Mathematics Mind Maps Class X MIND MAP G

Mathematics Mind Maps - Class X MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

REAL NUMBERS EUCLID’S DIVISION ALGORITHM I r r FINDING HCF a t PRODUCT OF ANY TWO NUMBERS IS EQUAL TO THE PRODUCT OF i THEIR HCFo AND LCM n IRRATIONAL NUMBERS a l RATIONAL NUMBERS ers DECIMAL REPRESENTATION b PROVING 3 or 5 + 8 IS AN IRRTIONAL NUMBER m n nu l u na DECIMAL REPRESENTATIONREAL NUMBER o i t a R m IS A RATIONAL OF THE FORM WHERE THE b PRIME FACTORISATION OF q IS OF THER e FORM 2 n 5 m r s MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

POLYNOMIALS Linear polynomial Zeros: one Quadratic polynomial Zeros: two Cubic polynomial Zeros: three MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL Intersects x-axis at one point Intersects x-axis at two points Intersects x-axis at three points COEFFECIENT OF A POLYNOMIALS ax 2 + bx + c -b/a WORD PROBLEMS ax 3 + bx 2 + cx + d -b/a QUADRATIC POLYNOMIAL c/a CUBIC POLYNOMIAL c/a DIVISION ALGORITHM p(x) g(x) q(x) r(x) -d/a

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES a 1 x+b 1 y+c 1=0 TEST FOR CONSISTENCY a 2 x+b 2 y+c 2=0 Condition Inference Consistency Geometrical a 1/a 2 ≠ b 1/b 2 Unique solution consistent intersecting a 1/a 2 = b 1/b 2 ≠ c 1/c 2 Infinitely many solutions consistent coincident a 1/a 2 = b 1/b 2 = c 1/c 2 No solutions inconsistent parallel Substitution method Elimination method Cross- multiplication method MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL rd s o W lem b pro

SI TRI MILA AN R GL ES S GLE AN I R T SSS AAA SAS *PROBLEMS* **RIDERS** T H E O CONVERSE BPT R OF BPT E M S H T CONVERSE OF PYTHAGORAS THEOREM EO R EM S PYTHAGORAS THEOREM MIND MAP. -CLASS- XG. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

circles Sec ant . to t n e a e l circ of c ircle g Tan pr ob le m s THEOREMS. MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

Introduction to trigonometry Trigonometric Ratios e s u n e t o p y h O p p o s i t e s i d e A Adjacent side 1. 2. 3. • Sin (90° - A) = Cos A • Cos (90° - A) = Sin A • Tan (90° - A) = Cot A • Cot (90° - A) = Tan A Trigonometric Identities • Sec (90° – A) = Cosec A • Cosec (90° - A) =Sec A Cos² A + Sin² A Sec² A – Tan² A Value of sin A or cos A never exceeds 1 Value of sec A or cosec A is always greater than 1 =1 =1 Cosec² A – Cot² A = 1 MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

Some Applications of Trigonometry ght i s f o tion a Line v e l of e e l g n A Horizontal level Angle of d epression Line of si ght Theodolite is e an instrument to find out horizontal or vertical angles and thus enable us to find heights and distances of objects in our daily life. Line of sight • Line drawn from the eye of an observer to the point in object viewed. Angle of elevation Angle of depression • Angle between line of sight and horizontal level. • Above horizontal • Angle formed between line of sight and horizontal level. • Below horizontal MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

Direct method Assumed Mean method Step deviation method Mode Median Less than Empirical formula of central tendency 3 Median = Mode + 2 Mean More MIND MAP. . . G. GIRIDHARA GOPAL than KENDRIYA VIDYALAYA KURNOOL Ogive curve

Experimental Theoretical Number of trials in which the event happened Total number of trials (Classical) Number of outcomes favourable to Event Number of all possible outcomes of experiment Elementary event Tossing 1 coin • 2¹ • = 2 • 2 outcomes • (Sample Space) Tossing 2 coins • 2² • = 4 • 4 outcomes • (Sample Space) Tossing 3 coins • 2³ • = 8 • 8 outcomes • (Sample Space) MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL P(E) + P ( ) = 1 = Not E

Quadratic Equations General form: ax²+bx+c > 0 descreminant • Roots are real distinct • = 0 Roots are distinct • Roots are real and equal • Roots are equal <0 • Roots are not real Factorisation Method MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL

Thank You MIND MAP. . . G. GIRIDHARA GOPAL KENDRIYA VIDYALAYA KURNOOL