MATH

interior angle sum

(n-2) x 180

singular interior angle

((n-2)x180)/n

n (number of sides)

360/ext

exterior angle

360/n

question only provides one angle (int/ ext). how to find other angle?

interior + exterior = 180

- subsitute

vertically oppsite angles are..

equal

corresponding angles are..

equal

alternate angles are..

equal

co interior angles equal..

180

lie between two lines and on the same side of a transversal.

supplementary

add up to 90 degrees

complementary

add up to 180

cos law finding angle

cos law finding side

sine rule finding sides

sine rule finding angles

sin A/a = sin B/b = sin C/c

non right angle triangle area formula

½ ab sin c

area of a circle formula

circumference of a circle

2πR

quadratic formula

FOIL

A method for expanding to brackets, where the first, outer, inner, and last terms are multiplied and then summed.

3 things you need to rmb about bearings

• 3 figures

• clockwise direction (measured in)

• start measuring from north

how to use a protractor

Line up the vertex of the angle with the dot at the center of the protractor.

Line up one side of the angle with 0 degrees on the protractor.

Read the protractor to see where the other side of the angle crosses the number scale.

cases when you use sine rule

• 2 sides known and non included angle (pairing)

• 2 angles and 1 side known

pairing

cases when you use cosine rule

• two sides and included angle

• all 3 sides known

how to correctly label a triangle

Label the vertices with capital letters and the sides with lowercase letters corresponding to the opposite vertices.

arc length formula

arc area formula

how to factorise a quadratic

how to recognize diff of squares

• when both term are squared numbers and are being subtracted

eg x²-9 -? (x+3) (x-3)

factor

x+6x+8=0

1. multiply coefficent of x and 8 = 8

2. find 2 numbers that multiply to 8 but also add up to 6

3. rewrite the middle term (6x) with said numbers

4. factorize in groupings

final answer: _(__) ± _(__)

semi circle area

½ π r²

semi circle perimter

½ π x diameter+diameter

area of a circle

πr²

circle circumference

2πr

trapezium area

½ (A+B)xh

perimeeter parallellogram

2(a+b)

area parralelogram

base x height

b x a x sindelta

Cylinder SA curved

curved surface area = 2πrh

cylinder total SA

total surface area = 2πr(h + r)

cone surface area curved

curved surface area = πrl

where l = √(r² + h²)

cone TSA

total surface area = πr(l + r)

sphere SA

Surface area = 4πr²

pyramid SA

Base area + area of the shapes in the sides

rectangular prism/cuboid SA

Surface area = 2(lb + bh + lh)

cube SA

Surface area = 6l²

hemisphere curved SA

Curved surface area = 2π r²

hemisphere volume

Volume = (2/3)πr³

cube volume

Volume = l³

cuboid volume

Volume = l × w × h

pyramid volume

Volume = (1/3) × base area × perpendicular height

sphere volume

Volume = (4/3)πr³

Volume, V, of prism, cross-sectional area A, length 1.

AxL

cone volume

v= 1/3pi r² x h

pythagoras

a²+b²=c²

c is hypothenuse

cube roots from 1-10

square roots from

how to round in significant figures eg, 2 sig. figures

• identifiy first 2 significant figure digits (non 0 digits)

• look at number next to said digit

  • if said number is 5 or above, change the digit before it to one up

  • if number is 4 or below, keep the digit

• if the original number is a decimal, the rest of the digits arent needed

• if the original number is a whole number, replace the digits with zeros

inches to cm

multiply the length value by 2.54

cm to inches

divide the length value by 2.54

km to m

multiply the length value by 1000

m to km

/1000

liter to ml

x1000

ml to l

/1000

during conversions, when the unit gets bigger eg (m to km), you __

divide

during conversion when the unit eg (km to m) gets smaller, you___

multiply

if you are converting to a small unit, you need lots of them so you __

multiply

if converting to a larger unit, you need less of them so you __

divide

cm to mm

x10

mm to cm

/10

g to kg

divide the mass value by 1000

kg to g

x1000

Method:

• Divide coefficients normally.

• Apply the rule 1yn=y−nyn1​=y−n if negative exponents are allowed.

percentage change formula

(change/og)x100

percentage increase formula

• find percentage of said number

• add result to said number

percenatge decrease formula

• find percentage of said number

• minus result to said number