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
adj
a
c
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:
Equation of a line
Gradient Formula:
Slope­Intercept Method:
y  mx  c
Point­Gradient Method:
Parallel lines have equal slope.
Perpendicular lines have negative reciprocal
gradients.
Angle Information
Parallel lines
Complementary angles ­ two angles whose
sum is 90.
Supplementary angles ­ two angles whose
sum is 180.
Corresponding angles are equal. 1= 5,
2= 6, 3= 7, 4= 8
General Triangle Information
Alternate Interior angles are equal. 3= 6,
4= 5
Alternate Exterior angles are equal.
Sum of angles of triangle = 180.
1= 8, 2= 7
Same side interior angles are supplementary.
Measure of exterior angle of triangle = the
sum of the two non­adjacent interior angles. m 3+m 5=180, m 4+m 6=180
Solving triangles
The sum of any two sides of a triangle is
greater than the third side.
A
Polygons
c
Sum of Interior Angles:
b
B
a
Sum of Exterior Angles:
Each Interior Angle (regular poly):
Each Exterior Angle (regular poly):
C
Sine rule
sin A sin B sin C
a
b
c




b
c
sin A sin B sin C or a
Used when any two sides and their corresponding
angles are involved to find one missing side or angle.
Cosine rule
a 2  b 2  c 2  2bc  cos A
Quadratic Formula
If
ax 2  bx  c  0
then
x
 b  b 2  4ac
2a
ce
Circle Facts
b 2  a 2  c 2  2ac  cos B
c 2  a 2  b 2  2ab  cos C
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 )
abc
2
Capital letters represent Angles
Common letters represent sides
where s 
Tangent
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
diameter
7. Angle between tangent to circle and chord at
the point of contact is eqaual to the to the
angle in the alternet segment
d
r
o
h
c
segment
2.
1a.
O
Sector
c
r
a
Diameter = 2× radius
4.
Area of circle = πr2
3.
Circumference of circle = 2πr or πd

Length of arc = 2πr × 360

2
Area of sector = πr × 360
5.
Area of Segment  Area of sec tor  Area of triangle
6.
  1 2


  r 2 
   r sin  
360   2


Angles in circles
T
B
7.
A
1. a,b,c,d Angle at the center in twice
D
2. Angle formed on the diameter in 90o
E
T
angle at the circumference.
1b.
1c.
3. Angles in the same segment are equal
4. opposite angles in a cyclic
Quadrilateral are supplimentary( add
up to 180o)
Matrices
1d.
Transformational Matrices
Adding or subtracting matrices
a b  e f  a  e b  f 




c d   g h  c  g d  h
Multiplying Matrices
 a b   e f   ae  bg af  bh 




 c d   g h   ce  dg cf  dh 
REFLECTION
Multiply matrices by each point to get reflection in
x­ axis
y­ axis
y=x
 1 0


 0 1
1 0 


 0  1
 0 1


1 0
y=­x
 0  1


 1 0 
TRANSLATION
Movement of x in x direction and y in ydirection add matrix
Determinant of 2×2 Matrix
a b
A

c d
 x
 
 y  to eack point to get its image.
A  ad  cb
If
A singular matrices has a determinant of 0
Adjoint of 2×2 matrix
a b
A

c d
 cos 
R 
 sin 
 d b 
A adjo int  

 c a 
1
 A adjoint
A
Sets
 d b 
1



ad  bc   c a 
x




a
ax
 0 1
R270 

 1 0
Multiply each point by scale factor K to get the image of the point
for an enlargment from the origin.
Reverse oppertions

_


 0  1
R90 

1 0 
Enlargment
or
A1
 sin  

cos  
 1 0 
R180 

 0  1
Inverse of 2×2 matrix
a b
A

c d
A1 
ROTATION
Multiply by matrices to get rotation of ϴ­degrees clockwise about
origin (0,0)
sin 
sin 1 
cos 
cos 1 
tan 
tan 1 
f ( x)
f 1 ( x )
  universal set
 is a member of
 is not a member of
  union
  intersect
 = null set
A' = Elements not in set A
Shape
Volume
Surface Area
Cube
l×l×l=l3
6l2
1
l
l
Cuboid
lwh
2lw+2hw+2lh
h
l
w
Prism
s
1
bhl
2
h
l
bh  lb  sl  hl
b
Cylinder
r
h
r 2 h
2r 2  2rh
or
2r ( r  h )
Cone
1 2
r h
3
r 2  rs
4 3
r
3
4 r 2
Sphere
©2006 D. Ferguson