AREA (A)

Square : A = Side × side

Rectangle: A = Length × Breadth

Parallelogram: A = Base × Height

Triangle : A = ½ × base × height

Circle : A = лr2 where л = 3.14 and r = radius

Trapezium A = ½ × (sum of parallel sides)×height

Sphere A = 4лr2

Area of a triangle = √s(s – a) (s – b) (s – c)

S = a + b + c / 2

ALGEBRAIC IDENTITIES

(x + y)2 = x2 + y2 + 2xy

(x – y)2 = x2 + y2 – 2xy

X2 – y2 = (x + y) (x – y)

(x + a) (x + b) = x2 + (a + b)x + ab

5 (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

6. (x + y)3 = x3 + y3 + 3xy (x + y)

7. (x – y)3 = x3 – y3 – 3xy (x – y)

8. x 3 + y 3 + z 3 – 3 x y z = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)

9. x 3 + y 3 = (x + y) (x 2 + y 2 – xy)

10. x 3 – y 3 = (x – y) (x 2 + y 2 + xy)

SURFACE AREA (SA)

Cube SA = 6×2 where x = any side

Cylinder (lateral) SA = 2лrh where л = 3.14, r = radius,

h = height

Surface area of cuboid = 2(lb + bh + hl)

Curved Surface Area of a Cylinder = 2лrh

Total Surface Area of a Cylinder = 2лr(r + h)

Curved Surface of a Cone = лrl

Total Surface Area of a right circular cone = лrl + лr2 or лr(r + l)

Surface Area of a Sphere of radius r = 4лr2

Curved Surface Area of a Hemisphere = 2лr2

Total Surface Area of a Hemisphere = 3лr2

PERIMETER(P)

Square P = 4 x where x = any side

Rectangle P = 2(L + B) where L = length, B = breadth

Triangle P = a + b + c ; where a = first side, b = second side

C = third side

Circle (Circumference) C = лd or 2лr ; л = 3.14, d = diameter, r =radius

VOLUME(V)

Cube V = x3 where x = any side

Cuboid V = l × b × h where l =length, b = breadth,

H = height

Square pyramid V = 1/3 × b2 × h; where b = base length, h = height

Cylinder V = лr2h ; where л = 3.14, r = radius, h= height

Cone V = 1/3 лr2h; where л = 3.14, r = radius, h=height

Sphere V = 4/3 лr3 ; л = 3.14, r = radius

Hemisphere of a Sphere V = 2 / 3 лr3

Right Circular cylinder V = лr2h ; л = 3.14 r radius h = height

Volume of a frustum of a cone = 1 / 3 ԓ h (r12 + r22 + r1r2)

Curved surface area of a frustum of a cone = ԓ l (r1 + r2) ; where

L = √ h 2 + (r1 – r2) 2

Distance between two points d = √(x2 – x1)2 + ( y2 – y1)2

Slope of a line m = y2 – y1 / x2 – x1 where (x1,x2) and (y1,y2) points

Standard equation of circle = (x – h)2 + (y – k)2 = r2 ; wher r = radius , (h,k) is the center.

Quadratic formula ; x=(-b±√(b^2-4ac))/2a

Point Slop Equation of a line y – y1 = m(x – x1); where m is the slope

And (x1, y1) is the point.

Slpoe- Intercept Equation of a line y = mx + c ;

Where m is the slpoe and c is the y- intercept

PYTHAGOREAN

a 2 + b 2 = c 2 ; where a and b are legs and c is the hypotenuse of a

Right angle

STATISTICS

Mean = (x1 + x2 +…….xn) / N ; where x’s are the value for the mean

Mean = ∑ fi xi / ∑ fi

The assumed mean method ; x̅ = a + ∑ fi di / ∑ fi

The step deviation method ; x̅ = a + (∑ fi ui / ∑ fi) ×h

With the assumption that the frequency of a class is centred at its mid point, called its mark.

The mode for grouped data can be found by using the formula:

Mode = l + (f1 – f0 / 2 f1- f0 – f2) × h

Where symbols have their usual meanings

Median : It is the value of the middle-most observation

If n is an odd number, the median = value of the (n + 1 / 2)th

Observation

If n is an even number, median = Mean of the values of the (n / 2)th

And (n / 2 + 1)th observation.