OMPT-G Syllabus

Chapter 1: Linear formulas and equations (13 topics)

1. Formulas (3 topics)

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

1. Linear functions (4 topics)

1. Linear formulas
2. Slope and Intercept
3. Composing a linear formula
4. Parallel and intersecting linear formulas

1. Linear equations and inequalities (6 topics)

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

Chapter 2: System of linear equations (8 topics)

1. 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

1. Two equations with two unknowns (4 topics)

1. Systems of linear equations
2. Solving systems of linear equations by substitution
3. Solving systems of equations by elimination
4. General solution system of linear equations

Chapter 3: Quadratic equations (13 topics)

1. Parabola (2 topics)

1. Quadratics
2. Parabola

1. Solving quadratic equations (4 topics)

1. Quadratic equations
2. Solving quadratic equations by factorization
3. Solving quadratic equations by completing the square
4. The quadratic formula

1. Drawing parabolas (4 topics)

1. Intersection of parabolas with the axes
2. Vertex of a parabola
3. Drawing of parabolas
4. Transformations of parabolas

1. Intersection points of parabolas (2 topics)

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

1. Quadratic inequalities (1 topic)

1. Quadratic inequalities

Chapter 4: Functions (29 topics)

1. Domain and range (5 topics)

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

1. Power functions (3 topics)

1. Power functions
2. Transformations of power functions
3. Equations with power functions

1. Higher degree polynomials (5 topics)

1. Polynomials
2. Equations with polynomials
3. Solving higher-degree polynomials with factorization
4. Solving higher-degree polynomials with the quadratic equation
5. Higher degree inequalities

1. Power functions and root functions (5 topics)

1. Root functions
2. Transformations of root functions
3. Root equations
4. Solving root equations with substitution
5. Inverse functions

1. Fractional functions (8 topics)

1. Asymptotes and hyperbolas
2. Power functions with negative exponents
3. Transformations of power functions with negative exponents
4. Linear fractional functions
5. Linear fractional equations
6. Inverse of linear fractional functions
7. Quotient functions
8. Long division with polynomials

1. Limits and asymptotes (5 topics)

1. The definition of a limit
2. Perforations and other discontinuities
3. Horizontal asymptotes
4. Vertical asymptotes
5. Oblique asymptotes

Chapter 5: Exponential functions and logarithms (13 topics)

1. Exponential functions (3 topics)

1. The exponential function
2. Exponential equations
3. Transformations of the exponential function

1. Logarithmic functions (10 topics)

1. The logarithmic function
2. Logarithmic equations
3. Exponential equations
4. Isolating variables
5. Rules for logarithms
6. More logarithmic equations
7. Change of base
8. Solving equations using substitution
9. Graph of logarithmic functions
10. Transformations of the logarithmic function

Chapter 6: Sequences and series (5 topics)

1. The notions of sequence and series (1 topic)

1. The notions of sequence and series

1. Arithmetic sequences and series (2 topics)

1. Arithmetics sequences
2. Arithmetic series

1. Geometric sequences and series (2 topics)

1. Geometric sequences
2. Geometric series

Chapter 7: Trigonometry (13 topics)

1. Angles with sine, cosine, and tangent (8 topics)

1. Angles
2. Triangles
3. Rules for right-angled triangles
4. Angles in radians
5. Symmetry in the unit circle
6. Special values of trigonometric functions
7. Addition formulas for trigonometric functions
8. Sines and cosines rules

1. Trigonometric functions (5 topics)

1. Trigonometric functions
2. Transformations of trigonometric functions
3. Inverse trigonometric functions
4. Trigonometric equations 1
5. Trigonometric equations 2

Chapter 8: Geometry - basics (8 topics)

1. Lines (2 topics)

1. Lines
2. Parallel and perpendicular lines

1. Angles and polygons (3 topics)

1. Angles
2. Triangles
3. Polygons

1. Calculations of triangles (3 topics)

1. Pythagorean theorem
2. Perimeter
3. Area

Chapter 9: Geometry - continued (9 topics)

1. Lines (4 topics)

1. Different descriptions of a line
2. Angles between lines
3. Perpendicular lines
4. Distance point and line

1. Circles (5 topics)

1. Different descriptions of a circle
2. Intersections of a line and a circle
3. Tangent line to a circle
4. Intersections of circles
5. Distance to a circle

Chapter 10: Physics (Mechanics) (4 topics)

1. One dimensional motion

1. Two-dimensional motion

1. Forces and Newton's laws

1. Work and Energy

Chapter 11: Chemistry (4 topics)

1. Substances and solutions

1. Chemical reactions

1. Acids and Bases

1. Redox chemistry