Maths Class/Revision Notes Y12

Question 1

what are the coordinates of the turning point of a quadratic in ax^2 + bx + c form?

Answer 1

(-b/2a), (c - b^2/4a)
- when finding the coefficients of ax^2 + bx + c from a given turning point it can be faster to input the coordinates to the equation and use the -b/2a equals the x coordinate

Question 2

if the roots of an equation are equal - what can we say about the values of a, b and c when the equation is expressed as ax^2 + bx + c?

Answer 2

b^2 - 4ac = 0 as there is one repeated root

Question 3

what are the internal angles of an equilateral triangle and how can this be important

Answer 3

120 degrees (as 360/3)
- when finding coordinates of an equilateral triangle, it can be easier (if you know the centre) to find the coordinates using the fact that the internal angle is 120 degrees

Question 4

why is the maximum area of a rectangle (with a set perimeter) when it is a square?

Answer 4

call the perimeter P
- the sides of the rectangle are x, y
- 2x + 2y = P
area = x(P/2 - x)
the maximum of that curve (after completing the square) is (p/4, p^2/16)
- taking only positive values of p this is when the sides are the same length (a square)

Question 5

give a great way to find a maximum area or volume

Answer 5

• find a formula for the sides in terms of x, then for the area/volume in terms of x and then find the maximum point of that curve

Question 6

how do you find the distance from the origin to a point on a circle

Answer 6

distance from centre to origin minus the radius obviously

Question 7

what is the faster method to find the centre of a circle given some points on the circle - subtracting equations (elimination) or finding intersecting lines

Answer 7

elimination!