Mathematics notes for High School Year 2 · Physics-Math
120 sections with theory, interactive examples, and 2,817 exercises graded instantly by AI.
Start from the beginning →Real numbers
Real numbers
Equations
Algebra
Equations
Systems of equations
Inequalities and systems of inequalities
Complex numbers
Vectors and geometry
Vectors
Scalar product
Trigonometry
Trigonometry
- Measuring angles: degrees and radians
- Trigonometric ratios of an angle
- Reciprocal trigonometric ratios
- Trigonometric ratios of the sum of two angles
- Trigonometric ratios of the difference of two angles
- Trigonometric ratios of double angles
- Sine rule
- Cosine rule
- Solving right-angled triangles
- Solving non-right-angled triangles
Conics
Functions
Real functions
Limits and continuity
- Monotonicity and extrema of a function
- Limit of a function
- Estimating limits using tables
- Calculating limits of functions
- Limit of a function as x → ∞
- Continuity of functions
- Inverse proportion function
- Sign of a function. Axis intercepts and asymptotes of a rational function
- Problems on limits and continuity
Common types of functions
Derivatives
Derivative
- Average rate of change of a function
- Definition of the derivative of a function at a point
- Graphical interpretation of the derivative
- Derivative function
- Physical interpretation of the derivative
- Derivative of a polynomial
- Differentiation rules
- Derivatives of standard functions
- Exercises on derivatives
- Tangent line to a curve
- Increasing and decreasing intervals and extrema using derivatives
- Sketching functions
- Optimisation problems