Maths Formula Sheet for CSEC

8/18/2019 Maths Formula Sheet for CSEC

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Formula Sheet 4 CXCArea and Perimeter Formula Trigonometric Formula

Perimeter = distance around the outside

(add all sides).

Opposite – side

opposite to angle

Adjacent –side beside(adjacent) to angle

Hypotenuse- longest

side

sin

cos

tan

opposite

hypotenus

adjacent

hypotenus

opposite

adjacent

hyp

θ c

adj hyp

a

opp

b

Remember: works only onright angle triangles

Pythagorean Theorem

Triples: 3,4,5 5,12,13 8,15,17C is the hypotenuse, a and b are the other sides.

Remember: works only on right angle triangles

Coordinate Geometry Formula

Distance Formula:

Midpoint Formula:

Gradient Formula:

Parallel lines have equal slope.

Perpendicular lines have negative reciprocal

gradients.

Volume and Surface Area

Equation of a line

Slope-Intercept Method:

y mx c

Point-Gradient Method:



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= 8Alternate 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

General Triangle Information

Sum of angles of triangle = 180.

Measure of exterior angle of triangle = the

sum of the two non-adjacent interior angles.

The sum of any two sides of a triangle is

greater than the third side.Solving triangles

cb

aC

Sine rule

sin sin sin

a b c

A B C or c

C sin

b

Bsin

a

Asin

Used when any two sides and their correspondingangles are involved to find one missing side or angle.

Cosine rule2 2 2

2 2 2

2 2 2

2 cos

2 cos

2 cos

a b c bc A

b a c ac B

c a b ab C

Used when three sides and an angle between them aregiven to find the other side

Heron’s FormulaArea of a triangle given only the length of the sides

( )( )( )

2

A s s a s b s c

a b cwhere s

Capital letters represent Angles

Common letters represent sides

Polygons

Sum of Interior Angles:

Sum of Exterior Angles:

Each Interior Angle (regular poly):

Each Exterior Angle (regular poly):

Quadratic Formula

If 2

0ax bx c

then

24

2

b b ac x

a

c e

Circle Facts



Tangent5. Radius to tangent is 90o at point of contact.

6. The tangents to a circle from an external

point T are equal in length.

7. Angle between tangent to circle and chord at

the point of contact is eqaual to the to the

angle in the alternet segment

2.

1a.

O

4.

3.

6.

5.

T

B

A

D E

T

7.

1b. 1c.

1d.

radius

diameter

chor d

a r c

segment

Sector

Diameter = 2× radius

Area of circle = πr2

Circumference of circle = 2πr or πd

Length of arc = 2πr × 360

sin2

1

360

sec

22

r r

triangleof Areator of AreaSegment of AreaArea of sector = πr2 × 360

Angles in circles

1. a,b,c,d Angle at the center in twice

angle at the circumference.

2. Angle formed on the diameter in 90o

3. Angles in the same segment are equal

4. opposite angles in a cyclic

Quadrilateral are supplimentary( add

up to 180o)

Matrices 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

Determinant of 2×2 Matrix

If

a b A

c d

A ad cb

A singular matrices has a determinant of 0

Adjoint of 2×2 matrix

int

a b Ac d

d b A adjo

c a

Inverse of 2×2 matrix

1

1

1 adjoint

1

a b A

c d

A A

A

or

d b A

ad bc c a

REFLECTION

Multiply matrices by each point to get reflection in

x - axis y- axis y=x y=-x

10

01

10

01

01

10

01

10

TRANSLATION Movement of x in x direction and y in ydirection add matrix

y

x

to eack point to get its image.

ROTATION

Multiply by matrices to get rotation of ϴ-degrees clockwise abou

origin (0,0)

cossin

sincos

R

01

10

R90

10

01 R180

01

10 R270

Enlargment Multiply each point by scale factor K to get the image of the poi

for an enlargment from the origin.

Setsuniversal set

is a member of

is not a member of

union

intersect

= null set

' A = Elements not in set A Reverse oppertions

_

x x a a

1

1

1

1

sin sin

cos cos

tan tan

( ) ( ) f x f x



Shape Volume Surface Area

Cube

1

l

l

l×l×l=l 3 6l 2

Cuboid

h

l

w

lwh 2lw+2hw+2lh

Prism s

h

l

b

bhl 2

1 hl sl lbbh

Cylinder

r

h hr 2

rh2r 2 2

or

)hr ( r 2

Cone

hr 3

1 2

2r 4

rsr 2

Sphere

3r 3

4

©2006 D. Ferguson

Maths Formula Sheet for CSEC

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