CTET Mathematics Study Notes

Natural Numbers: Counting numbers starting from 1 (1, 2, 3, ...).
Whole Numbers: Natural numbers including 0 (0, 1, 2, 3, ...).
Integers: Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
Rational Numbers: Numbers expressed as a fraction of two integers (a/b where b ≠ 0).
Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves (e.g., 2, 3, 5, 7).
Composite Numbers: Natural numbers greater than 1 that are not prime (e.g., 4, 6, 8).
Factors and Multiples:
- Factors: Numbers that divide another number completely.
- Multiples: Product of a number and an integer.

Algebraic Expressions: Combinations of variables and constants using operations (e.g., 3x + 2).
Equations: Mathematical statements that assert the equality of two expressions (e.g., 2x + 3 = 7).
Polynomials: Expressions that involve variables raised to whole number powers (e.g., x² + 4x + 4).
Linear Equations: Equations of the first degree (e.g., y = mx + b).
Inequalities: Mathematical expressions involving <, >, ≤, ≥.
Functions: Relations that uniquely associate each input with exactly one output.

Basic Shapes:
- 2D Shapes: Circle, triangle, square, rectangle.
- 3D Shapes: Sphere, cube, cylinder, cone.
Properties of Shapes:
- Triangle: Sum of angles = 180°.
- Quadrilateral: Sum of angles = 360°.
Perimeter and Area:
- Perimeter: Total distance around a shape.
- Area: Measure of the space enclosed within a shape.
Volume: Measure of the space occupied by a 3D object.
Symmetry: A shape has symmetry if it can be divided into two identical parts.

Basic Operations: Addition, Subtraction, Multiplication, Division.
Order of Operations: PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
Properties:
- Commutative: a + b = b + a; a × b = b × a.
- Associative: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c).
- Distributive: a(b + c) = ab + ac.

Constructivist Approach: Emphasizes active learning where students construct their own understanding.
Differentiated Instruction: Tailoring teaching environments and practices to create appropriate learning experiences for different students.
Assessment Strategies: Continuous formative assessment to gauge understanding and adapt teaching methods.
Mathematical Discourse: Encouraging students to discuss and explain their thinking to develop deeper understanding.
Use of Manipulatives: Incorporating physical objects to help students visualize and understand mathematical concepts.

Natural numbers start from 1 and include all positive integers (1, 2, 3,...).
Whole numbers include natural numbers and 0 (0, 1, 2, 3,...).
Integers encompass whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3,...).
Rational numbers can be represented as fractions of two integers (a/b where b ≠ 0).
Prime numbers are natural numbers greater than 1 with no divisors other than 1 and themselves (e.g., 2, 3, 5, 7).
Composite numbers are natural numbers greater than 1 that have divisors other than 1 and themselves (e.g., 4, 6, 8).
Factors are integers that divide another integer completely, while multiples are results of multiplying a number by an integer.

Algebraic expressions combine variables and constants using operational symbols (e.g., 3x + 2).
Equations assert equality between two mathematical expressions (e.g., 2x + 3 = 7).
Polynomials consist of variables raised to whole number powers (e.g., x² + 4x + 4).
Linear equations represent first-degree relationships (e.g., y = mx + b).
Inequalities express relationships between quantities using symbols like <, ≤, ≥.
Functions define relationships where each input correlates to one unique output.

2D shapes include fundamental figures like circles, triangles, squares, and rectangles.
3D shapes encompass volumes like spheres, cubes, cylinders, and cones.
In a triangle, the sum of the interior angles equals 180°; for a quadrilateral, it equals 360°.
The perimeter is the total distance around a shape, while area measures the space enclosed within a shape.
Volume quantifies the space occupied by three-dimensional objects.
A shape is symmetrical if it can be divided into two identical halves.

The four basic arithmetic operations are addition, subtraction, multiplication, and division.
Order of operations is guided by PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Commutative property states that addition and multiplication can be performed in any order (a + b = b + a; a × b = b × a).
Associative property indicates that when adding or multiplying, the grouping of numbers does not change the result ((a + b) + c = a + (b + c); (a × b) × c = a × (b × c)).
The distributive property allows multiplication over addition (a(b + c) = ab + ac).

The constructivist approach promotes active learning and encourages students to build their own understanding.
Differentiated instruction caters to diverse learning needs by adapting teaching practices and environments.
Continuous formative assessments are essential in gauging student understanding and adjusting teaching methods accordingly.
Mathematical discourse enhances learning by allowing students to articulate and discuss their reasoning.
The use of manipulatives helps students visualize and comprehend mathematical concepts through physical interaction.