OMPT-A Syllabus

Chapter 1: Numbers (17 topics)

1. Integers (3 topics)

1. Calculating with integers
2. Integers
3. Division of integers

2. Negative numbers (1 topic)

1. Absolute value

3. Fractions (7 topics)

1. Fractions
2. Equivalent fractions
3. Simplifying fractions
4. Addition and subtraction of fractions
5. Multiplication and division of fractions
6. Integer powers of fractions
7. Decimal numbers

4. Powers and roots (6 topics)

1. Exponents
2. Calculating with powers
3. Roots of integers
4. Roots of fractions
5. Standard notation of higher roots
6. Order of operations for powers and roots

Chapter 2: Algebra (26 topics)

5. Variables (6 topics)

1. Variables
2. Sum and product of variables
3. Substitution
4. Simplification of multiplications
5. Simplification of additions and subtractions
6. Simplification with algebraic rules

6. Calculating with exponents and roots (7 topics)

1. Integer powers
2. Rules for calculating with integer exponents
3. Square roots
4. Rules for calculating with square roots
5. Higher degree roots
6. Calculating with fractional exponents
7. Order of operations

7. Expanding brackets (2 topics)

1. Expanding single brackets
2. Expanding double brackets

8. Factorization (2 topics)

1. Factorization
2. Product sum method

9. Notable products (2 topics)

1. The square sum of a sum or a difference
2. The difference of two squares

10. Adding and subtracting fractions (9 topics)

1. Fractions with variables
2. Similar fractions
3. Simplifying fractions
4. Addition and subtraction of like fractions
5. Making fractions similar
6. Addition and subtraction of fractions
7. Multiplication of fractions
8. Division of fractions
9. Fraction decomposition

Chapter 3: Linear formulas and equations (17 topics)

11. Formulas (3 topics)

1. Formulas
2. Dependent and independent variables
3. Graph of a formula

12. Linear functions (6 topics)

1. Linear formulas
2. Slope
3. Determining the slope from two points
4. Intercept
5. Composing a linear formula
6. Parallel and intersecting linear formulas

13. Linear equations and inequalities (8 topics)

1. Linear equations
2. Equivalent linear equations
3. The general solution of a linear equation (rules of reduction)
4. Intersection points of linear formulas with the axes
5. Intersection point of two linear formulas
6. Linear inequalities
7. Equivalent inequalities
8. General solution of a linear inequality

Chapter 4: System of linear equations (10 topics)

14. An equation of a line (4 topics)

1. A linear equation with two unknowns
2. Solution of linear equations with two unknowns (rules of reduction)
3. The equation of a line
4. Composing the equation of a line

15. Two equations with two unknowns (6 topics)

1. Systems of linear equations
2. Solving systems of linear equations by substitution
3. Solving systems of equations by elimination
4. Consistent systems of linear equations
5. Inconsistent systems of linear equations
6. Dependent systems of linear equations

Chapter 5: Quadratic equations (21 topics)

16. Parabola (3 topics)

1. Quadratics
2. Parabola
3. Plotting the graph of the quadratic

17. Solving quadratic equations (7 topics)

1. Quadratic equations with two solutions
2. Quadratic equations with one solution
3. Quadratic equations with no solutions
4. Solving quadratic equations by factorization
5. Solving quadratic equations by completing the square
6. The quadratic formula and the discriminant
7. Solving quadratic equations using the quadratic formula

18. Drawing parabolas (7 topics)

1. Intersection of parabolas with the axes
2. Vertex of a parabola
3. Determining the vertex by completing the square
4. Determining the vertex by substitution
5. Drawing of parabolas
6. Transformations of parabolas
7. Multiple transformations of parabolas

19. Intersection points of parabolas (2 topics)

1. Intersection points of a parabola with a line
2. Intersection points of parabolas

20. Quadratic inequalities (2 topics)

1. Quadratic inequalities
2. Solving a quadratic inequality

Chapter 6: Functions (35 topics)

21. Domain and range (6 topics)

1. Function and formula
2. Function rule
3. Intervals
4. Domain
5. Limited domain
6. Range

22. Power functions (4 topics)

1. Power functions
2. Transformations of power functions
3. Multiple transformations of power functions
4. Equations with power functions

23. Higher degree polynomials (7 topics)

1. Polynomials
2. The leading coefficient
3. Equations with polynomials
4. Solving higher degree polynomials by factoring out
5. Solving higher degree polynomials with factorization
6. Solving higher degree polynomials with the quadratic equation
7. Higher degree inequalities

24. Root functions (7 topics)

1. Root functions
2. Transformations of root functions (upwards, to the right, and relative to the x-axis)
3. Multiple transformations of root functions
4. Root equations
5. Solving root equations with substitution
6. Inverse functions
7. Determining the inverse function

25. Fractional functions (11 topics)

1. Asymptotes and hyperbolas
2. Power functions with negative exponents
3. Transformations of power functions with negative exponents (upwards, to the right, and relative to the x-axis)
4. Linear fractional functions
5. Determining asymptotes of a linear fractional function
6. Linear fractional equations
7. Solving linear fractional equations by cross multiplication
8. Inverse of linear fractional functions
9. Isolating a variable when determining the inverse
10. Quotient functions
11. Perforation

Chapter 7: Exponential functions and logarithms (14 topics)

26. Exponential functions (3 topics)

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

27. Logarithmic functions (11 topics)

1. The logarithmic function
2. Logarithmic equations
3. Exponential equations
4. Isolating variables
5. Rules for solving logarithms
6. Solving logarithmic equations with calculation rules and the quadratic formula
7. Change of base
8. Solving logarithmic equations using substitution
9. Solving exponential equations using substitution
10. Graph of logarithmic functions
11. Transformations of the logarithmic function (upwards, to the right, and relative to the x-axis)

Chapter 8: Differentiation (34 topics)

28. The derivative (6 topics)

1. The difference quotient
2. The difference quotient at a point
3. The difference quotient on an interval of length h
4. The tangent line
5. Finding the slope using the difference quotient
6. Calculating the derivative of a function

29. The derivative of power functions (4 topics)

1. The derivative of power functions
2. The power rule
3. The derivative of the root
4. The power rule with a constant

30. Sum and product rule (4 topics)

1. The constant rule
2. The sum rule
3. The product rule
4. The derivative of a product

31. Chain rule (2 topics)

1. Composite functions
2. The chain rule

32. The derivative of standard functions (8 topics)

1. The derivative of sine
2. The derivative of cosine
3. The derivative of tangent
4. The base e
5. The natural logarithm
6. The derivative of exponential functions
7. The derivative of logarithms
8. The derivative of the natural logarithm

33. The quotient rule (1 topic)

1. The quotient rule

34. Applications of derivatives (9 topics)

1. Determining the interval at which a function increases/decreases
2. Extreme values: local maxima and minima
3. Extreme values on a restricted domain
4. Global maxima and minima
5. Calculating extreme values
6. The second derivative
7. Types of increasing and decreasing
8. Inflection points
9. Higher order derivatives