Algebra: Real Numbers, Polynomials, and Quadratic Equations

Study Notes

Real Numbers:
- Introduction to real numbers
- Properties of real numbers (commutative, associative, distributive)
- Representation of real numbers on a number line
Polynomials:
- Introduction to polynomials
- Types of polynomials (monomials, binomials, trinomials)
- Addition, subtraction, and multiplication of polynomials
- Factorization of polynomials
Quadratic Equations:
- Introduction to quadratic equations
- Solution of quadratic equations (factorization method, quadratic formula)
- Graph of quadratic equations
Linear Equations in Two Variables:
- Introduction to linear equations in two variables
- Solution of linear equations in two variables (graphical method, algebraic method)
- Applications of linear equations in two variables

Pair of Linear Equations in Two Variables:
- Introduction to pair of linear equations in two variables
- Solution of pair of linear equations in two variables (graphical method, algebraic method)
- Applications of pair of linear equations in two variables
Quadratic Expressions and Equations:
- Introduction to quadratic expressions and equations
- Factorization of quadratic expressions
- Solution of quadratic equations (factorization method, quadratic formula)
Inequalities:
- Introduction to linear inequalities
- Solution of linear inequalities (graphical method, algebraic method)
- Applications of linear inequalities

Introduction to Geometry:
- Points, lines, and planes
- Angles and their types (acute, obtuse, right, straight, reflex)
Properties of Angles:
- Complementary and supplementary angles
- Adjacent angles, vertically opposite angles, and corresponding angles
Triangles:
- Introduction to triangles
- Properties of triangles (angle sum property, exterior angle property)
- Congruent and similar triangles
Quadrilaterals:
- Introduction to quadrilaterals
- Properties of quadrilaterals (angle sum property, diagonal properties)
- Types of quadrilaterals (rectangle, square, rhombus, trapezium)

Areas and Perimeters:
- Areas and perimeters of triangles, quadrilaterals, and polygons
- Applications of areas and perimeters
Surface Areas and Volumes:
- Surface areas and volumes of cubes, cuboids, and cylinders
- Applications of surface areas and volumes

Data Handling:
- Introduction to data handling
- Measures of central tendency (mean, median, mode)
- Range and interquartile range
Probability:
- Introduction to probability
- Experimental probability and theoretical probability
- Addition theorem of probability

Real numbers can be represented on a number line and have commutative, associative, and distributive properties.
Polynomials can be added, subtracted, and multiplied, and can be factorized into simpler forms.
Quadratic equations can be solved using factorization or the quadratic formula, and have graphs that are parabolas.
Linear equations in two variables can be solved using graphical or algebraic methods, and have applications in real-world problems.

A pair of linear equations in two variables can be solved using graphical or algebraic methods, and have applications in real-world problems.
Quadratic expressions can be factorized, and quadratic equations can be solved using factorization or the quadratic formula.
Linear inequalities can be solved using graphical or algebraic methods, and have applications in real-world problems.

Geometry involves the study of points, lines, and planes, as well as angles and their types.
Angles have properties such as being complementary, supplementary, adjacent, or vertically opposite.
Triangles have properties such as angle sum and exterior angle, and can be congruent or similar.
Quadrilaterals have properties such as angle sum and diagonal properties, and can be classified into different types.

Areas and perimeters can be calculated for triangles, quadrilaterals, and polygons, and have practical applications.
Surface areas and volumes can be calculated for cubes, cuboids, and cylinders, and have practical applications.

Data handling involves the study of measures of central tendency, range, and interquartile range.
Probability can be experimental or theoretical, and has an addition theorem.