Unit 4 Partial Fractions

Welcome to the Solutions of Unit 4 Partial Fractions for Class 10 Math, a valuable resource created to support you through each step of this challenging topic. This post provides complete, step-by-step solutions for every exercise in Unit 4 Partial Fractions, covering essential concepts such as resolving fractions with different types of factors. These solutions are crafted to deepen your understanding and make this unit easier, especially for exam preparation. By studying these solutions, you’ll gain the confidence needed to tackle complex questions, giving you a solid foundation to excel in exams.

Unit 4 Partial Fractions. A Cover image with proper and improper fractions on it.

Key Concepts

“Unit 4 Partial Fractions” of Class 10 math covers the following concepts:

  1. Definitions:
  • Proper Fraction: A fraction where the numerator is less than the denominator.
  • Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.
  • Rational Fraction: A fraction where both the numerator and denominator are polynomials.
  1. Partial Fractions:
  • Resolving into Partial Fractions:
    • Non-repeated Linear Factors: Breaking down a fraction where the denominator has distinct linear factors.
    • Repeated Linear Factors: Decomposing a fraction where the denominator includes repeated linear factors.
    • Non-repeated Quadratic Factors: Handling fractions with distinct quadratic factors in the denominator.
    • Repeated Quadratic Factors: Dealing with fractions where the quadratic factors in the denominator are repeated.
      If these solutions were helpful then do check solutions of unit 5 sets and functions.

Multiple Choice Questions Test for Unit 4 Partial Fractions

To reinforce your understanding of Unit 4 Partial Fractions, try our interactive online MCQ quiz! This test covers all key concepts, including proper and improper fractions, rational fractions, and resolving partial fractions by factor type. Testing yourself with these questions is a great way to prepare for exams, allowing you to apply what you’ve learned and identify any areas needing more practice. It’s an excellent tool for solidifying your knowledge.

Unit 4 MCQ's Test for 10 Class Math

1 / 10

Partial fractions of x2+1(x+1)(x−1)\frac{x^2 + 1}{(x + 1)(x - 1)} are of the form:

2 / 10

Partial fractions of x+2(x+1)(x2+2)\frac{x + 2}{(x + 1)(x^2 + 2)} are of the form:

3 / 10

Partial fractions of x−2(x−1)(x+2)\frac{x - 2}{(x - 1)(x + 2)} are of the form:

4 / 10

x3+1(x−1)(x+2)\frac{x^3 + 1}{(x - 1)(x + 2)} is:

5 / 10

(x+3)2=x2+6x+9(x + 3)^2 = x^2 + 6x + 9 is:

6 / 10

2x+1(x+1)(x−1)\frac{2x + 1}{(x + 1)(x - 1)} is:

7 / 10

A fraction in which the degree of the numerator is less than the degree of the denominator is called:

8 / 10

A fraction in which the degree of the numerator is greater or equal to the degree of the denominator is called:

9 / 10

A function of the form f(x)=N(x)D(x)f(x) = \frac{N(x)}{D(x)}, with D(x)≠0D(x) \neq 0 where N(x)N(x) and D(x)D(x) are polynomials in xx, is called:

10 / 10

The identity (5x+4)2=25x2+40x+16(5x + 4)^2 = 25x^2 + 40x + 16 is true for:

Your score is

The average score is 0%

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Benefits of PDF Solutions

Using the PDF Solutions of Unit 4 Partial Fractions provides several advantages for Class 10 students preparing for exams. First, having all solutions in a downloadable PDF format means you can easily access them anytime, even offline. This convenience allows you to study from anywhere without needing constant internet access, making it perfect for students on the go.

The PDF format also organizes each solution in a clear, step-by-step manner. This structure helps you understand the logic and methods required to tackle each type of partial fraction problem, from non-repeated linear factors to repeated quadratic factors. By following these steps, you’ll develop a solid understanding of the techniques needed to solve similar questions on your own, strengthening your problem-solving skills and boosting your confidence for exams.

Another benefit is that these solutions mimic the structure and types of questions you’re likely to encounter in exams. By reviewing the PDF, you can familiarize yourself with the exam-style format, which is invaluable for effective preparation. You’ll be able to recognize patterns in problem-solving, allowing you to approach similar questions in exams more quickly and accurately.

Finally, the PDF format makes revisiting difficult questions easy. You can bookmark challenging problems and revisit them as you continue studying, enabling you to focus on areas where you need the most practice. This personalized approach makes your study sessions more effective, helping you target and overcome any specific difficulties within Unit 4 Partial Fractions.

We hope these Solutions of Unit 4 Partial Fractions have been a special resource in your Class 10 exam preparation. Regular practice with these solutions will help you approach partial fractions confidently and ensure you’re well-prepared for any related exam questions. For continued learning, explore partial fractions visually with GeoGebra, a versatile tool that allows you to graph and manipulate equations interactively. to build on your math skills. Keep practicing, stay focused, and you’ll see the results in both your understanding and confidence. Best of luck with your studies!

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