This course covers the topics shown below**Curriculum:** 242 topics**Recommended study time:** 120 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 (8 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
- Linear inequalities
- Equivalent inequalities
- General solution of a linear inequality

Chapter 4: System of linear equations (10 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 (6 topics)

- Systems of linear equations
- Solving systems of linear equations by substitution
- Solving systems of equations by elimination
- Consistent systems of linear equations
- Inconsistent systems of linear equations
- Dependent systems of linear equations

Chapter 5: Quadratic equations (21 topics)

- Parabola (3 topics)

- Quadratics
- Parabola
- Plotting the graph of the quadratic

- Solving quadratic equations (7 topics)

- Quadratic equations with two solutions
- Quadratic equations with one solution
- Quadratic equations with no solutions
- Solving quadratic equations by factorization
- Solving quadratic equations by completing the square
- 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

- Quadratic inequalities (2 topics)

- Quadratic inequalities
- Solving a quadratic inequality

Chapter 6: Functions (40 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

- Higher degree polynomials (7 topics)

- Polynomials
- The leading coefficient
- Equations with polynomials
- Solving higher degree polynomials by factoring out
- Solving higher degree polynomials with factorization
- Solving higher degree polynomials with the quadratic equation
- Higher degree inequalities

- Power functions and root functions (7 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
- Inverse functions
- Determining the inverse function

- 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

- Limits and asymptotes (5 topics)

- The concept of a limit
- Limits in connection with asymptotes
- Horizontal asymptotes
- Vertical asymptotes
- Diagonal asymptotes

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)

Chapter 8: Differentiation (34 topics)

- The derivative (6 topics)

- The difference quotient
- The difference quotient at a point
- The difference quotient on an interval of length h
- The tangent line
- Finding the slope using the difference quotient
- Calculating the derivative of a function

- The derivative of power functions (4 topics)

- The derivative of power functions
- The power rule
- The derivative of the root
- The power rule with a constant

- Sum and product rule (4 topics)

- The constant rule
- The sum rule
- The product rule
- The derivative of a product

- Chain rule (2 topics)

- Composite functions
- The chain rule

- The derivative of standard functions (8 topics)

- The derivative of sine
- The derivative of cosine
- The derivative of tangent
- The base e
- The natural logarithm
- The derivative of exponential functions
- The derivative of logarithms
- The derivative of the natural logarithm

- The quotient rule (1 topic)

- The quotient rule

- Applications of derivatives (9 topics)

- Determining the interval at which a function increases/decreases
- Extreme values: local maxima and minima
- Extreme values on a restricted domain
- Global maxima and minima
- Calculating extreme values
- The second derivative
- Types of increasing and decreasing
- Inflection points
- Higher order derivatives

Chapter 9: Trigonometry (27 topics)

- Angles with sine, cosine, and tangent (16 topics)

- Angles
- Right-angled triangles
- The sum of the three angles of a triangle
- Pythagorean theorem
- Sine in a right-angled triangle
- Cosine in a right-angled triangle
- Tangent in a right-angled triangle
- The unit circle
- Angles in radians
- Large and negative angles
- Symmetry in the unit circle
- Special values of trigonometric functions
- Addition formulas for trigonometric functions
- Double-angle formulas
- Law of sines
- Law of cosines

- Trigonometric functions (11 topics)

- The sine function
- The cosine function
- The tangent function
- Equilibrium, period and amplitude
- Transformations of trigonometric functions (upwards, to the right, and relative to the x-axis)
- Inverse function of sine
- Inverse function of cosine
- Inverse function of tangent
- Properties of the arcsin
- Properties of the arccos
- Properties of the arctan

Chapter 10: Geometry (11 topics)

- Parametric Curves (6 topics)

- Parametric curves
- Lissajous figures
- Vectors
- Length of vectors
- Vectors and parametric equations
- Derivatives of parametric curves

- More geometry (5 topics)

- Some notions on lines
- Different descriptions of a circle
- Calculations with circles
- Some notions on triangles
- Calculations with triangles

Chapter 11: Integration (23 topics)

- Antiderivatives (7 topics)

- The antiderivative of a function/the indefinite integral
- The constant of integration
- The antiderivative of a power function
- Sum rule for finding antiderivatives
- Constant rule for finding antiderivatives
- Antiderivatives of known functions
- Antiderivatives and the chain rule

- The definite integral (8 topics)

- The definite integral
- Area
- Calculating the area of an enclosed domain
- Calculating the area of a surface between curves
- Solid of revolution
- The volume of a solid of revolution
- The volume of a solid of revolution between two graphs
- The volume of a solid of revolution around the y-axis

- Integration techniques (8 topics)

- Substitution method
- Trigonometric integrals
- Integration by parts
- Repeated integration by parts
- Repeated integration by parts using reduction
- Known antiderivatives of some quotient functions
- Long division with polynomials
- Finding the antiderivatives of quotient functions

Register for OMPT

Registration for OMPT does not require you to also take the test