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A=s²

Area of a square

C=2πr or C=πd

Circumference of a circle

A=lw or A=bh

Area of a Rectangle

A=bh

Area of a Parallelogram

A=½(b₁+b₂)h

Area of a Trapezoid

A=πr²

Area of a Circle

A=½bh

Area of a Triangle (use base and height)

A=(s²√3)÷4

Area of Equilateral Triangle

A=½d₁d₂

Area of a Rhombus

SA=4πr²

Surface Area of a Sphere

V=(4/3)πr³

Volume of a Sphere

V=lwh

Volume of a Rectangular Prism

V=πr²h

Volume of a Circular Cylinder

V=(1/3)πr²h

Volume of a Circular Cone

V=(1/3)Ah

Volume of a Pyramid (Use A for area of base)

nCr=n!÷(r!×(n-r)!)

Combinations

a²+b²=c²

Pythagorean Theorem

x(n-1)÷2

Used to find the nth row in Pascals Triangle (use x as the previous number)

opposite/hypotenuse

sine (SIN)

adjacent/hypotenuse

cosine (COS)

opposite/adjacent

tangent (TAN)

A=√s(s-a)(s-b)(s-c)

Area of a Triangle (use the side lengths)

A=½ab×sin(C)

Area of a Triangle (use two side lengths and the included angle)

c²=a²+b²-2ab×cos(C)

Find the third side of a triangle given two side lengths and the included angle

r²=(s-a)(s-b)(s-c)÷s

Find the radius of a circle inscribed in a triangle

-d-e-f

Find the coefficient of x² in a cubic polynomial (find a in x³+ax²+bx+c=0 with solutions d, e, and f)

de+df+ef

Find the coefficient of x in a cubic polynomial (find b in x³+ax²+bx+c=0 with solutions d, e, and f)

-def

Find the intercept in a cubic polynomial (find c in x³+ax²+bx+c=0 with solutions d, e, and f)

SA=6s²

Surface area of a cube

SA=2πr²+2πrh

Surface area of a cylinder

(l+w)!÷(l!w!)

Find the number of paths in a 2-D rectangle from one corner to the opposite corner without going backwards

(l+w+h)!÷(l!w!h!)

Find the number of paths in a 3-D rectangular prism from one corner to the opposite corner without going backwards

S÷n

Find the arithmetic mean of n quantities (use S for sum of quantities or P for product of quantities)

ⁿ√P

Find the geometric mean of n quantities (use S for sum of quantities or P for product of quantities)

t₁+d(n-1)

Find the nth term in an arithmetic sequence

t₁×rⁿ⁻¹

Find the nth term in a geometric sequence

A=½aP

Area of regular polygon (use P=perimeter)

y=mx+b

Line equation

Standard

ax+by=c

Discriminate

b2-4ac

exponential

domain-all real numbers

exponential growth

increase starts slowly then increases very quickly to infinity

exponential decay

decreasing very quickly, but never reaching zero

Half Life

N(t) = n° • e^ -kt

Compound Interest

A = P(1+r/n)^(nt)

Explicit Arithmatic

an = a1 + (n-1) x d

Geometric Explicit

a(n)=a x r to the n - 1

Vertex Form Quadradic

y=a(x times h) to the 2 + k

Standard Quadradic

ax squared + bx + c = fx

Exterior angle

angle on the outside of intersected parallel lines

Interior angle

angle on the inside of intersected parallel lines

Area of triangle

(1/2) b h

Area of parallelogram

B x H

Area of trapezium

1/2 x (total of parallel sides) x H

Area of circle

π x r2

Circumference of circle

π x D

Area of sector

Angle of sector / 360 x Area of circle

Length of arc

Angle of sector / 360 x Circumference of circle

Volume of cuboid

L x W x H

Volume of prism

Cross sectional area x length

Volume of sphere

V = 4/3πr^3

Volume of pyramid

1/3 x Base Area x H

Volume of cone

1/3 x π x r2 x H

Volume of frustum

V of origional cone - V of removed cone

Area of net

Surface area of solid

Surface area of sphere

4 x π x r2

Surface area of cone

(π x r x l) + (π x r2)

Surface area of cylinder

(2 x π x r x h) + (2 x π x r2)

Angles in a triangle

Add up to 180

Add up to 180

Angles on a straight line

Angles in a quadrilateral

Add up to 360

Angles round a point

Add up to 360

Exterior angle of a triangle

equals sum of opposite interior angles

isosceles triangle

Triangle with 2 equal sides and 2 equal angles.

When one straight line crosses two parallel lines

The two bunches of angles are the same

Are the same

Alternate angles (Z angles)

Supplementary angles (U angles)

Add up to 180

Sum of interior angles (irregular polygons)

(number of sides - 2) x 180

360

Sum of exterior angles (irrregular polygons)

Density

M / V

Mass

D x V

volume

M / D

m

The formula triangle for mass, density and volume would be?

Distance

S x T

Speed

D / T

Time

D / S

d

The formula triangle for distance, speed and time would be?

Pythagoras' theorem

a2 + b2 = h2

SOKATOA! 'soh cah toa'

What is the mnemonic word to decide which formula triangle to use trigonometry?

Sin Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent

What are the formula triangles known as 'soh cah toa'?

The sine rule

a / sinA = b / sinB = c / sinC

The cosine rule

a2 = b2 + c2 - 2bc COS A or

Probability-the AND rule

P of A and B happening is (P of A) times (P of B)

Probability-the OR rule

P of A or B happening is (P of A) add (P of B)

Rise / Run

slope

y=mx+c

What formula is used to determine where an x point meets a y point on a particular line?

plus then a minus

In factorising quadratic equations a minus and a minus makes a?

minus then a minus

In factorising quadratic equations, a minus then a plus makes a?

plus then a plus

In factorising quadratic equations a plus then a plus makes a?

What is a acute angle?

An angle between 0 and 90

What is a obtuse angle?

An angle between 90 and 180

What is a reflex angle?

An angle between 180 and 360

What is a right angle?

An angle that is exactly 90

-b±[√b²-4ac]/2a

Quadratic Formula

slope

(y₂-y₁)/(x₂-x₁)

Slope-Intercept

y=mx+b

a³-b³

(a-b)(a²+ab+b²)

a³+b³

(a+b)(a²-ab+b²)

a²-b²

(a-b)(a+b)

a²-2ab+b²

(a-b)²

a²+2ab+b²

(a+b)²

(a+b)(c+d)

ac+ad+bc+bd

a(b+c)

ab+ac

sine ratio

opposite ÷ hypotenuse

cosine ratio

adjacent ÷ hypotenuse

tangent ratio

opposite ÷ adjacent

always

|x| ≥ 0

y=kx

Direct Variation

y=k/x

inverse variation

y-y₁=m(x-x₁)

Point-Slope form

standard form

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

Undefined

tan 270

zero

When there is a horizontal line that has different x points, but the same y point

You must flip the sign

Dividing by a negative number in an inequality

dotted line

Graphing < or > on a coordinate plane

solid line

Graphing ≥ or ≤ on a coordinate plane

shade upwards or to the right

Graphing ≥ or > on a coordinate plane

shade downwards or to the left

Graphing ≤ or < on a coordinate plane

Infinitely many solutions

when the system of equations have the same slope and y-intercept

One Solution

Lines intersect at one point

No Solution

If an inquality is equivalent to an inequality that is false, such as 4 < -2.

linear functions

All direct variations are ____________________________________________

graphs

A linear function is a function that _____________________________ a line

Equation

A mathematical sentence that contains an equals sign

Linear parent function

y=x or f(x)=x

elimination method

The process of removing one of the variables in a system of equations using addition or subtraction in conjunction with multiplication or division and solving the system of equations.

Solution of the system of linear equations

Any ordered pair in a system that makes all the equations true

Graphing method

Graphing the system of equations and finding the point at which they intersect

substitution method

In this method, solve an equation for one variable, then replace that solution in the other equation, and solve.

Absolute value equation

An equation that contains an absolute value expression

translation

It is a transformation that moves points the distance and in the same direction.

Πr²

Area of circle

Area of a square

s², where s = length of a side

Area of a triangle

A = ½ bh (or) A = bh÷2

Area of a trapezoid

1/2 (b+b)h or mh

Perimeter of a rectangle

2Length + 2width [or (length + width) x 2]

Perimeter of a square

4s (where s = length of a side)

2 pi r

Perimeter (circumference) of a circle

∏d OR 2∏r

Circumference of a circle

area of a sector

a fractional part of the area of a circle

length of a sector

x°/360 times (2 pi r), where x is the degrees in the angle

Circle

r= asin(theta)

Radius (Radii)

A segment connecting the center of a circle to any point on the circle

diameter

A straight line passing through the centre of a circle to touch both sides of the circumference.

Chord

is a segment whose endpoints lie on the circle

sector

an area enclosed by two radii of a circle and an intercepted arc

arc

part of a circle

Central Angle

an angle whose vertex is the center of the circle

Circumference Formula

C =∏d

A=∏r2

Area of Circles