Maths Formula Sheet for CSEC

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 cos tan

adj  a

adjacent 

c hyp

opp  b

hypotenus opposite

Remember: works only on right angle triangles

adjacent 

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:

Slope-Intercept Method:

 y

mx

c

Point-Gradient Method:

Parallel lines have equal slope. Perpendicular lines have negative reciprocal gradients.

Angle Information Complementary angles - two angles whose sum is 90. Supplementary angles - two angles whose sum is 180.

General Triangle Information Sum of angles of triangle = 180. Measure of exterior angle of triangle = the sum of the two non-adjacent interior angles.

Parallel lines

Corresponding angles are equal. 1= 5, 2= 6, 3= 7, 4= 8 Alternate Interior angles are equal. 3= 6, 4= 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

The sum of any two sides of a triangle is greater than the third side.

Solving triangles

Polygons c

Sum of Interior Angles:

b

a

Sum of Exterior Angles:

Each Interior Angle (regular poly):

Each Exterior Angle (regular poly):

Quadratic Formula

If 

ax 2

  then

bx

c

 x 

0

b

b2

4ac

2a

C 

Sine rule a

b

sin A

c

       e         c

sin 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 a2

b2

c2

2bc cos A

b2

a2

c2

2ac cos B

c 2 a2 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

where s

a )( s a

b

b )( s

c)

c

2 Capital letters represent Angles Common letters represent sides

Circle Facts

sin B

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  c r o h  

segment

2. 1a.

O

c r  a 

Sector Diameter = 2× radius

4.

Area of circle = πr2

3.

Circumference of circle = 2πr or πd

Length of arc =

2πr ×

360

Area of sector = πr × 360  Area of   Segment   Area of  sec tor   Area of  triangle

6.

2

5.

       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

angle at the circumference.

2. Angle formed on the diameter in 90o

E  T 

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 c

d

g

h

c

g

d

g

h

d

h

 x - axis

 y- axis

1 0

 Multiplying Matrices a b e f ae c

f  

 REFLECTION  Multiply matrices by each point to get reflection in

ce

bg

af

bh

dg

cf

dh

0

1

1

y=x

0

0

0

1

y=-x 

1

0

1 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   A

 If

ad

 x   y

cb

 A singular matrices has a determinant of 0  Adjoint of 2×2 matrix  a b  A c d  d

 A adjo int

1

1

cos sin

sin

 R90

cos

c

a

 R180

1 0

0

 R270

1

universal set

ad

d bc

c

b

is a member of 

a

is not a member of  union intersect

 Reverse oppertions

 _ 

 x 

a

a x 

1

0

0

1

1 0

 Multiply each point by scale factor K to get the image of the point  for an enlargment from the origin.

 Sets 1

1

 Enlargment 

or  1

0

b

A  adjoint

 A

 A

 ROTATION   Multiply by matrices to get rotation of ϴ-degrees clockwise about origin (0,0)

 R

 Inverse of 2×2 matrix  a b  A c d   A

to eack point to get its image.

sin

sin

1

cos

cos

1

tan

tan

1

 f ( x )

f

1

( x )

= null set '   A = Elements not in set A

Shape

Volume

Surface Area

Cube l×l×l=l 3

2 6l 

1 l  l 

Cuboid lwh

2lw+2hw+2lh

h l  w

Prism s

1

h

2

bhl 

bh

lb

sl  hl 

l  b

Cylinder  r 

r 2 h

h

2 r 2

2 rh or 

2 r ( r  h ) Cone

1 3

2

r  h

r 2

Sphere

4 3

©2006 D. Ferguson

r 3

4 r 2

rs