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Level 470

Formulas


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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