\r\n| \r\n Natural Numbers<\/span><\/p>\r\n<\/td>\r\n | \r\n N ={ 1, 2,3,4,5 \u2026 }\u00a0<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n| \r\n Whole Numbers\u00a0<\/span><\/p>\r\n<\/td>\r\n | \r\n W={ 0, 1, 2, 3, 4, 5\u2026 }<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n| \r\n Rational Numbers<\/span><\/p>\r\n<\/td>\r\n | \r\n Those numbers that can be presented as a\/b are called Rational Numbers.\u00a0<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n| \r\n Real Numbers\u00a0<\/span><\/p>\r\n<\/td>\r\n | \r\n Real Numbers can be found on a number line\u00a0<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n| \r\n LCM (P, Q, R)<\/span><\/p>\r\n<\/td>\r\n | \r\n P.Q.R.H.C.F(P, Q, R) \/ [HCF ( P, Q) . HCF( Q, R). HCF ( P, R)]<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n| \r\n HCF (P, Q, R)<\/span><\/p>\r\n<\/td>\r\n | \r\n P.Q.R.L.C.M(P, Q, R) \/ [LCM ( P, Q). LCM ( Q, R). LCM ( P, R)]<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nChapter 2 – Polynomials\u00a0<\/b><\/h3>\r\n\r\n- (a+b)<\/span>2<\/span> = a<\/span>2<\/span>+2ab+b<\/span>2<\/span><\/li>\r\n
- (a\u2212b)<\/span>2<\/span>=a<\/span>2<\/span>\u22122ab+b<\/span>2<\/span><\/li>\r\n
- (x+a)(x+b) = x<\/span>2<\/span>+(a+b)x+ab<\/span><\/li>\r\n
- a<\/span>2<\/span>\u2212b<\/span>2<\/span> = (a+b)(a\u2212b)<\/span><\/li>\r\n
- a<\/span>3<\/span>\u2212b<\/span>3<\/span> = (a\u2212b)(a<\/span>2<\/span>+ab+b<\/span>2<\/span>)<\/span><\/li>\r\n
- a<\/span>3<\/span>+b<\/span>3<\/span> = (a+b)(a<\/span>2<\/span>\u2212ab+b<\/span>2<\/span>)<\/span><\/li>\r\n
- (a+b)<\/span>3<\/span> = a<\/span>3<\/span>+3a<\/span>2<\/span>b+3ab<\/span>2<\/span>+b<\/span>3<\/span><\/li>\r\n
- (a\u2212b)<\/span>3<\/span> = a<\/span>3<\/span>\u22123a<\/span>2<\/span>b+3ab<\/span>2<\/span>\u2212b<\/span>3<\/span><\/li>\r\n<\/ul>\r\n
Chapter 3 –\u00a0 Pair of linear equations in two variables<\/b><\/h3>\r\n\r\n\r\n\r\n| \r\n Linear equations in one, two, and three variables have the following forms:<\/span><\/p>\r\nLinear Equation in one Variable ax + b=0 Where a \u2260 0 and a & b are real numbers<\/span><\/p>\r\nLinear Equation in Two Variables ax + by + c = 0 Where a \u2260 0 & b \u2260 0 and a, b & c are real numbers<\/span><\/p>\r\nLinear Equation in Three Variables ax + by + cz + d = 0 Where a \u2260 0, b \u2260 0, c \u2260 0 and a, b, c, d are real numbers<\/span><\/p>\r\nThe pair of linear equations in two variables are given as:<\/span><\/p>\r\na1x+b1+c1=0 and a2x+b2+c2=0<\/span><\/p>\r\nWhere a1, b1, c1, & a2, b2, c2 are real numbers & a12+b12 \u2260 0 & a22 + b22 \u2260 0<\/span><\/p>\r\nQuick Note: Linear equations can also be represented in graphical form.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nChapter 4 – Algebra & Quadratic Equations<\/b><\/h3>\r\n\r\n\r\n\r\n| \r\n To know the algebra formulas for Class 10, first, you must get familiar with Quadratic Equations.<\/span><\/p>\r\nThe Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:<\/span><\/p>\r\nNow you know the basic quadratic equation.<\/span><\/p>\r\nLet us now go through the list of algebra formulas for Class 10\u2013<\/span><\/p>\r\n(a+b )\u00a0 = a+ b22 + 2ab<\/span><\/p>\r\n(a-b)2 = a2 + b2\u2013 2ab<\/span><\/p>\r\n(a+b) (a-b) = a2 \u2013 b2<\/span><\/p>\r\n(x + a)(x + b) = x2 + (a + b)x + ab<\/span><\/p>\r\n(x + a)(x \u2013 b) = x2 + (a \u2013 b)x \u2013 ab<\/span><\/p>\r\n(<\/span>a<\/span><\/i> +b)3 = a3+\u00a0 b3 + 3ab(a + b)<\/span><\/p>\r\n(<\/span>a<\/span><\/i>-b)3 = a3 \u2013\u00a0 b3 \u2013 3ab(a \u2013 b)<\/span><\/p>\r\n(x \u2013 a)(x + b) =\u00a0 x2 + (b \u2013 a)x \u2013 ab<\/span><\/p>\r\n(x \u2013 a)(x \u2013 b) = x2 \u2013 (a + b)x + ab<\/span><\/p>\r\n(x + y +z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz<\/span><\/p>\r\n(x + y \u2013 z)2 =\u00a0 x2 +\u00a0 y2 +\u00a0 z2 + 2xy \u2013 2yz \u2013 2xz<\/span><\/p>\r\n(x \u2013 y + z)2 = x2 +\u00a0 y2 +\u00a0 z2 \u2013 2xy \u2013 2yz + 2xz<\/span><\/p>\r\n(x \u2013 y \u2013 z)2 = x2 +\u00a0 y2 +\u00a0 z2\u2013 2xy + 2yz \u2013 2xz<\/span><\/p>\r\nx2 +\u00a0 y2 +\u00a0 z2 \u2013 3xyz = (x + y + z)(x2 +\u00a0 y2 +\u00a0 z2 \u2013 xy \u2013 yz -xz)<\/span><\/p>\r\ny2 +\u00a0 z2 =\u00bd [(x +y)2 + (x \u2013 y)2]<\/span><\/p>\r\n(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc<\/span><\/p>\r\n(x3 +\u00a0 y3= (x + y) (x2 \u2013 xy + y2)<\/span><\/p>\r\nx3 \u2013 y3 = (x \u2013 y) (x2 + xy + y2)<\/span><\/p>\r\nx2 +\u00a0 y2 +\u00a0 z2 -xy \u2013 yz \u2013 zx = \u00bd [(x-y)2 + (y-z)2 + (z-x)2]<\/span><\/p>\r\nQuick Note: These formulas will be important in higher classes and various competitive examinations. So, memorize them and understand them well.<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nChapter 5 – Arithmetic Progressions\u00a0<\/b><\/h3>\r\n\r\n- \r\n
\r\n- \r\n
\r\n- The nth term of AP = nth term = a + (n-1) d<\/span><\/li>\r\n
- Sum of n terms in AP = Sn = n\/2[2a + (n \u2212 1) \u00d7 d]<\/span><\/li>\r\n
- Sum of all terms in AP with the last term \u2018l\u2019 = n\/2(a + l)<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n
Chapter 6 – Triangles\u00a0<\/b><\/h3>\r\n\r\n- \r\n
\r\n- \r\n
\r\n- A = Area of Triangle<\/span><\/li>\r\n
- B = Base of Triangle<\/span><\/li>\r\n
- H = Height of a Triangle<\/span><\/li>\r\n
- Area of Triangle = A = \u00bd (b \u00d7 h) square units\u00a0<\/span><\/li>\r\n
- Area of an Isosceles Triangle = 1\/4 b\u221a(4a<\/span>2<\/span> \u2013 b<\/span>2<\/span>)<\/span><\/li>\r\n
- Area of a Right Triangle = A = 1\/2 \u00d7 Base \u00d7 Height<\/span><\/li>\r\n
- Area of an Equilateral Triangle = A = (\u221a3)\/4 \u00d7 side<\/span>2<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n
Chapter 7 – Coordinate Geometry\u00a0<\/b><\/h3>\r\n\r\n- \r\n
\r\n- \r\n
\r\n- Distance Formula to find distance between two points P(x1,y1) and Q(x2,y2) is = \u221a[(x2 \u2013 x1)2 + (y2 \u2013 y1)2 ]<\/span><\/li>\r\n
- Distance of a point P(x, y) from the origin is = \u221ax<\/span>2<\/span> + y<\/span>2<\/span><\/li>\r\n
- The coordinates of the point P(x, y) which divides the line segment joining the points A(x1 , y1 ) and B(x2 , y2 ) internally in the ratio m1 : m2 = Section Formula = ((m1x2 + m2x1)\/m1+ m2 , (m1y2 + m2y1)\/m1+ m2)<\/span><\/li>\r\n
- The midpoint of the line segment joining the points P(x1, y1) and Q(x2, y2 ) = [(x1+x2\/2), (y1+y2\/2)<\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n
Chapter 8 – Introduction to Trigonometry\u00a0<\/b><\/h3>\r\n | | | | | | | |