Formula Sheet 4 CXC
Area and Perimeter Formula
Perimeter = distance around the outside
(add all sides).
Trigonometric Formula
Opposite – side
opposite to angle
Adjacent –side beside
(adjacent) to angle
hyp
θ
Hypotenuse- longest
side
opposite
sin  
hypotenus
adjacent
cos  
hypotenus
opposite
tan  
adjacent
c
adj
a
hyp
opp
b
Remember: works only
on right angle triangles
Pythagorean Theorem
Triples: 3,4,5
5,12,13
8,15,17
C is the hypotenuse, a and b are the other sides.
Remember: works only on right angle triangles
Coordinate Geometry Formula
Volume and Surface Area
Distance Formula:
Midpoint Formula:
Gradient Formula:
Equation of a line
Slope-Intercept Method:
y  mx  c
Point-Gradient Method:
Parallel lines have equal slope.
Perpendicular lines have negative reciprocal
gradients.
Parallel lines
Angle Information
Complementary angles - two angles whose
sum is 90.
Supplementary angles - two angles whose
sum is 180.
Corresponding angles are equal.
2=
General Triangle Information
Sum of angles of triangle = 180.
3=
7,
4=
Alternate Interior angles are equal.
Measure of exterior angle of triangle = the
6,
sum of the two non-adjacent interior angles.
The sum of any two sides of a triangle is
greater than the third side.
6,
1=
4=
5,
8
3=
5
Alternate Exterior angles are equal.
1=
8,
2=
7
Same side interior angles are supplementary.
m
3+m
5=180, m
4+m
6=180
Solving triangles
A
Polygons
c
Sum of Interior Angles:
b
B
a
Sum of Exterior Angles:
Each Interior Angle (regular poly):
Sine rule
Each Exterior Angle (regular poly):
Cosine rule
a
b
c
sin A sin B sin C




or
a
b
c
sin A sin B sin C
Used when any two sides and their corresponding
angles are involved to find one missing side or angle.
a 2  b 2  c 2  2bc  cos A
b 2  a 2  c 2  2ac  cos B
Quadratic Formula
C
c 2  a 2  b 2  2ab  cos C
If
Used when three sides and an angle between them
are given to find the other side
Heron’s Formula
Area of a triangle given only the length of the
sides
A  s( s  a )( s  b)( s  c )
ax 2  bx  c  0
then
x
 b  b 2  4ac
2a
abc
2
Capital letters represent Angles
Common letters represent sides
where s 
Tangent
Circle Facts
5. Radius to tangent is 90o at point of contact.
6. The tangents to a circle from an external
point T are equal in length.
radius
7. Angle between tangent to circle and chord
at the point of contact is eqaual to the to
the angle in the alternet segment
diameter
2.
segment
1a.
O
Sector
4.
Diameter = 2× radius
3.
Area of circle = πr2
Circumference of circle = 2πr or πd

360

2
Area of sector = πr ×
360
Length of arc = 2πr ×
6.
5.
Area of Segment  Area of sec tor  Area of triangle
 

  r 2 

360 

 1 2

r sin  
 2


T
B
Angles in circles
7.
A
E
D
T
1.
a,b,c,d Angle at the center in twice
1b.
1c.
angle at the circumference.
2.
Angle formed on the diameter in 90o
3.
Angles in the same segment are equal
1d.
4.
opposite angles in a cyclic
Quadrilateral are supplimentary( add
up to 180o)
Transformational Matrices
Matrices
Adding or subtracting matrices
a  e b  f
 a b  e  f 

 
 

c  g d  h
 c d  g  h 
Multiplying Matrices
ae  bg af 
 a b  e  f 
 bh

 
 

ce  dg cf 
 c d  g  h 
 dh
Determinant of 2×2 Matrix
 a b
A

If
 c d
A  ad  cb
A singular matrices has a determinant of 0
Adjoint of 2×2 matrix
 a b
A

 c d
 d  b

 c a 
A adjo int  
Inverse of 2×2 matrix
REFLECTION
Multiply matrices by each point to get reflection in
x- axis
y- axis
 1
 0

 1
 0

0

1

0 

 1 
y=x
 0
 1

y=-x
1
 0
  1


0

 1

0 
TRANSLATION
Movement of x in x direction and y in ydirection add matrix
 x
 
 y
to eack point to get its image.
ROTATION
Multiply by matrices to get rotation of ϴ-degrees clockwise
about origin (0,0)
 cos 
 sin 
R 
 1
 0
R180 
 sin  

 0
 1
 1
0
1
R90 
cos  
0 

 1 

R270 
 1

0 

0 
Enlargment
Multiply each point by scale factor K to get the image of the
point for an enlargment from the origin.
Sets
  universal set
 is a member of
 is not a member of
  union
  intersect
 = null set
A' = Elements not in set A
 a b

 c d
1
A 1 
 A adjoint
A
A
or
A 1 
 d  b
1


ad  bc   c a 
Reverse oppertions

_


sin 
sin 1 




cos 
cos 1 
tan 
tan 1 
f ( x)
f 1 ( x )
x
a
ax
Shape
Volume
Surface Area
Cube
l×l×l=l3
6l2
1
l
l
Cuboid
lwh
2lw+2hw+2lh
h
l
w
Prism
bh  lb  sl  shl
h
1
bhl
2
l
b
Cylinder
r
2r2r2 h
2rh
h
or
2r ( r  h )
Cone
1
r hrs
3r 2
2
Sphere
4
r 3
3
4 r 2
©2006 D. Ferguson