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Chapter 1: Real Numbers

    Introduction

    The Fundamental Theorem of Arithmetic

    Irrational Numbers

    Exponentials Revisted

    Exercise 1.1

    Exercise 1.2

    Exercise 1.3

    Exercise 1.4

    Exercise 1.5

    What We Have Discussed

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 1: Real Numbers > Enhanced Curriculum Support

Enhanced Curriculum Support

This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:

Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.

Exam Preparedness: Sample Question Papers provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.

About the Section

Sec A

(1) Expand log10385.

(2) Prime factorization of 98 is :
(A) 22 × 7 (B) 22 × 72 (C) 2 × 72 (D) 23 × 7

(3) Find the value of log636.

(4) Find the HCF of 24 and 33 by using division algorithm.

(5) The ten's digit of the product 620 × 52 is :

(A) 0

(B) 6

(C) 4

(D) 5

(6) The LCM of the given numbers x and y where y is a multiple of x is :

(A) x (B) y

(C) xy (D) x + y

(7) Find the HCF of 24 and 33 by using division algorithm.

Sec B

(1) Express 360 as a product of prime factors.

(2) Express 360 as a product of prime factors.

(3) Find the HCF of 220 and 40 by using Euclid Division Lemma.

(4) Show that log162343 + 2log79 - log17 = log 2

(5) Expand loga3b2c5.

Sec C

(1) If x2+y2 = 10xy, then prove that:

2 log(x + y) = log x + log y + 2 log 2 + log 3.

(2) Find the sum of all two digit odd multiples of 3.

(3) Prove that 2+7 is an irrational number.

(4) Prove that 3+5 is an irrational number.

(5) Show that cube of any positive integer will be in the form of 8m or 8m+1 or 8m+3 or 8m+5 or 8m+7, where m is a whole number.

Sec D

(1) Prove that 35+7 is an irrational number.

(2) Prove that 23+6 is an irrational number.

(3) If x2 + y2 = 27xy, then show that 2 log (x – y) = 2 log 5 + log x + log y.

Sec E

(1) Prove that 2 + 5 is irrational.

(2) Prove that 5+7 is an irrational number.