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1. MATHEMATICS CP01 / CP08 Mr. Shivaraj Heralgi

2. CONTENT 1.0 FUNDAMENTALS OF MATHEMATICS 1.1 a 1.1 b 1.1 c 1.1 d 1.2 a 1.2 b 1.2 c 1.3 1.4 1.5 1.6

3. 1.1 LCM and HCF Highest Common Factor Factors Common factors Highest among them Commonly divided Exercise problems Tricks Maya has two pieces cloth ---- strips of equal width A shop keeper ---- only one measurer Jasmin art project ---- equal in width Leo's hockey league ---- same number of backs. 1.1 a 4 Problems Exercise key answer a) 6 b) 6 c) 7 d ) 9 15 ltrs 11 backward - 5 & forward - 2 HCF - 16

4. 1.1 b 5 problems Lowest Common Multiple * Common Multiple * smallest or least of their common multiples * Remainder should be 1 Exercise problems Tricks *Ram exercises --- How many days * Six bells --- how many times * Joseph and Sridhar -- total pins *Yadira's mom buying hot dogs -- smallest total number least number - (LCM) Exercise Key Answers a) 360 b) 2400 c) 300 15 + 1 times( ( 120 sec = 2 min ) (30 min / 2min = 15 min)) ==16 times On dividing 9999 by 600 remainder is 399 = 9999-399= 9600 72 36

5. 1.1 c 4 problems Exercise Key Answers HCF - 3 kg LCM - 6930 cm HCF - 75 LCM – 540 , 540+ 8=548 Exercise problems Tricks Renu purchases two bags -- maximum value (HCF) Three boys step off -- minimum distance (LCM) The length, breadth --- longest tape (HCF) least number - (LCM)

6. 1.1 d 2 Problems a x b = LCM (a, b) x HCF (a, b) Exercise Key Answers b = 75 b = 80

7. 1.2 Fractions-Definition, Types of fractions, Algebra of fractions (It is a part of the whole or part of collection). 1 8 𝑛𝑢𝑚𝑎𝑟𝑎𝑡𝑜𝑟 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 (DOWN) Types of fractions: Ex: Ex: Ex: Ex: 1. Proper fraction : 2. Improper fraction : 3. Mixed fraction: 4.Decimal fraction:

8. 1.2 a ADDITION (4 problem) CASE 1 (Same denominator) CASE 2 (Different denominator) CASE 3 (Mixed Fraction) Directly simply Take LCM then Simplify Convert mixed fraction to improper fraction and then do the addition. Exercise Key Answers a) 6/7 b) 16/11 c) 283/90 d) 335/24 e) 703/60 f) 17/5 g) 4853/693 h) 475/63 389 56 314

9. 1.2 b Subtraction (5 problems) CASE 1 (Same denominator) CASE 2 (Different denominator) CASE 3 (Mixed Fraction) Directly simply Take LCM then Simplify Convert mixed fraction to improper fraction and then do the subtraction. Exercise Key Answers 1. a) 9 b) 16/7 c) 31/3 d)251/24 e) -21/5 f) 7/5 g)49/21 43/30 18 km 13/24*24=13 3/2

10. 1.2 c MULTIPLICATION AND DIVISION (6 Problem) Exercise Key Answers a) 48/5 b) 70/36 c) 875/27 d) 119/52 e) 329/152 40 kg 21/2 42 packets 23/25 45/8

11. 1.3 Indices and Laws of Indices (Indices are a useful way of more simply expressing large numbers) Exercise Key Answers 1. a) a10 b) X 12 c) 6 Problems

12. 1.4 Solving Linear Equations 1.5 Solutions of Quadratic Equations By Factorization 1.6 Solutions of Quadratic Equations By Formula General form is ax+ b = 0 Linear Equations Quadratic Equations General form is 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 6 Problems 5 Problems 3 Problems