formulas Flashcards by Navya Sara Jaiswal

area of a triangle

0.5 x b x h

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the sum of a two triangles is more or less the other side

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the difference of two sides is more or less the other side

less

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what is the exterior angle rule of a triangle

two angles opposite to the exterior angle is equal

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angle opposite to the largest side is the ___

largest

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angle opposite to the smallest side is the ____

smallest

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when the power goes to the other side it becomes

the reciprocal

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d1 + d2
———— av speed?
T1 + T2

d1+d2/T1+T2

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S1 + S2
———— av speed?
T1 + T2

(s1 x t1) + (s2 x t2) / T1 + T2

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d1 + d2
———— av speed?
s1 + s2

d1 + d2 / (x1/v1) (x2/v2)

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when two objects move in same direction you ___ the speeds

subtract

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when two objects move in different direction you ___

the speeds

add

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mean

sum of all observations/ number of observations

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weighted mean
eg: if in one class 10 students get 90% and in second class 20 students gets 70% what would be the average of two classes

(10 x 90) + (20 x 70) / 30

( (average x number of students) + (average x number of students) ) / total number of students

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median

middle term - arrange in consecutive order. it is the (n+1)/2 th term if odd
if even it is the (n/2) and (n+1)/2 th terms average

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mode

most frequently repeated term

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circle formula if centre is (0,0)

A^2 + B^2 = R^2

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circle formula with any centre (h,k)

(x-h)^2 + (y-k)^2 = R^2

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area of circle

pi 2 squared

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circumference of circle

2 pi r

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when a tangent is drawn next to a circle the radius is…

perpendicular

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If two tangents are drawn by a circle and intersect at one point they are….

equal

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in a circle two lines are drawn (a+b) and (c+d), they intersect. What is the relation

a x b = c x d

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arc length in degrees

theta/360 x 2 pi r

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sector area in degrees

theta/360 x pi r square

from centre of a circle (a,b) a line is drawn that hits the circumference at (x,y) what is the relation?

x = a + r cos theta y = b + r sin theta (theta is taken from positive x axis in anti-clockwise direction)

distance formula

root ( x2 - x1 )^2 + (y2- y1)^2

mid point

coordinate is ( ( x1 + y2) / 2 , (y1 + y2) /2 )

slope

y2-y1/x2-x1

gradients of two perpendicular lines

negative reciprocal

area of rectangle

perimeter of rectangle

2(l+b)

in a rectangle are diagonals equal and bisect

yes at 90

parallelogram area

b x h

parallelogram perimeter

2 (b + h )

do diagonals bisect and are they equal in parallelogram

bisect (not a 90) but are not equal

rhombus perimeter

rhombus area

p x q / 2

trapezium area

(a + b)2 x h

sum of interior angles

(n-2) x 180

one angle in a regular polygon

180(n-2)/n

sum of exterior angles

360

volume and sa of cuboid

``` volume= l x b x h sa = 2(lb+bh+hl) ```

diagonal of cuboid from top left vertex to bottom right

root of l^2 + b^2 + h^2

volume and sa of cube

``` volume = a^3 sa = 6a^2 ```

sa of cone

pi r (slant height x radius)

sa of sphere

4 pi r squared

if a sphere is inscribed in a cube what is the diameter of a sphere

the length of the side of the cube

if a cuboid is inscribed in a sphere what is the diagonal fo the cuboid

diameter of sphere

volume of object immersed in water

base area of container x h (water amount rises)

i =

root - 1

i squared =

-1

i cubed =

-i

i ^ 4 =

how do you conjugate a complex number

change sign of imaginary number

when are two complex numbers equal

when both imaginary and real numbers are equal

how to find magnitude of complex number

root of imaginary squared + real squared

radian to degree

multiply by 180/pi

degree to radian

multiple by pi/180

length of arc in radians

theta into radius

area of sector in radians

theta/2 pi x pi r squared

cosec theta

1/sintheta

sec theta

1/cos theta

cot theta

1/ tan theta

unit circle order

CAST and SECACOSCOT

sin 90 - theta

cos theta

cos 90 - theta

-sin theta

adding c to all observations

mean median mode increase by c, SD and range is same

multiplying c to all observations

everything multiples by c

what is mean, sd, median and mode on calculator

x̅, σ, med, mod

best fit line on calculator ?

geometric progression

nth term = ar ^ (n-1) ``` a= first term n = number of terms r = common ratio ```

exponential growth equation

final - initial (growth multiplier) ^ (time required/time period)

arithmetic progression

a + (n-1) d ``` a= first term n= number of terms d = common difference ```

quadratic formula

-b plus minus root b squared - 4ac / 2a

how to complete the square

a (x+d) squared + e = 0 d = b/2a e = c - (b square/ 4a)