Competition Maths Notes
Introduction
1. Number Systems
1.1 Natural Numbers
Positive integers starting from 1 (1, 2, 3, ...).
1.2 Whole Numbers
Natural numbers including zero (0, 1, 2, 3, ...).
1.3 Integers
Whole numbers including negative numbers (..., -3, -2, -1, 0, 1, 2, 3, ...).
1.4 Rational Numbers
Numbers that can be expressed as a fraction (1/2, 3/4).
1.5 Real Numbers
Includes both rational and irrational numbers.
2. Fractions
2.1 Proper Fractions
Numerator is less than the denominator (3/4).
2.2 Improper Fractions
Numerator is greater than or equal to the denominator (5/3).
2.3 Mixed Numbers
A whole number combined with a fraction (2 1/2).
2.4 Operations
Addition, subtraction, multiplication, and division of fractions.
3. Decimals
3.1 Place Value
Understanding tenths, hundredths, thousandths (0.25 is 25/100).
3.2 Conversion
Converting fractions to decimals (3/4 = 0.75).
3.3 Operations
Addition, subtraction, multiplication, and division of decimals.
4. Percentages
4.1 Calculations
Finding a percentage of a number (20% of 150 = 30).
4.2 Increase/Decrease
Calculating percentage increase or decrease between two values.
5. Ratios and Proportions
5.1 Ratios
Comparing two quantities (2:3).
5.2 Proportions
Setting up equations to solve proportional relationships (2/3 = x/9).
6. Algebra
6.1 Linear Equations
Equations of the form ax + b = c.
6.2 Quadratic Equations
Equations of the form ax² + bx + c = 0.
6.3 Polynomials
Expressions with multiple terms (ax² + bx + c).
7. Geometry
7.1 Basic Shapes
Triangles, circles, squares, etc.
7.2 Area and Perimeter
Calculations for various shapes (A = πr² for a circle).
7.3 Volume
Calculating volume for 3D shapes (V = l × w × h for a cuboid).
8. Trigonometry
8.1 Trigonometric Ratios
Sine, cosine, and tangent functions.
8.2 Applications
Using trigonometry to find heights and distances.
9. Statistics and Probability
9.1 Mean, Median, Mode
Measures of central tendency.
9.2 Probability
Calculating the likelihood of events (P(E) = favorable outcomes / total outcomes).
9.3 Data Interpretation
Analyzing data from charts, graphs, and tables.
10. Arithmetic
10.1 Basic Arithmetic Operations
Addition, subtraction, multiplication, and division of whole numbers.
10.2 Laws of Arithmetic
Commutative, associative, and distributive laws.
10.3 Time and Work
Calculations involving work done by one or more persons.
10.4 Speed, Distance, and Time
Solving problems related to speed, distance, and time.
10.5 Simple and Compound Interest
Calculating interest on principal amounts over time.
Why is Maths so important?
Mathematics provides structure to our life and reduces ambiguity. Learning Mathematics improves our reasoning power, creativity, abstract or spatial thinking, critical thinking, problem-solving abilities, and even effective communication skills.
Maths References
At Studnet Dost you will find complete references about Number system and basic Arithmetic Algebra Trigonometry Geometry and Cartesian Geometry Calculus- Differential and Integral Matrix Algebra Probability and Statistics l and more: