Class 10

Algebra

• Variables and Expressions: Letters or symbols that represent unknown values or values that can change.
• Equations and Inequalities: Statements that express the equality or inequality of two mathematical expressions.
• Linear Equations: Equations in which the highest power of the variable is 1.
• Quadratic Equations: Equations in which the highest power of the variable is 2.
• Functions: Relations between a set of inputs (called the domain) and a set of possible outputs (called the range).

Geometry

• Points, Lines, and Planes: Basic geometric objects used to define shapes and figures.
• Angles and Measurements: Types of angles (acute, obtuse, right, straight) and measurements (degrees, radians).
• Properties of Shapes: Characteristics of 2D and 3D shapes, such as congruence, similarity, and symmetry.
• Theorems and Proofs: Statements and logical arguments used to establish geometric truths.
• Coordinate Geometry: Representation of geometric objects using coordinates (x, y, z) in a Cartesian system.

Calculus

• Limits: The behavior of a function as the input approaches a certain value.
• Derivatives: Rates of change of a function with respect to the input.
• Differentiation Rules: Rules for finding derivatives, such as the power rule and product rule.
• Applications of Derivatives: Optimization, motion, and related rates.
• Integrals: Accumulation of quantities over a defined interval.
• Integration Techniques: Methods for finding integrals, such as substitution and integration by parts.

Statistics

• Data Types: Quantitative (numerical) and qualitative (categorical) data.
• Descriptive Statistics: Measures that summarize and describe data, such as mean, median, and standard deviation.
• Inferential Statistics: Making conclusions or predictions about a population based on a sample.
• Probability: The study of chance events and their likelihood.
• Hypothesis Testing: Testing a statement about a population using a sample.

Trigonometry

• Angles and Triangles: Relationships between angles and side lengths in triangles.
• Trigonometric Functions: Sine, cosine, and tangent, and their relationships with angles and triangles.
• Identities and Formulas: Equations and formulas that relate trigonometric functions.
• Graphs and Inverses: Graphs of trigonometric functions and their inverse functions.
• Applications of Trigonometry: Real-world problems involving right triangles, such as navigation and physics.

Algebra

• Variables are letters or symbols that represent unknown values or values that can change, and are used to express mathematical expressions.
• Equations are statements that express the equality of two mathematical expressions, and can be linear or quadratic.
• Linear equations are equations in which the highest power of the variable is 1, and can be written in the form ax + by = c.
• Quadratic equations are equations in which the highest power of the variable is 2, and can be written in the form ax^2 + bx + c = 0.
• Functions are relations between a set of inputs (called the domain) and a set of possible outputs (called the range), and can be represented as f(x) = y.

Geometry

• Points, lines, and planes are basic geometric objects used to define shapes and figures.
• Angles can be acute, obtuse, right, or straight, and can be measured in degrees or radians.
• Properties of shapes include congruence, similarity, and symmetry, and can be used to describe 2D and 3D shapes.
• Theorems and proofs are statements and logical arguments used to establish geometric truths.
• Coordinate geometry is a system of representation of geometric objects using coordinates (x, y, z) in a Cartesian system.

Calculus

• Limits describe the behavior of a function as the input approaches a certain value.
• Derivatives are rates of change of a function with respect to the input, and can be used to find the slope of a tangent line.
• Differentiation rules, such as the power rule and product rule, are used to find derivatives.
• Applications of derivatives include optimization, motion, and related rates.
• Integrals are accumulation of quantities over a defined interval, and can be used to find the area under a curve.
• Integration techniques, such as substitution and integration by parts, are methods for finding integrals.

Statistics

• Data can be quantitative (numerical) or qualitative (categorical).
• Descriptive statistics, such as mean, median, and standard deviation, are used to summarize and describe data.
• Inferential statistics involves making conclusions or predictions about a population based on a sample.
• Probability is the study of chance events and their likelihood.
• Hypothesis testing involves testing a statement about a population using a sample.

Trigonometry

• Angles and triangles are related through the use of trigonometric functions.
• Trigonometric functions, such as sine, cosine, and tangent, are used to describe relationships between angles and side lengths in triangles.
• Identities and formulas, such as the Pythagorean identity, are used to relate trigonometric functions.
• Graphs of trigonometric functions and their inverse functions are used to model periodic phenomena.
• Applications of trigonometry include real-world problems involving right triangles, such as navigation and physics.