Maths formulas

=( =(ab)n If an=a m If n even & an=b n If n odd & an=bn If m even & If m odd & If ax=y where x,a,y If f(x)=f(-x) If f(x) is a polynomial function If f(x) = where N(x) and G(x) are polynomial If f(x)= TRIGONOMETRY SINE RULE COSINE Rule ; CosA= sin A cos A= A Sin(-X)=-sin(X) Tan(-X)=-tan(X) cos(-X)=cos(X) in any triangleABC: A+B=180-C THEN SIN(A+B)=SINC COS(A+B)=-COSC ,TAN(A+B)=-TANC IF one angle is obtuse then the other two are acute Pythagorean Theorem If c22+a2 then is obtuse If c2b2+a2 then is acute AREA AND VOLUME S.A of circle= Circumference=2 S.Aof Surface area of triangle Volume of the cube=x3 Total surface area=6x2 Volume of cuboid=lwh Total surface area of cuboid=2(lw+lh+wh) Volume of sphere=r3 Surface area of sphere=4r2 Linear Equation Slope –intercept form: y=mx+c m=slope;b=y-intercept 2.point-slope form : y-y1=m(x-x1) 3.standard form : ax+by=c m= 4.Slope(m)= If if If If At x-axis y=0, AT y-axis x=0 Slope of tangent=of the curve at the point of tangency=m Slope of the normal= Distance between two points= Mid-point=(,) If If At x-axis y=0, AT y-axis x=0 Slope of tangent=of the curve at the point of tangency=m Slope of the normal= If U=f(x) and V=g(x) The variation Variation function f(x2)-f(x1) V(x)=f(+h) Average rate of change function A(h)== A(h)= Rate of change= LIMIT 1-cosA=2sin2 1-cos2A=sin2A CosA=sin( CosA=-sin( SinA=sin( sinA=-sin( sinA=-sin(2 tanA=-tan( tanA=tan tanA=-tan(2 cotA=tan cotA=-tan cotA=-tan cotA=tan ARITHEMATIC SEQUENCE A.S.(a,a+d,a+2d,a+3d,…….) ,d The general form of an A.S (1)A.S (a , a + d , a+2d , ……., L - 2d. l- d, L) a= First term d= Difference L Last term (2)The General term (3) The number of terms = order of the last term (4)To get the first "last"negative term Solve 0 (5) To get the first"last"positive term Solve Tn˃o (6) The order of the middle term = (7)Arithmetic mean(A.M.) A.S b is called A.M of a and c i.e. 2T2=T1+T3 (8)IF a and L are two numbers to insert n A.Ms between a and L L=Tn+2 (9)IF a and L are two numbers with n A.M between them A.S (a, a+d, a+2d, a+3d,………,L-3d, L-2d, L-d, L) A.M 1ST 2nd 3rd (n-2) (n-1) nth (10)The sum of n terms of an A.S Where : n = number of terms Sum of n terms a = starting term “ not always ” L = last term = (11)THREE NUMBERS IN AN A.S. a- d, a , a+d (12)FOUR NUMBERS IN AN A.S. a-3d , a-d ,a+d , a+3d (13)THE MAXIMUM SUM =THE SUM OF THE POSITIVE TERMS