Educational Math Guide
1. Basic Arithmetic
Arithmetic is the branch of mathematics dealing with numbers and basic operations such as addition,
subtraction, multiplication, and division. These are the foundation for all higher-level math.
Example: 7 × (5 + 3) = 7 × 8 = 56. Operations inside parentheses are performed first according to the
order of operations (PEMDAS/BODMAS).
2. Algebra
Algebra introduces the use of symbols (usually letters) to represent unknown values. It allows us to
form and solve equations.
Example: Solve for x in 2x + 4 = 10 → 2x = 6 → x = 3.
3. Geometry
Geometry deals with the study of shapes, sizes, and properties of space. It includes points, lines,
angles, surfaces, and solids.
Example: The area of a triangle is given by (1/2) × base × height.
4. Trigonometry
Trigonometry studies the relationships between the sides and angles of triangles. The main
trigonometric ratios are sine, cosine, and tangent.
Example: In a right triangle, sin(θ) = opposite/hypotenuse.
5. Calculus
Calculus focuses on change and motion. It has two main branches: differential calculus (rates of
change) and integral calculus (accumulation of quantities).
Example: The derivative of x² is 2x, and the integral of x² is (x³)/3 + C.
6. Statistics and Probability
Statistics deals with collecting, analyzing, and interpreting data, while probability measures the
likelihood of an event occurring.
Example: The probability of rolling a 4 on a fair six-sided die is 1/6.
7. Practice Exercises
Try solving the following problems to test your understanding:
1. Simplify: 12 ÷ (3 + 1) × 2
2. Solve for x: 5x − 7 = 18
3. Find the perimeter of a rectangle with length 8 cm and width 5 cm.
4. Calculate sin(30°).
5. Find the derivative of 3x³.
6. What is the mean of the numbers: 4, 8, 6, 10?