Coordinate Geometry

Question 1

What is the formula for the Gradient of a straight line:

y2-y1
———
x2-x1

Answer 1

y2-y1
———
x2-x1

Question 2

WhT is the formula for the Length of a line

Answer 2

Root [(x2-x1)^2 + (y2-y2)]

Question 3

Formula for the mid point of a line joining two points

Answer 3

x1+x2, y1+y2
——-, ———
2. 2

Question 4

If two lines with gradient m1 and m2 are perpendicular…

Answer 4

m1=-1/m2

Question 5

How to answer a ‘verify’ question

Answer 5

Use the answer

Question 6

How to answer a ‘show’ question

Answer 6

Pretend you don’t know the answer, showing all working

Question 7

State a fact about the normal to a tangent of a circle

Answer 7

It passes through the centre of the circle

Question 8

What is the max point of a circle with centre (a,b). Do max in x then max in y

Answer 8

Max/min in x: a+/- r

Max/ min in y: b+/- r

Question 9

What is the shortest distance between a line and a point?

Answer 9

Perpendicular to the line

Question 10

When is function concave

Answer 10

f’’(x)<0

Question 11

When does the change of sign method fail when finding a root

Answer 11

If the interval contains a max/min point (no change of sign)

The interval contains an asymptote (sign change but no root)

Question 12

Why are parametrics useful

Answer 12

You can use functions to represent 1-many and many-many as well as usual

Question 13

When is the trapezium rule an overestimate and an underestimate

Answer 13

Over: concave
under: convex

Question 14

What must be exactly stated when finding a point of inflection?

Answer 14

If f”(a)= 0 then the point when x=a will be a point of inflection when f”(a+0.1) and f”(a-0.1) show a change in sign