General ntes for ESAT

• Unit cost is cost of one item

• In an elastic collision, u₁-u₂=v₁-v₂

• To check whether a number is divisible by 7, subtract twice the last digit from the other digits and see if the new number is divisible by 7.

• When there is a common second difference, a sequence is a quadratic sequence, where a = second common difference / 2.

• Sum of internal angles of a polygon = 180 x (n-2)

• Supplementary angles sum to 180

• Complimentary angles sum to 360

The exterior angle of a triangle is equal to teh sum of the interior opposite angles; so d = a + b.

• s = 0.5 (u+v)t

Sum to infinity of a geometric series = a/(1-r), providing |r|<1

• A kite has one line of symmetry. It’s diagonals meet at 90 degrees

• A rhombus has 4 sides of equal length, and 2 sets of parallel lines

• All angles of an acute triangle are less than 90 degrees

• A negative scale factor indicates that the object and image are on different sides of the centre of enlargement

Q: enlarge the shape with coordinates A (2,2), B (4,2), C (2,6) about the point P (0,4).

A:

• The vector PA = (2,-2), so PA’ = (-4,4) = -4,8

• B’ = (-8,-4), C’ = (-4,0)

To rotate a point A 90 degrees about P:

• Find AP as (x,y)

• A’ = P + (y,x)

Circle Theorems

• The angle at the centre is twice the angle at the circumference\

• The area of a parallelogram is equal the product of its base and height

• The area of a parallelogram, including rhombuses, is equal to the product of its diagonals multiplied by 1/2, multiplied by the angle between the diagonals

• So the area of a square or rhombus is equal to half the product of its diagonals.