  Precalculus

Open course Precalculus offered by the Teaching and Learning Centre of FNWI.

Author: André Heck

Available languages:  Course content
Using the formula editor
Working with numbers
THEORY
T
1.
Entering numbers and operations
PRACTICE
P
2.
Entering numbers
6
Working with symbols
THEORY
T
1.
Working with symbolic expressions
PRACTICE
P
2.
Working with symbols
5
Calculating with numbers
Computing with integers
THEORY
T
1.
Natural numbers and integers
PRACTICE
P
2.
Recognising basis properties of integers
3
THEORY
T
3.
Arithmetic calculations with integers
PRACTICE
P
4.
Doing basic calculations with natural numbers
4
THEORY
T
5.
Division with remainder
PRACTICE
P
6.
Division with remainder
2
THEORY
T
7.
Long division
PRACTICE
P
8.
Carrying out a long division
3
THEORY
T
9.
Divisors, prime numbers, and prime factorisations
PRACTICE
P
10.
Decomposing a number into prime factors
4
THEORY
T
11.
The gcd and the lcm
PRACTICE
P
12.
Computing the gcd and lcm
5
Calculating with fractions
THEORY
T
1.
Rational numbers
PRACTICE
P
2.
Rewriting fractions
7
THEORY
T
3.
PRACTICE
P
4.
4
THEORY
T
5.
Multiplication and division of fractions
PRACTICE
P
6.
Multiplying and dividing fractions
5
Calculating with powers and roots
THEORY
T
1.
Powers with integer exponents
PRACTICE
P
2.
Calculating with powers with integer exponents
4
THEORY
T
3.
Properties of powers
PRACTICE
P
4.
Appying properties of powers
4
THEORY
T
5.
The square root of a natural number
PRACTICE
P
6.
Converting square roots in standard form
4
THEORY
T
7.
The square root of a fraction
PRACTICE
P
8.
Converting square roots of fractions in standard form
4
THEORY
T
9.
The cube root of an integer
PRACTICE
P
10.
Converting cube roots in standard form
3
THEORY
T
11.
Quartic and higher roots in standard form
PRACTICE
P
12.
Converting quartic and higher roots in standard form
3
THEORY
T
13.
Fractional powers
PRACTICE
P
14.
Calculating with fractional powers
5
Decimal numbers
THEORY
T
1.
Decimal numbers
PRACTICE
P
2.
Decimal numbers
4
THEORY
T
3.
Ordering of decimal numbers
PRACTICE
P
4.
Ordering of decimal numbers
2
THEORY
T
5.
Arithmetic operations with decimal numbers
PRACTICE
P
6.
Doing basic calculations with decimal numbers
4
THEORY
T
7.
Repeating decimals
PRACTICE
P
8.
Repeating decimals
2
THEORY
T
9.
Infinite non-repeating decimals
PRACTICE
P
10.
Infinite non-repeating decimals
1
THEORY
T
11.
Significance and precision
PRACTICE
P
12.
significant digits and decimals
3
THEORY
T
13.
Calculation rules for significance in multiplication and division
PRACTICE
P
14.
Multiplication and division
3
THEORY
T
15.
Calculation rules for significance with sum and difference
PRACTICE
P
16.
3
THEORY
T
17.
Scientific notation
PRACTICE
P
18.
Rewriting in scientific notation
2
PRACTICE
P
19.
Converting units
5
THEORY
T
20.
Dimension of a physical quantity and SI-units
PRACTICE
P
21.
Dimension of a physical quantity
1
THEORY
T
22.
Extra: a bird's eye view of error analysis
Calculating with letters
Computing with letters
THEORY
T
1.
Basic rules
PRACTICE
P
2.
Applying priority rules
9
THEORY
T
3.
Computing with powers
PRACTICE
P
4.
Simplifying expressions with powers
10
THEORY
T
5.
Expansion of single brackets
PRACTICE
P
6.
Expanding brackets
8
THEORY
T
7.
The banana method for expanding double brackets
PRACTICE
P
8.
Applying the banana method
9
THEORY
T
9.
Factorisation
PRACTICE
P
10.
Factorising expressions
4
THEORY
T
11.
Factorisation of a quadratic polynomial via the sum-product method
PRACTICE
P
12.
Factorising via the sum-product method
4
Special products
THEORY
T
1.
The square of a sum or a difference
PRACTICE
P
2.
Expanding brackets
5
THEORY
T
3.
The difference of two squares
PRACTICE
P
4.
Decomposing expressions into factors
6
Fractions with letters
THEORY
T
1.
Splitting and writing with a common denominator
PRACTICE
P
2.
Splitting and writing with a common denominator
6
THEORY
T
3.
Simplification of fractions with letters
PRACTICE
P
4.
Simplifying fractions
3
THEORY
T
5.
Product and quotient of fractions with letters
PRACTICE
P
6.
Multiplying and dividing fractions with letters
3
Solving linear equations and inequalities
Linear equations in one unknown
THEORY
T
1.
The notion of linear equation in one unknown
PRACTICE
P
2.
Practising basic notions of linear equations
4
THEORY
T
3.
General solution rules
PRACTICE
P
4.
Solving a linear equation
10
THEORY
T
5.
Reduction to a linear equation
PRACTICE
P
6.
Solving by reduction to a linear equation
9
Linear inequalities in one unknown
THEORY
T
1.
The notion of linear inequality in one unknown
PRACTICE
P
2.
Practising basic notions of linear inequalities
5
THEORY
T
3.
Solving a linear inequality by reduction
PRACTICE
P
4.
Solving a linear inequality by reduction
2
THEORY
T
5.
Solving a linear inequality via equations
PRACTICE
P
6.
Solving a linear inequality via equations
2
THEORY
T
7.
Solving a system of inequalities with one unknown
PRACTICE
P
8.
Solving a system of inequalities with one unknown
2
THEORY
T
9.
Reduction to a linear inequality
PRACTICE
P
10.
Solving an inquality by reduction to a linear inquality
4
An equation of a straight line in a plane
THEORY
T
1.
A linear equation with two unknowns
PRACTICE
P
2.
Practising basic notions of linear inequalities
4
THEORY
T
3.
Solution of a linear equation with two unknowns
PRACTICE
P
4.
Solving a linear equation with two unknowns
4
THEORY
T
5.
An equation of a line in the plane
PRACTICE
P
6.
Working with equations of a straight line
4
Systems of linear equations in two unknowns
THEORY
T
1.
The notion of a system of linear equations
THEORY
T
2.
Solving systems of equations by the substitution method
PRACTICE
P
3.
Solving by the substitution method
2
THEORY
T
4.
Solving systems of equations by the elimination method
THEORY
T
5.
Solving systems of equations by Gaussian elimination
PRACTICE
P
6.
Solving by the row reduction method
4
An equation of a plane in space
THEORY
T
1.
An equation of a plane in space
PRACTICE
P
2.
Working with equations of a plane in space
2
THEORY
T
1.
The notion of a quadratic equation in one unknown
THEORY
T
2.
The concept of quadratic function and parabola
THEORY
T
3.
PRACTICE
P
4.
9
THEORY
T
5.
The solution method of completing the square
PRACTICE
P
6.
Solving a quadratic equation by completing the square
6
THEORY
T
7.
Factorisation of a quadratic equation by inspection
PRACTICE
P
8.
Solving a quadratic equation via factorisation by inspection
2
THEORY
T
9.
PRACTICE
P
10.
7
THEORY
T
11.
PRACTICE
P
12.
6
THEORY
T
1.
A quadratic inequality in basic form
THEORY
T
2.
Solving quadratic inequalities via reduction and/or factorisation
PRACTICE
P
3.
Solving quadratic inequalities via reduction and/or factorization
3
THEORY
T
4.