Important note:

The current COVID-19 situation **does not have** an impact on OMPT operations. This includes the time it takes to check and grade your exams.

This course covers the topics shown below**Curriculum:** 120 topics**Recommended study time:** 60 hours** This is an estimate and can differ per learner*

Chapter 1: Numbers (17 topics)

- Integers (3 topics)

- Calculating with integers
- Integers
- Division of integers

- Negative numbers (1 topic)

- Absolute value

- Fractions (7 topics)

- Fractions
- Equivalent fractions
- Simplifying fractions
- Addition and subtraction of fractions
- Multiplication and division of fractions
- Integer powers of fractions
- Decimal numbers

- Powers and roots (6 topics)

- Exponents
- Calculating with powers
- Roots of integers
- Roots of fractions
- Standard notation of higher roots
- Order of operations for powers and roots

Chapter 2: Algebra (28 topics)

- Variables (6 topics)

- Variables
- Sum and product of variables
- Substitution
- Simplification of multiplications
- Simplification of additions and subtractions
- Simplification with algebraic rules

- Calculating with exponents and roots (7 topics)

- Integer powers
- Rules for calculating with integer exponents
- Square roots
- Rules for calculating with square roots
- Higher degree roots
- Calculating with fractional exponents
- Order of operations

- Expanding brackets (2 topics)

- Expanding single brackets
- Expanding double brackets

- Factorization (2 topics)

- Factorization
- Product sum method

- Notable products (2 topics)

- The square sum of a sum or a difference
- The difference of two squares

- Adding and subtracting fractions (9 topics)

- Fractions with variables
- Similar fractions
- Simplifying fractions
- Addition and subtraction of like fractions
- Making fractions similar
- Addition and subtraction of fractions
- Multiplication of fractions
- Division of fractions
- Fraction decomposition

Chapter 3: Linear formulas and equations (17 topics)

- Formulas (3 topics)

- Formulas
- Dependent and independent variables
- Graph of a formula

- Linear functions (6 topics)

- Linear formulas
- Slope
- Determining the slope from two points
- Intercept
- Composing a linear formula
- Parallel and intersecting linear formulas

- Linear equations and inequalities (5 topics)

- Linear equations
- Equivalent linear equations
- The general solution of a linear equation (rules of reduction)
- Intersection points of linear formulas with the axes
- Intersection point of two linear formulas

Chapter 4: System of linear equations (6 topics)

- An equation of a line (4 topics)

- A linear equation with two unknowns
- Solution of linear equations with two unknowns (rules of reduction)
- The equation of a line
- Composing the equation of a line

- Two equations with two unknowns (2 topics)

- Systems of linear equations
- Solving systems of linear equations by substitution

Chapter 5: Quadratic equations (17 topics)

- Parabola (3 topics)

- Quadratics
- Parabola
- Plotting the graph of the quadratic

- Solving quadratic equations (5 topics)

- Quadratic equations with two solutions
- Quadratic equations with one solution
- Quadratic equations with no solutions
- The quadratic formula and the discriminant
- Solving quadratic equations using the quadratic formula

- Drawing parabolas (7 topics)

- Intersection of parabolas with the axes
- Vertex of a parabola
- Determining the vertex by completing the square
- Determining the vertex by substitution
- Drawing of parabolas
- Transformations of parabolas
- Multiple transformations of parabolas

- Intersection points of parabolas (2 topics)

- Intersection points of a parabola with a line
- Intersection points of parabolas

Chapter 6: Functions (26 topics)

- Domain and range (6 topics)

- Function and formula
- Function rule
- Intervals
- Domain
- Limited domain
- Range

- Power functions (4 topics)

- Power functions
- Transformations of power functions
- Multiple transformations of power functions
- Equations with power functions

- Power functions and root functions (5 topics)

- Root functions
- Transformations of root functions (upwards, to the right, and relative to the x-axis)
- Multiple transformations of root functions
- Root equations
- Solving root equations with substitution

- Fractional functions (11 topics)

- Asymptotes and hyperbolas
- Power functions with negative exponents
- Transformations of power functions with negative exponents (upwards, to the right, and relative to the x-axis)
- Linear fractional functions
- Determining asymptotes of a linear fractional function
- Linear fractional equations
- Solving linear fractional equations by cross multiplication
- Inverse of linear fractional functions
- Isolating a variable when determining the inverse
- Quotient functions
- Perforation

Chapter 7: Exponential functions and logarithms (14 topics)

- Exponential functions (3 topics)

- The exponential function
- Exponential equations
- Transformations of the exponential function (upwards, to the right, and relative to the y-axis)

- Logarithmic functions (11 topics)

- The logarithmic function
- Logarithmic equations
- Exponential equations
- Isolating variables
- Rules for solving logarithms
- Solving logarithmic equations with calculation rules and the quadratic formula
- Change of base
- Solving logarithmic equations using substitution
- Solving exponential equations using substitution
- Graph of logarithmic functions
- Transformations of the logarithmic function (upwards, to the right, and relative to the x-axis)

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