Visit www.eduNgr.com for career and educational resources, guides and tips. Mathematics Formula Free educational resources Algebra Formula (a + b)2 = a2 + 2ab + b2 (a − b)2 = a2 − 2ab + b2 a2 + b2 = (a + b)2 − 2ab a2 + b2 = (a − b)2 + 2ab (a + b)3 = a3 + b3 + 3ab(a + b) (a − b)3 = a3 − b3 − 3ab(a − b) a3 + b3 = (a + b)3 − 3ab(a + b) Visit www.eduNgr.com for career and educational resources, guides and tips. 3 www.eduNgr.com 3+ career and3ab(a educational aVisit − b3 = (a −for b) −resources, b) guides and tips. a2 − b2 = (a + b)(a − b) a3 − b3 = (a − b)(a2 + ab + b2) a3 + b3= (a + b)(a2 − ab + b2) a4 – b4 = (a2 – b2)(a2 + b2) = (a + b)(a + b) (a2 + b2) a4 + b4 = (a2 + b2)2 – 2a2b2 = (a2 + √2ab + b2)(a2 – √2ab + b2) a5 + b5 = (a + b)(a4 – a3b + a2b2 – ab3 + b4 ) a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4) an − bn = (a − b)(an−1 + an−2 b + an−3 b2 + ··· + bn−1n−1) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) Visit www.eduNgr.com for career and educational resources, guides and tips. 3 www.eduNgr.com 2 + and career and aVisit + b3 + c3 –for 3abc =educational (a + bresources, + c)(aguides b2tips.+ c2 – ab – bc – ca) If a + b + c = 0, then the above identity reduces to a3 + b3 + c3 = 3abc Statistics Math Formulas SETS : A = {2, 3, 4, 7, 8, 9, 12} 3∈A Visit www.eduNgr.com for career and educational resources, guides and tips. 5 ∉VisitAwww.eduNgr.com for career and educational resources, guides and tips. SUBSET: B = {3, 8, 9} ⇒ B ⊆ A C = {1, 5} ⇒ C ⊄ A STATISTICS : MEAN : The mean value is obtained the arithmetic mean or average of a set of numbers Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. is expected value. The mean value is calculated by adding up all the values, and then dividing that sum by the number of values . Mean = Sum of all data values / Number of data values Symbolically , Where (read as ” x bar”) is the mean of the set of x values, Σ x is the sum of all the x values, and n is the number of x values. Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. MEDIAN : The median is the middle value in a set of values. So to find the midian you need to order the numbers from largest to smallest and then you have to choose the value in the middle. MODE : Mode is the value that the highest frequency in the data set.means values that occur most frequently and there can be more than one mode in a set. Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career educational resources, guides and tips. numerical value thatandoccurs most of the times. F (Xmode) = max INTERSECTION : In intersection A ∩ B of two sets A and B is the set that contains all elements of B also belong to A (or similarly all elements of B that also belong to A) but no other elements. The symbol intersection is inverted U. Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com career and educational resources, guides tips. B If Set A containforelement A = {1,2,3} andandset contains B = {2,3,4} and the element in having common ares 2 and 3 and this intersection area formed a new set containing 2 and 3. UNION : The union of two sets A and B includes all elements which are members of either A or B. If sets A and B have any elements in common then this elements which are members of both sets are only include one in the union. Visit www.eduNgr.com for career and educational resources, guides and tips. www.eduNgr.com resources, and tips. ForVisitexample : for Ifcareer setsandAeducational contains theguides elements 1,2, and 3 and set B contains 2,3 and 4 the elements which are members of A or B are 1,2,3 and 4. This form a new set containing 1,2,3 and 4. when we write the union 2 and 3 are only listed once. RELATIVE COMPLEMENT OF A IN B : The relative complement of A in B denoted, B \ A, is the set of elements in B but not in A. Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com educational Symbolically :Bfor \career A =and{x | x ∈resources, B ∧ xguides ∉ and A}tips. ABSOLUTE COMPLEMENT : In a Set theory a complement of a set A refers to things not in A. Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. SYMMETRIC DIFFERENCE : Operations on sets : A∪A=A A∩A=A A∪B=B∩ A A∩B=B∩A Visit www.eduNgr.com for career and educational resources, guides and tips. for career and ∪ educational (AVisit ∪ www.eduNgr.com B) ∪ C = A ∪ (B C) resources, guides and tips. (A ∩ B) ∩ C = A ∩ (B ∩ C) ∪′ = ø (A′)′ = A A∩ø=ø A∩U=A A ∩ A′ = ø (A ∪ B)′ = A′ ∩ B′ (A ∩ B)′ = A′ ∪ B′ Visit www.eduNgr.com for career and educational resources, guides and tips. Geometry Formula Visit www.eduNgr.com for career and educational resources, guides and tips. P = Perimeter A = Area S = Side d = diameter P=4xs A = S2 d = a x √2 Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. Rectangle P = Perimeter A = Area d = diameter P=2x(a+b) A=axb d = √a2 + b2 Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. Triangle P = Perimeter A = Area P=a+b+c A=bxh/2 A = √s(s-a)(s-b)(s-c); Visit www.eduNgr.com for career and educational resources, guides and tips. s =Visit a www.eduNgr.com + b + c / 2for=career p / and 2.educational resources, guides and tips. α + β + γ = 180o Circle P = Perimeter A = Area Visit www.eduNgr.com for career and educational resources, guides and tips. www.eduNgr.com for career and educational resources, guides and tips. P =Visit2πr A = πr2 π = 3.14 Parallelogram P = (a + b) x 2 P = 2a + 2b Visit www.eduNgr.com for career and educational resources, guides and tips. www.eduNgr.com A =Visitbh = ab sinforαcareer and educational resources, guides and tips. Circular Sector L = πr = θ / 180 0 A = πr2 θ/360 0 Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. Pythagorean Theorem : a2 + b2 = c2 c = √a2 + √b2 Circular Ring Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. A = π (R2 – r2) Sphere 2 S =Visit4πr www.eduNgr.com for career and educational resources, guides and tips. 2/3 www.eduNgr.com for career and educational resources, guides and tips. V =Visit4πr Trapezoid P=a+b +c+d A=hx a+b/2 Rectangular Box Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. A = 2ab + 2ac + 2bc V = abc Right Circular Cone : Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. A = πr2 + πrs S = √r2 +√h2 V = 1 x πr2 h / 3 Cube Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. A = 6l2 V = l3 Cylinder A =Visit2πr( r + h) www.eduNgr.com for career and educational resources, guides and tips. 2h for career and educational resources, guides and tips. V =Visitπrwww.eduNgr.com Frustum of a Cone V = 1 x πh (r2 + rR + R2) / 3 Visit www.eduNgr.com for career and educational resources, guides and tips. Trigonometry Formula Visit www.eduNgr.com for career and educational resources, guides and tips. Trigonometry Function Formulas of a Right Triangle : sin α = a / c = opposite / hypotenuse cos α = b / c = adjacent / hypotenuse tan α = a / b = opposite / adjacent cot α = b / a = adjacent / opposite Visit www.eduNgr.com for career and educational resources, guides and tips. resources, secVisitα www.eduNgr.com = c / b for career and educational Cosec α =guides c / and a tips. Basic Formula : sin2 α + cos2 α = 1 tan α . cot tan α = 1 tan α = sin α / cos α = 1 / cot tan α cot tan α = cos α / sin α = 1 / tan α 1 + tan2 α = 1 / cos2 α = sec2 α 1 + cot tan2 α = 1 / sin2 α = cos sec2 α Visit www.eduNgr.com for career and educational resources, guides and tips. Trigonometric Table Visit www.eduNgr.com for career and educational resources, guides and tips. 00 0 1 0 ∞ 1 ∞ α sin α cos α tan α cot α sec α cosec α 300 1/2 √3/2 1/√3 √3 2/√3 2 450 √2/2 √2/2 1 1 √2 √2 600 √3/2 1/2 √3 1/√3 2 2/√3 900 1 0 ∞ 0 ∞ 1 1200 √3/2 -1/2 -√3 -1/√3 -2 2/√3 1800 0 -1 0 ∞ -1 ∞ 2700 -1 0 ∞ 0 ∞ -1 3600 0 1 0 ∞ 1 ∞ Co-Ratios 900 – α sin -sin α +cos α cos +cos α +sin α tan -tan α +cot α cot -cot α +tan α 900 + α +cos α -sin α -cot α -tan α 1800 – α +sin α -cos α -tan α -cot α 1800 + α -sin α -cos α +tan α +cot α 2700 – α -cos α -sin α +cot α +tan α 2700 + α -cos α +sin α -cot α -tan α 3600k – α -sin α +cos α -tan α -cot α 3600k – α +sin α +cos α +tan α +cot α -α Visit www.eduNgr.com for career and educational resources, guides and tips. Trigonometry Addition Visit www.eduNgr.com for career and educational resources, guides and tips. Formula: sin(A + B) = sinA cosB + cosA sinB sin(A – B) = sinA cosB – cosA sinB cos(A + B) = cosA cosB – sinA sinB cos(A – B) = cosA cosB + sinA sinB tan (A + B) = tanA + tanB / 1 – tanA tanB tan(A – B) = tanA – tanB / 1 + tanA tanB Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com career and educational and tips. cot (A+ B) =forcotA cotB – 1resources, / cotAguides + cotB Product of Trigonometric Functions: sin α cos β = 1/2 [ sin (α + β) + sin(α – β)] cos α cos β = 1/2 [ sin (α + β) + sin(α – β)] cos α cos β = 1/2 [ cos (α + β) + cos(α – β)] sin α sin β = 1/2 [ cos (α – β) + cos(α + β)] Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com career tips. tan α tan β = fortan α and + educational tan β / resources, cot tanguides α +andcot tanβ = – tanα – tan β / cot tan α – cot tan β Trigonometric Formula with t = tan(x/2) sinx = 2t / 1 + t2 cos x = 1 – t2 / 1 + t2 tan x = 2t / 1 – t2 cot x = 1 – t2 / 2t Visit www.eduNgr.com for career and educational resources, guides and tips. Visit www.eduNgr.com for career and educational resources, guides and tips. Trigonometric Relation Between Functions: Visit www.eduNgr.com for career and educational resources, guides and tips. Angle of a Plane Triangle : Visit www.eduNgr.com for career and educational resources, guides and tips. A, B, C are 3 angles of a triangle sin A + sin B + sin c = 4 cos(A / 2) cos(B/2) cos(C/2) cosA + cos B + cos C = 4 sin(A/2) sin(B/2) sin(C/2) + 1 sinA + sinB – sinC = 4sin (A/2) sin (B/2) cos (C/2) Sources Visit the sources: math-shortcut-tricks.com byjus.com/math-formulas mathportal.org/mathformulas.php Visit www.eduNgr.com for career and educational resources, guides and tips.