Math Problem Solver

a) Find the value of

8 7 28 12 16 3 + + − ( ) . (3 marks)

b) If

x =1

and

y = 3

, then find the value of

( )

2 3

2 2

2

3 3

y x y

y x x xy

+

−

− −

. (4 marks)

c) Let

A, B , C

be three points with the coordinates

(1,2), (3,4), (5,6)

respectively,

and

P

be the mid-point of

AB

. Determine the coordinates of the mid-point of PC.

Find the gradients of the straight lines

PC

and

AB

. Are

PC

and

AB

perpendicular?

(9 marks)

d) Let

a

be a real constant such that

a 0

. Find the gradient, y-intercept, and

the x-intercept of the cartesian equation

2

ay a x = +1

. Does the point

(1,1)

locate on the straight line

2

ay a x = +1

?