EV Class 9-10 Higher Math Guide | Complete SSC Notes, MCQs, CQs & Solutions | FreeLearning365

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📊 EV · SSC · Class 9-10 · NCTB Aligned

📐 Higher Math Guide — Complete & Interactive

Master every chapter with notes, MCQs, CQs, and visual learning tools.

📚 All Chapters (click to jump to detail below)

🔽 Scroll down to explore Chapter One interactive detail with MCQs, CQs, and more.

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✨ Chapter One: Set and Function

Interactive notes, MCQs, Creative Questions & Board patterns.

📖 Core Concepts of Set and Function

🔹 Set Theory Basics

A set is a well-defined collection of distinct objects. Notation: { }, ∈, ∉, ⊆, ⊂, ∪, ∩, complement.

🔹 Types of Sets

Finite, infinite, empty set, singleton, equal sets, equivalent sets, universal set, power set.

🔹 Operations on Sets

Union, intersection, difference, symmetric difference, complement. Venn diagrams.

🔹 Relations and Functions

A relation is a subset of Cartesian product. Function is a special relation where each input has exactly one output.

🔹 Domain, Codomain, Range

Domain: set of all inputs. Codomain: set of possible outputs. Range: set of actual outputs.

🔹 Types of Functions

One-to-one (injective), onto (surjective), bijective, constant, identity, linear, quadratic.

💡 Fun Fact: The concept of sets was introduced by Georg Cantor in the late 19th century. It's the foundation of modern mathematics!

🔬 MCQ Practice (with instant feedback)

📌 Creative Question 1: Set Operations

If U = {1,2,3,4,5,6,7,8,9,10}, A = {2,4,6,8,10}, B = {1,3,5,7,9}. Find:

a) A ∪ B
b) A ∩ B
c) A' (complement)
d) (A ∪ B)'

Solution: A ∪ B = U, A ∩ B = ∅, A' = B, (A ∪ B)' = ∅.

📌 Creative Question 2: Functions

Let f(x) = 2x + 3. Find:

a) f(2)
b) f(-1)
c) the value of x for which f(x) = 7
d) the range if domain = {0,1,2}.

Solution: f(2)=7, f(-1)=1, x=2, range = {3,5,7}.

📌 Creative Question 3: Venn Diagram

In a class of 50 students, 30 play cricket, 25 play football, and 10 play both. Draw a Venn diagram and find how many play neither.

Solution: Only cricket = 20, only football = 15, both = 10, neither = 50 - (20+15+10) = 5.

🎯 Last Decade Board Recurrence

• ⭐⭐⭐⭐⭐ Set operations (union, intersection, complement)
• ⭐⭐⭐⭐⭐ Venn diagram problems
• ⭐⭐⭐⭐⭐ Domain and range of functions
• ⭐⭐⭐⭐ Types of sets (finite, infinite, empty)
• ⭐⭐⭐⭐ One-to-one and onto functions
• ⭐⭐⭐⭐⭐ Function evaluation

⭐ Top 15 Exam Focus Questions

1. What is a set? Give examples.
2. Define subset, proper subset, and superset.
3. What are the basic operations on sets?
4. Explain the complement of a set.
5. What is a Cartesian product?
6. Define relation and function.
7. What is the difference between codomain and range?
8. Define one-to-one function with example.
9. Define onto function with example.
10. What is a bijective function?
11. How to find the domain of a function?
12. Explain the vertical line test for functions.
13. What are the types of functions based on mapping?
14. Solve a real-life problem using Venn diagram.
15. Explain the union and intersection of two sets with examples.

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