or a calculator program.You can use the book without a calculator, but it will be much harder.

The demands for a calculator/calculator program are:

Part 1. All calculators/programs.

Part 2. Calculators/programs with functions, - almost all kinds have that.

Part 3. Advanced calculators/programs able to differentiate and integrate and for plotting curves in diagrams.

Part 4. The setup of vectors is not beneficial using calculators/programs, but if so, an advanced calculator/program is necessary.

Part 5. Advanced calculators/programs for regression.

 

We start with the four basic arithmetic operations, and finish in the first or second semester of the study for bachelor or candidate.

 

Overall Content:

This exercise book has a main part with problems followed by a main part with proposed solutions to the problems.

Each main partis divided into five parts(corresponding with the five parts of the textbook), and each part is with a section A and a section B. Section A contains general math problems, while section B contains more practical math problems within the same subject.

1. Basics
2. The coordinate system in the plane (2D) and functions
3. Differentiation and integration
4. Vectors
5. Statistics (including Probability)

 

Numbers and Complex numbers

 

Content in details:

Part 1. Basics

The four basic arithmetic operations: Sum, Difference, Product, Division

Fractions (Quotients)

Percent and Percentage point

Calculation with letters (algebra)

Parenthesis, Square rules, Squareroot

Exponentiation

Equations, Second degree equations, Higher degree equations, Two equations with two unknowns

Functions and proportionality

Intervals and inequalities

Imaginary numbers, briefly

 

Part 2. The coordinate system in the plane(2D) and functions

The coordinate system and distance, The straight line, The parabola, Polynomials

Functions and the four basic arithmetic operations, Composite functions, Inverse functions

The right triangles

The circle

Sine, Cosine and Tangent

Radian, Angle, Arc length, Survey

The sine function and the sine oscillation

The not right-angled triangles (arbitrary triangles)

Proof of the sine-relation and the cosine-relations

Exponential functions

Logarithm functions:log 10-logarithm, natural logarithm: ln (log e)

Other functions

Hyperbola, Third degree polynomial function, Fourth degreepolynomial function, Fractional polynomial function, A special thirddegree polynomial function, Partly defined functions

Part 3. Differentiation and Integration

Differential calculus

The horizontal line, The straight line, The parabola, The square rootfunction, Polynomials, The natural exponential function, The naturallogarithm function

Differentiation and the four basic arithmetic operations

Sum, Difference, Product, Division

Differentiation of composite functions

The e^kx function, The exponential function, The sine function, Thecosine function, The tangent function

Differentiable, non-differentiable

Integral calculus

Integration and the four basic arithmetic operations

Sum, Difference, Product

Integration by substitution

Integration by parts

The specific integral

Areas, Volumes, Guldin’s rules, Curve length

Differential equations

Typical differential equations, The logistic differential equation

Slope fields

Functions of two variables

The gradient

Part 4. Vectors

2D vectors in the plane

Basics, Special vectors, Computations, Angle, Projection,Determinant, Area and angle, The parametric equation for a straightline, Distance point-line

Polar coordinates in 2D

Vector functions (parametric curves) in 2D

The vector function for a straight line, The vector function for acircle.

Differentiation of vector functions: the line, the circle, Doublepoints

3D vectors in the space

Distance point-point, Cross product, Angle between vectors, Area,Equation of a plane, Distance point-plane, The straight line in thespace, Distance between skewed lines, Distance point-line, Distancebetween two parallel planes, Angle between two planes, Anglebetween line and plane

The sphere

 

Part 5. Statistics

Data (Observations), Non-grouped data, Grouped data

The normal distribution, variance and standard deviation

Goodness of fit (Chi to the power of two - testing)

Regression, Linear - , Power - , Exponential -

 

Probability and combination, Introduction, Theory, Examples

Binomial distribution, random sample, and confidence interval

Complex numbers