Further Pure

Question 1

What are the vector equations for the area of a parallelogram or triangle?

Answer 1

Ap=1/2|axb|, At=1/2|axb|

Question 2

What are the vector equations for the volume of a parallelepiped and tetrahedron?

Answer 2

Vp = a·(bxc), Vt = 1/6(a·(bxc))

Question 3

What are the generic cartesian and parametric equations for a parabola?

Answer 3

y²=4ax
x=at², y=2at

Question 4

What is the differential of y²=4ax?

Answer 4

dy/dx= 2a/y

Question 5

What are the generic cartesian and parametric equations for a hyperbola?

Answer 5

xy=c²
x=ct, y=c/t

Question 6

What is the t-formula for sinθ?

Answer 6

sinθ = (2t) / (1+t²)

Question 7

What’s the t-formula for cosθ?

Answer 7

cosθ = (1-t²) / (1+t²)

Question 8

What’s the t-formula for tanθ?

Answer 8

tanθ = (2t) / (1-t²)

Question 9

What’s the equation of the tangent of a general parabola?

Answer 9

ty = x + at²

Question 10

What’s the equation of the normal of a general parabola?

Answer 10

y + tx = 2at + at³

Question 11

What’s the equation of the tangent of a general hyperbola?

Answer 11

x + t²y = 2ct

Question 12

What’s the equation of the normal of a general hyperbola?

Answer 12

t³x -ty = c(t⁴ - 1)