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Learn MoreLatest Blog: Mastering Trigonometry for Class 10 Board Exams
Trigonometry forms a crucial part of the Class 10 CBSE Mathematics curriculum and carries significant weightage in board exams. Understanding trigonometric concepts thoroughly can help students score well in both theory and practical problems.
In this comprehensive guide, we'll cover trigonometric ratios, identities, applications of trigonometry, and important theorems. We provide step-by-step solutions to typical board exam problems, highlighting common mistakes students make and how to avoid them.
Additionally, we'll discuss the importance of trigonometry in real-life applications and provide a curated list of practice questions from NCERT textbook and previous year papers. By the end of this guide, you'll have a solid understanding of trigonometry and be able to solve any trigonometry-related problem in your board exams.
Read Full Article →Mathematics for Class 10
Chapter 1: Real Numbers
This chapter covers Euclid's division lemma, Fundamental Theorem of Arithmetic, irrational numbers, and decimal expansions.
Key Concepts:
- Euclid's Division Lemma: For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, 0 ≤ r < b
- Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes
- Irrational Numbers: Numbers that cannot be expressed as p/q where p and q are integers
- Rational Numbers: Numbers with terminating or repeating decimal expansions
Example Problem:
Prove that √5 is irrational.
Solution:
Let us assume, to the contrary, that √5 is rational.
Then, there exist coprime integers a and b (b ≠ 0) such that √5 = a/b
Squaring both sides: 5 = a²/b² ⇒ a² = 5b²
This means 5 divides a² ⇒ 5 divides a (by Fundamental Theorem of Arithmetic)
Let a = 5k for some integer k
Substituting: (5k)² = 5b² ⇒ 25k² = 5b² ⇒ 5k² = b²
This means 5 divides b² ⇒ 5 divides b
Thus, 5 is a common factor of both a and b, contradicting our assumption that a and b are coprime.
Hence, our initial assumption is false and √5 is irrational.
Practice Worksheet (Downloadable PDF)
Download Real Numbers WorksheetChapter 2: Polynomials
This chapter covers zeros of polynomials, relationship between zeros and coefficients, and division algorithm for polynomials.
Science for Class 10
Chapter 1: Chemical Reactions and Equations
This chapter covers chemical reactions, types of reactions, balancing chemical equations, and effects of oxidation.
Key Concepts:
- Chemical Reactions: Combination, decomposition, displacement, double displacement
- Balancing Equations: Law of conservation of mass
- Oxidation-Reduction: Gain or loss of oxygen/electrons
- Corrosion and Rancidity: Effects of oxidation in daily life
Interactive Diagram: Types of Chemical Reactions
Fig 1.1: Different types of chemical reactions and their examples
Activity:
Perform and observe the following reactions and classify them:
1. Burning of magnesium ribbon in air
2. Heating of lead nitrate
3. Reaction between iron nails and copper sulphate solution
English for Class 10
Grammar: Tenses and Modals
This section covers present, past and future tenses along with modal verbs and their usage in different contexts.
| Tense | Form | Example |
|---|---|---|
| Present Perfect | has/have + V3 | I have finished my work |
| Past Perfect | had + V3 | I had eaten before he arrived |
| Future Perfect | will have + V3 | I will have completed the project by tomorrow |
Exercise:
Fill in the blanks with correct form of verbs given in brackets:
- By next month, I _____ (complete) my project.
- She _____ (study) for three hours when her friend called.
Literature: First Flight
Detailed analysis of prose and poetry from First Flight textbook with important questions and answers.
Poem: Dust of Snow
"The way a crow
Shook down on me
The dust of snow
From a hemlock tree
Has given my heart
A change of mood
And saved some part
Of a day I had rued."
- Robert Frost
Questions:
- What is the significance of the crow and hemlock tree in the poem?
- How does the poet's mood change in the poem?
हिंदी - कक्षा 10
पाठ 1: सूरदास के पद
सूरदास द्वारा रचित पदों की व्याख्या एवं महत्वपूर्ण प्रश्नोत्तर।
"उधौ, मन न भए दस बीस।
एक हुतो सो गयौ स्याम संग, को आराधै इन्हैं...
जा तन की झाँई परै, प्यारी होइ है सोइ।
ज्यों ज्यों बढ़ै साँवलियत, त्यों त्यों उज्ज्वल होइ।"
महत्वपूर्ण प्रश्न:
- कवि ने गोपियों की किस विशेषता का वर्णन किया है?
- 'ज्यों ज्यों बढ़ै साँवलियत, त्यों त्यों उज्ज्वल होइ' - पंक्ति का भाव स्पष्ट कीजिए।
Computer Science for Class 10
Chapter 1: Networking
Introduction to computer networks, types of networks, network devices, and internet protocols.
Network Types:
- PAN: Personal Area Network (Bluetooth devices)
- LAN: Local Area Network (School/Office network)
- MAN: Metropolitan Area Network (City-wide network)
- WAN: Wide Area Network (Internet)
Network Devices:
- Modem, Router, Switch, Hub, Repeater
Practical Exercise:
Draw a diagram showing different types of networks and label the network devices used in each.
CBSE Board Exam Preparation
Time Management Strategy
Allocate time based on marks distribution. Follow 50-10 rule (50 minutes study, 10 minutes break). Solve sample papers within time limit.
Sample Papers
Solve last 10 years CBSE board papers to understand pattern, marking scheme and frequently asked questions.
Revision Techniques
Create one-page notes for each chapter with formulas, dates, definitions. Use mnemonics for memorization.
Board Exam Pattern
| Subject | Total Marks | Theory | Practical | Duration |
|---|---|---|---|---|
| Mathematics | 80 | 80 | - | 3 hours |
| Science | 100 | 80 | 20 | 3 hours |
| Social Science | 80 | 80 | - | 3 hours |
Social Science for Class 10
Chapter 1: The Rise of Nationalism in Europe
This chapter covers the rise of nationalism, unification of Germany and Italy, and the French Revolution's impact.
Key Features:
Nationalism
Meaning and growth of nationalism in 19th century Europe
Unification
Processes of unification of Germany and Italy
French Revolution
Impact on nationalism across Europe
Activity:
Prepare a timeline showing important events in the unification of Germany and Italy from 1815 to 1871.