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Basic maths plus
Algebra, precalculus and calculus for college and university students. Contains topics ranging from numbers to differentiation, integration and geometry. It covers all topics from the standard Basic Mathematics course, and some extra topics on sequences and series, limits and geometry. And it contains some extra exercises on the Bloom levels Application and Analyses, where the basic material is more on a knowledge and comprehension level, and just a little analyses.
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Course content
Algebra
Variables
THEORY
T
1.
Variables
PRACTICE
P
2.
Variables
4
THEORY
T
3.
Sum and product of variables
PRACTICE
P
4.
Sum and product of variables
5
THEORY
T
5.
Substitution
PRACTICE
P
6.
Substitution
7
THEORY
T
7.
Simplification
PRACTICE
P
8.
Simplification
5
THEORY
T
9.
Simplification with algebraic rules
PRACTICE
P
10.
Simplification with algebraic rules
5
Calculating with exponents and roots
THEORY
T
1.
Integer exponents
PRACTICE
P
2.
Integer exponents
7
THEORY
T
3.
Calculating with integer exponents
PRACTICE
P
4.
Calculating with integer exponents 1
10
PRACTICE
P
5.
Calculating with integer exponents 2
10
PRACTICE
P
6.
Calculating with integer exponents 3
7
PRACTICE
P
7.
Calculating with integer exponents 4
6
THEORY
T
8.
Square roots
PRACTICE
P
9.
Square roots
5
THEORY
T
10.
Calculating with square roots
PRACTICE
P
11.
Calculating with square roots
5
THEORY
T
12.
Higher degree roots
PRACTICE
P
13.
Higher degree roots
8
THEORY
T
14.
Calculating with fractional exponents
PRACTICE
P
15.
Calculating with fractional exponents
7
THEORY
T
16.
Order of operations
PRACTICE
P
17.
Order of operations
5
Expanding brackets
THEORY
T
1.
Expanding brackets
PRACTICE
P
2.
Expanding brackets 1
9
PRACTICE
P
3.
Expanding brackets 2
5
THEORY
T
4.
Expanding double brackets
PRACTICE
P
5.
Expanding double brackets 1
10
PRACTICE
P
6.
Expanding double brackets 2
10
PRACTICE
P
7.
Expanding double brackets 3
6
Factorization
THEORY
T
1.
Factoring out
PRACTICE
P
2.
Factoring out
8
THEORY
T
3.
Factorization
PRACTICE
P
4.
Factorization 1
7
PRACTICE
P
5.
Factorization 2
10
PRACTICE
P
6.
Factorization 3
6
Notable Products
THEORY
T
1.
The square of a sum or a difference
PRACTICE
P
2.
The square of a sum or a difference
7
THEORY
T
3.
The difference of two squares
PRACTICE
P
4.
The difference of two squares
8
Adding and subtracting fractions
THEORY
T
1.
Fractions
PRACTICE
P
2.
Fractions
5
THEORY
T
3.
Simplifying fractions
PRACTICE
P
4.
Simplifying fractions 1
2
PRACTICE
P
5.
Simplifying fractions 2
5
THEORY
T
6.
Addition and subtraction of like fractions
PRACTICE
P
7.
Addition and subtraction of like fractions
5
THEORY
T
8.
Making fractions similar
PRACTICE
P
9.
Making fractions similar
5
THEORY
T
10.
Addition and subtraction of fractions
PRACTICE
P
11.
Addition and subtraction of fractions
8
THEORY
T
12.
Multiplication of fractions
PRACTICE
P
13.
Multiplication of fractions
8
THEORY
T
14.
Division of fractions
PRACTICE
P
15.
Division of fractions
6
THEORY
T
16.
Fraction decomposition
PRACTICE
P
17.
Fraction decomposition
5
Linear formulas and equations
Formulas
THEORY
T
1.
Formula
PRACTICE
P
2.
Formulas
6
THEORY
T
3.
Dependent and independent variables
PRACTICE
P
4.
Dependent and independent variables
5
THEORY
T
5.
Graphs
PRACTICE
P
6.
Graphs
8
Linear functions
THEORY
T
1.
Linear formula
PRACTICE
P
2.
Linear formula
6
THEORY
T
3.
Slope and intercept
PRACTICE
P
4.
Slope and intercept
6
THEORY
T
5.
Composing a linear formula
PRACTICE
P
6.
Composing a linear formula
5
THEORY
T
7.
Parallel and intersecting linear formulas
PRACTICE
P
8.
Parallel and intersecting linear formulas
6
Linear equations and inequalities
THEORY
T
1.
Linear equations
PRACTICE
P
2.
Linear equations
12
THEORY
T
3.
The general solution of a linear equation
PRACTICE
P
4.
The general solution of a linear equation
10
THEORY
T
5.
Intersection points of linear formulas with the axes
PRACTICE
P
6.
Intersection points of linear formulas with the axes
7
THEORY
T
7.
Intersection point of two linear formulas
PRACTICE
P
8.
Intersection point of two linear formulas
10
THEORY
T
9.
Linear inequalities
PRACTICE
P
10.
Linear inequalities
7
THEORY
T
11.
General solution of a linear inequality
PRACTICE
P
12.
General solution of a linear inequality
10
Systems of linear equations
An equation of a line
THEORY
T
1.
A linear equation with two unknowns
PRACTICE
P
2.
A linear equation with two unknowns
5
THEORY
T
3.
Solution linear equation with two unknowns
PRACTICE
P
4.
Solution linear equation with two unknowns
5
THEORY
T
5.
The equation of a line
PRACTICE
P
6.
The equation of a line
10
THEORY
T
7.
Composing the equation of a line
PRACTICE
P
8.
Composing the equation of a line
7
Two equations with two unknowns
THEORY
T
1.
Systems of linear equations
PRACTICE
P
2.
Systems of linear equations
5
THEORY
T
3.
Solving systems of linear equations by substitution
PRACTICE
P
4.
Solving systems of linear equations by substitution
10
THEORY
T
5.
Solving systems of equations by elimination
PRACTICE
P
6.
Solving systems of equations by elimination
6
THEORY
T
7.
General solution system of linear equations
PRACTICE
P
8.
General solution system of linear equations
9
Mixed exercises
PRACTICE
P
1.
Mixed exercises
7
Quadratic equations
Parabola
THEORY
T
1.
Quadratics
PRACTICE
P
2.
Quadratics
8
THEORY
T
3.
Parabola
PRACTICE
P
4.
Parabola
6
Solving quadratic equations
THEORY
T
1.
Quadratic equations
PRACTICE
P
2.
Quadratic equations
5
THEORY
T
3.
Solving quadratic equations by factorization
PRACTICE
P
4.
Solving quadratic equations by factorization
10
THEORY
T
5.
Solving quadratic equations by completing the square
PRACTICE
P
6.
Solving quadratic equations by completing the square
5
THEORY
T
7.
The quadratic formula
PRACTICE
P
8.
The quadratic formula 1
9
PRACTICE
P
9.
The quadratic formula 2
10
Drawing parabolas
THEORY
T
1.
Intersection of parabolas with the axes
PRACTICE
P
2.
Intersections of parabolas with the axes
10
THEORY
T
3.
Vertex of a parabola
PRACTICE
P
4.
Vertex of a parabola
6
THEORY
T
5.
Drawing of parabolas
PRACTICE
P
6.
Drawing of parabolas
16
THEORY
T
7.
Transformations of parabolas
PRACTICE
P
8.
Transformations of parabolas
8
Intersection points of parabolas
THEORY
T
1.
Intersection points of a parabola with a line
PRACTICE
P
2.
Intersection points of a parabola with a line
8
THEORY
T
3.
Intersection points of parabolas
PRACTICE
P
4.
Intersection points of parabolas
11
Quadratic inequalities
THEORY
T
1.
Quadratic inequalities
PRACTICE
P
2.
Quadratic inequalities
8
Mixed exercises
PRACTICE
P
1.
Mixed exercises
9
Functions
Domain and range
THEORY
T
1.
Function and formula
PRACTICE
P
2.
Function and formula
6
THEORY
T
3.
Function rule
PRACTICE
P
4.
Function rule
5
THEORY
T
5.
Intervals
PRACTICE
P
6.
Intervals
8
THEORY
T
7.
Domain
PRACTICE
P
8.
Domain
6
THEORY
T
9.
Range
PRACTICE
P
10.
Range
6
Power functions
THEORY
T
1.
Power functions
PRACTICE
P
2.
Power functions
5
THEORY
T
3.
Transformations of power functions
PRACTICE
P
4.
Transformations of power functions
12
THEORY
T
5.
Equations with power functions
PRACTICE
P
6.
Equations with power functions
5
Higher degree polynomials
THEORY
T
1.
Polynomials
PRACTICE
P
2.
Polynomials
7
THEORY
T
3.
Equations with polynomials
PRACTICE
P
4.
Equations with polynomials
4
THEORY
T
5.
Solving higher degree polynomials with factorization
PRACTICE
P
6.
Solving higher degree polynomials with factorization
4
THEORY
T
7.
Solving higher degree polynomials with the quadratic equation
PRACTICE
P
8.
Solving higher degree polynomials with the quadratic equation
2
THEORY
T
9.
Higher degree inequalities
PRACTICE
P
10.
Higher degree inequalities
11
Power functions and root functions
THEORY
T
1.
Root function
PRACTICE
P
2.
Root functions
5
THEORY
T
3.
Transformations of root functions
PRACTICE
P
4.
Transformations of root functions
5
THEORY
T
5.
Root equations
PRACTICE
P
6.
Root equations
6
THEORY
T
7.
Solving root equations with substitution
PRACTICE
P
8.
Solving root equations with substitution
7
THEORY
T
9.
Inverse functions
PRACTICE
P
10.
Inverse functions
5
Fractional functions
THEORY
T
1.
Asymptotes and hyperbolas
PRACTICE
P
2.
Asymptotes and hyperbolas
5
THEORY
T
3.
Power functions with negative exponents
PRACTICE
P
4.
Power functions with negative exponents
2
THEORY
T
5.
Transformations of power functions with negative exponents
PRACTICE
P
6.
Transformations of power functions with negative exponents
12
THEORY
T
7.
Linear fractional functions
PRACTICE
P
8.
Linear fractional functions
7
THEORY
T
9.
Linear fractional equations
PRACTICE
P
10.
Linear fractional equations
3
THEORY
T
11.
Inverse of linear fractional function
PRACTICE
P
12.
Inverse of linear fractional function
4
THEORY
T
13.
Quotient functions
PRACTICE
P
14.
Quotient functions
16
THEORY
T
15.
Long division with polynomials
PRACTICE
P
16.
Long division with polynomials
5
Limits and asymptotes
THEORY
T
1.
The definition of a limit
PRACTICE
P
2.
The definition of a limit
8
THEORY
T
3.
Perforations and other discontinuities
PRACTICE
P
4.
Perforations and other discontinuities
6
THEORY
T
5.
Horizontal asymptotes
PRACTICE
P
6.
Horizontal asymptotes
7
THEORY
T
7.
Vertical asymptotes
PRACTICE
P
8.
Vertical asymptotes
6
THEORY
T
9.
Oblique asymptotes
PRACTICE
P
10.
Oblique asymptotes
6
Mixed exercises
PRACTICE
P
1.
Mixed exercises
9
Exponential functions and logarithms
Exponential functions
THEORY
T
1.
The exponential function
PRACTICE
P
2.
The exponential function
4
THEORY
T
3.
Exponential equations
PRACTICE
P
4.
Exponential equations
5
THEORY
T
5.
Transformations of the exponential function
PRACTICE
P
6.
Transformations of the exponential function
2
Logarithmic functions
THEORY
T
1.
The logarithmic function
PRACTICE
P
2.
The logarithmic function
9
THEORY
T
3.
Logarithmic equations
PRACTICE
P
4.
Logarithmic equations
5
THEORY
T
5.
Exponential equations
PRACTICE
P
6.
Exponential equations
5
THEORY
T
7.
Isolating variables
PRACTICE
P
8.
Isolating variables
6
THEORY
T
9.
Rules for logarithms
PRACTICE
P
10.
Rules for logarithms
5
THEORY
T
11.
More logarithmic equations
PRACTICE
P
12.
More logarithmic equations
5
THEORY
T
13.
Change of base
PRACTICE
P
14.
Change of base
5
THEORY
T
15.
Solving equations using substitution
PRACTICE
P
16.
Solving equations using substitution
5
THEORY
T
17.
Graph of logarithmic function
PRACTICE
P
18.
Graph of logarithmic function
2
THEORY
T
19.
Transformations of the logarithmic function
PRACTICE
P
20.
Transformations of the logarithmic function
2
The base e and the natural logarithm
THEORY
T
1.
The base e and the natural logarithm
PRACTICE
P
2.
The base e and the natural logarithm
5
Mixed exercises
PRACTICE
P
1.
Mixed exercises
6
Sequences and series
The notions of sequence and series
THEORY
T
1.
The notions of sequences and series
PRACTICE
P
2.
The notions of sequences and series
5
Arithmetic sequences and series
THEORY
T
1.
Arithmetic sequences
PRACTICE
P
2.
Arithmetics sequences
6
THEORY
T
3.
Arithmetic series
PRACTICE
P
4.
Arithmetic series
8
Geometric sequences and series
THEORY
T
1.
Geometric sequences
PRACTICE
P
2.
Geometric sequences
10
THEORY
T
3.
Geometric series
PRACTICE
P
4.
Geometric series
8
Trigonometry
Angles with sine, cosine and tangent
THEORY
T
1.
Angles
PRACTICE
P
2.
Angles
1
THEORY
T
3.
Triangles
PRACTICE
P
4.
Triangles
1
THEORY
T
5.
Rules for right-angled triangles
PRACTICE
P
6.
Rules for right-angled triangles 1
9
PRACTICE
P
7.
Rules for right-angled triangles 2
6
THEORY
T
8.
Angles in radians
PRACTICE
P
9.
Angles in radians
8
THEORY
T
10.
Symmetry in the unit circle
PRACTICE
P
11.
Symmetry in the unit circle
10
THEORY
T
12.
Special values of trigonometric functions
PRACTICE
P
13.
Special values of trigonometric functions
5
THEORY
T
14.
Addition formulas for trigonometric functions
PRACTICE
P
15.
Addition formulas for trigonometric functions
7
THEORY
T
16.
Sine and cosine rules
PRACTICE
P
17.
Sine and cosine rules
8
Trigonometric functions
THEORY
T
1.
Trigonometric functions
PRACTICE
P
2.
Trigonometric functions
4
THEORY
T
3.
Transformations of trigonometric functions
PRACTICE
P
4.
Transformations of trigonometric functions
15
THEORY
T
5.
Inverse trigonometric functions
PRACTICE
P
6.
Inverse trigonometric functions
4
THEORY
T
7.
Trigonometric equations 1
PRACTICE
P
8.
Trigonometric equations 1
6
THEORY
T
9.
Trigonometric equations 2
PRACTICE
P
10.
Trigonometric equations 2
6
Mixed exercises
PRACTICE
P
1.
Mixed exercises
8
Differentiation
The derivative
THEORY
T
1.
The difference quotient
PRACTICE
P
2.
The difference quotient
5
THEORY
T
3.
The difference quotient at a point
PRACTICE
P
4.
The difference quotient at a point
5
THEORY
T
5.
The tangent line
PRACTICE
P
6.
The tangent line
2
THEORY
T
7.
The notion of derivative
PRACTICE
P
8.
The notion of derivative
14
The derivative of power functions
THEORY
T
1.
The derivative of power functions
PRACTICE
P
2.
The derivative of power functions 1
7
PRACTICE
P
3.
The derivative of power functions 2
8
PRACTICE
P
4.
The derivative of power functions 3
5
Sum and product rule
THEORY
T
1.
The sum rule
PRACTICE
P
2.
The sum rule
7
THEORY
T
3.
The product rule
PRACTICE
P
4.
The product rule
6
Chain rule
THEORY
T
1.
Composite functions
PRACTICE
P
2.
Composite functions
8
THEORY
T
3.
The chain rule
PRACTICE
P
4.
The chain rule
9
The derivative of standard functions
THEORY
T
1.
The derivative of trigonometric functions
PRACTICE
P
2.
The derivative of trigonometric functions 1
8
PRACTICE
P
3.
The derivative of trigonometric functions 2
10
THEORY
T
4.
The base e and the natural logarithm (revisited)
PRACTICE
P
5.
The base e and the natural logarithm
5
THEORY
T
6.
The derivative of exponential functions and logarithms
PRACTICE
P
7.
The derivative of exponential functions and logarithms 1
7
Quotient rule
THEORY
T
1.
The quotient rule
PRACTICE
P
2.
The quotient rule 1
6
PRACTICE
P
3.
The quotient rule 2
7
More differentiation exercises (mixed functions)
PRACTICE
P
1.
More differentiation exercises (mixed functions)
15
Applications of derivatives
THEORY
T
1.
Increasing and decreasing
PRACTICE
P
2.
Increasing and decreasing
8
THEORY
T
3.
Extreme values
PRACTICE
P
4.
Extreme values
10
THEORY
T
5.
The second derivative
PRACTICE
P
6.
The second derivative
5
THEORY
T
7.
Concavity
PRACTICE
P
8.
Types of increasing and decreasing
5
THEORY
T
9.
Inflection points
PRACTICE
P
10.
Inflection points
6
THEORY
T
11.
Higher order derivatives
PRACTICE
P
12.
Higher order derivatives
5
Mixed exercises
PRACTICE
P
1.
Mixed exercises
7
Geometry
Lines
THEORY
T
1.
Different descriptions of a line
PRACTICE
P
2.
Different descriptions of a line
9
THEORY
T
3.
Angles between lines
PRACTICE
P
4.
Angles between lines
6
THEORY
T
5.
Perpendicular lines
PRACTICE
P
6.
Perpendicular lines
6
THEORY
T
7.
Distance point and line
PRACTICE
P
8.
Distance point and line
5
Circles
THEORY
T
1.
Different descriptions of a circle
PRACTICE
P
2.
Different descriptions of a circle
5
THEORY
T
3.
Intersections of a line and a circle
PRACTICE
P
4.
Intersections of a line and a circle
6
THEORY
T
5.
Tangent line to a circle
PRACTICE
P
6.
Tangent line to a circle
5
THEORY
T
7.
Intersections of circles
PRACTICE
P
8.
Intersections of circles
4
THEORY
T
9.
Distance to a circle
PRACTICE
P
10.
Distance to a circle
7
Parametric curves and vectors
THEORY
T
1.
Parametric curves
PRACTICE
P
2.
Parametric Curves
4
THEORY
T
3.
Lissajous figures
PRACTICE
P
4.
Lissajous figures
4
THEORY
T
5.
Vectors
PRACTICE
P
6.
Vectors
5
THEORY
T
7.
The dot product
PRACTICE
P
8.
The dot product
6
THEORY
T
9.
Vectors and parametric equations
PRACTICE
P
10.
Vectors and parametric equations
9
THEORY
T
11.
Derivatives of parametric curves
PRACTICE
P
12.
Derivatives of parametric curves
8
Mixed exercises
PRACTICE
P
1.
Mixed exercises
18
Integration
Antiderivatives
THEORY
T
1.
The antiderivative of a function
PRACTICE
P
2.
The antiderivative of a function
5
THEORY
T
3.
The antiderivative of a power function
PRACTICE
P
4.
The antiderivative of a power function
5
THEORY
T
5.
Rules of calculation for antiderivatives
PRACTICE
P
6.
Rules of calculation for antiderivatives
9
THEORY
T
7.
Antiderivatives of some known functions
PRACTICE
P
8.
Antiderivatives of some known functions
5
THEORY
T
9.
Antiderivatives and the chain rule
PRACTICE
P
10.
Antiderivatives and the chain rule
6
The definite integral
THEORY
T
1.
Definite integral
PRACTICE
P
2.
Definite integral
6
THEORY
T
3.
Area
PRACTICE
P
4.
Area
5
THEORY
T
5.
Area of a surface between curves
PRACTICE
P
6.
Area of a surface between curves
5
THEORY
T
7.
Solid of revolution
PRACTICE
P
8.
Solid of revolution
6
Integration techniques
THEORY
T
1.
Substitution method
PRACTICE
P
2.
Substitution method
10
THEORY
T
3.
Trigonometric integrals
PRACTICE
P
4.
Trigonometric integrals
8
THEORY
T
5.
Integration by parts
PRACTICE
P
6.
Integration by parts
7
THEORY
T
7.
Repeated integration by parts
PRACTICE
P
8.
Repeated integration by parts
5
THEORY
T
9.
Known antiderivatives of some quotient functions
PRACTICE
P
10.
Known antiderivatives of some quotient functions
6
THEORY
T
11.
Finding the antiderivatives of quotient functions 1
PRACTICE
P
12.
Finding the antiderivatives of quotient functions 1
6
THEORY
T
13.
Fraction decomposition
PRACTICE
P
14.
Fraction decomposition
5
THEORY
T
15.
Finding the antiderivatives of quotient functions 2
PRACTICE
P
16.
Finding the antiderivatives of quotient functions 2
6
Mixed exercises
PRACTICE
P
1.
Mixed exercises
10
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