SSC TRICKS FOR MATHS

CUBE d = side VOLUME : V = d^2 SURFACE AREA : S = 6(d^2) RECTANGULAR SOLID l = length, w = width, h = height VOLUME: V = lwh SURFACE AREA : S = 2lw + 2lh + 2wh SPHERE r = radius VOLUME : V = 4/3*pi*r^3 SURFACE AREA : S = 4*pi*r^2 RIGHT CIRCULAR CYLINDER r = radius, h = height VOLUME : V = pi*r^2*h SURFACE AREA : S = 2*pi*r*h + 2 *pi*r^2 TORUS r = tube radius, R = torus radius VOLUME : V = 2*pi^2*r^2*R SURFACE AREA : S = 4*pi^2*r*R PYRAMID A = area of base , h = height VOLUME : V = 1/3*A*h RIGHT CIRCULAR CONE r = radius, h = height VOLUME : V = 1/3*pi*r^2*h SURFACE AREA : S = pi*r*[sqrt(r^2 + h^2)] + pi*r^2 FRUSTUM OF A CONE r = radius, R = base radius, h = height, s = slant height VOLUME : V = pi/3(r^2 + rR + R^2)h SURFACE AREA : S = pi*s(R+r) + pi*r^2 + pi*R^2 SQUARE PYRAMID s = side, h = height VOLUME : V = ...

CIRCLE r = radius; d = diameter DIAMETER : d = 2r AREA : A = (pi) r^2 CIRCUMFERENCE : C = 2(pi)r = (pi)d SECTOR r = radius; angle(AOB) = angle in radius AREA : A = 1/2 (pi) r^2 ARC LENGTH : s = angle(AOB) r ELLIPSE a = semimajor axis b = semiminor axis AREA : A = (pi) ab CIRCUMFERENCE : C = (pi)[3(a+b) - sqrt{(a+3b)(b+3a)} ANNULUS  (COCENTRIC CIRCLES) r = inner radius, R = outer radius AVERAGE RADIUS = 1/2(r+R) WIDTH : w = R-r AREA : A = pi(R^2 - r^2) or A = 2*pi*22/7*average radius*width REGULAR POLYGON s = side length, n = number of sides CIRCUMFERENCE : R = 1/2*s*cos(pi/n) AREA : A = 1/4*n*s^2*cot(pi/n) or A = 1/2*n*R^2*sin(2*pi/n)

SOME RESULTS ON CIRCLES THEOREM 1. IF TWO ARCS OF A CIRCLE ARE CONGRUENT THEN THE CORRESPONDING CHORDS ARE EQUAL. THEOREM 2. THE PERPENDICULAR FROM THE CENTRE OF A CIRCLE TO A CHORD BISECT THE CHORD. THEOREM 3.  THE LINE JOINING THE CENTRE TO THE MID POINT OF A CHORD IS PERPENDICULAR TO THE CHORD. THEOREM 4.  THE PERPENDICULAR BISECTORS OF THE CHORDS OF A CIRCLE INTERSECT AT ITS CENTRE. THEOREM 5.  THERE IS ONE AND ONLY ONE CIRCLE PASSING THROUGH THREE NON COLLINEAR POINTS. (I) AN INFINITE NUMBER OF CIRCLE CAN BE DRAWN TO PASS THROUGH A SINGLE POINT. (II) AN INFINITE NUMBER OF CIRCLE CAN BE DRAWN TO PASS THROUGH TWO GIVEN POINTS. (III) A UNIQUE CIRCLE CAN BE DRAWN TO PASS THROUGH THREE GIVEN NON COLLINEAR POINTS. THEOREM 6.  EQUAL CHORDS OF CONGRUENT CIRCLES ARE EQUIDISTANT FROM THE CORRESPONDING CENTRES ARE EQUAL. THEOREM 7. CHORDS WHICH ARE EQUIDISTANT FROM THE CORRESPONDING CENTRES ARE EQUAL. THEOREM 8.  EQUAL CHORDS OF A ...

FATHER OF ALGEBRA IMPORTANT FORMULAE OF ALGEBRA 1. (a+b)^2 = a^2 + b^2 + 2ab 2. (a-b)^2 = a^2 + b^2 - 2ab 3. (a+b)^2 = (a-b)^2 + 4ab 4. (a-b)^2 = (a+b)^2 - 4ab 5. a^2 - b^2 = (a-b)(a+b) 6. a^3 + b^3 = (a+b)(a^2 + b^2 - 2ab) 7. a^3 - b^3 = (a-b)(a^2 + b^2 + 2ab) 8. (a+b)^3 = a^3 + b^3 + 3ab(a+b) 9. (a-b)^3 = a^3 - b^3 - 3ab(a-b) 10. a^3 + b^3 = (a+b)^3 - 3ab(a+b) 11. a^3 - b^3 = (a-b)^3 + 3ab(a-b) 12. a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ac)                                         OR       a^3 + b^3 + c^3 - 3abc = (a+b+c)1/2{2(a^2) + 2(b^2) + 2(c^2) - 2ab -2bc -2ac}                                         OR ...

SQUARE 1. PERIMETER = 4 * side = 4 * a  WHERE a = SIDE OF SQUARE 2. AREA = (side)^2 3. DIAGONAL = side * sqrt(2) 4. AREA OF THE PATH WHICH IS OUTSIDE OF SQUARE = 4 * (a + x) 5. AREA OF THE PATH WHICH IS INSIDE OF SQUARE = 4 * (a - x) WHERE x = WIDTH OF THE PATH TRAPEZIUM IT IS A QUADRILATERAL WHOSE OPPOSITE SIDES ARE PARALLEL. OTHER TWO OPPOSITE SIDES ARE OBLIQUE. 1. AREA = 1/2 * HEIGHT * (SUM OF PARALLEL SIDES)   HEIGHT IS THE DISTANCE BETWEEN THE TWO PARALLEL SIDES 2. MEDIAN = 1/2 * (SUM OF PARALLEL SIDES) MEDIAN IS THE SEGMENT JOINING THE MIDPOINTS OF OBLIQUE SIDES RHOMBUS IT IS PARALLELOGRAM WHOSE ALL SIDES ARE EQUAL.  ITS DIAGONALS BISECT EACH OTHER AT RIGHT ANGLE. 1. AREA = 1/2 * PRODUCT OF DIAGONALS 2. SIDE = sqrt {(D1/2)^2 + (D2/2)^2} 3. PERIMETER = 4 * SIDE WHERE D1 AND D2 ARE DIAGONALS

TRIANGLE 1. AREA = 1/2*BASE*HEIGHT   OR, √[s(s-a)(s-b)(s-c)] WHERE a, b, c  ARE THE LENGTHS OF THE SIDES OF TRIANGLE AND  s=(s+b+c)/2 2. AREA OF AN EQUILATERAL TRIANGLE =  √3/4 * (side)^2 3. AREA OF AN ISOSCELES TRIANGLE = b/4  √4(a^2)-(b^2) 4. PERIMETER OF AN EQUILATERAL TRIANGLE = 3 * SIDE RECTANGLE 1. AREA = LENGTH * BREADTH 2. PERIMETER = 2 (LENGTH + BREADTH) 3. DIAGONAL =  √(LENGTH)^2 + (BREADTH)^2 4. AREA OF PATH (OUTSIDE THE RECTANGLE) = 2 * (LENGTH + BREADTH + 2x) WHERE x= WIDTH OF THE PATH 5. AREA OF THE PATH INSIDE OF THE RECTANGLE = 2 * (LENGTH + BREADTH -2x) WHERE x= WIDTH OF THE PATH