Pure math 1

Question 1

How can I find the domain of a composite function

Answer 1

Use the domain of the inner function to find values in the range of that same inner function that are in the domain of the outer function

Question 2

Formula for translation of a function by vector (0,a)

Answer 2

f(x) + a

Question 3

Formula for translation of a function by vector (a,0)

Answer 3

f(x-a)

Question 4

Formula for stretching by vector a parallel to y-axis

Answer 4

af(x)

Question 5

Formula for stretching by vector a parallel to x-axis

Answer 5

f(x/a)

Question 6

Formula for reflection in x-axis

Answer 6

-f(x)

Question 7

Formula for reflection in y-axis

Answer 7

f(-x)

Question 8

Formulas of a circle

Answer 8

X^2+y^2+2gx+2fx+c=0
(-g,-f) = centre
radius = sqrt(g^2+f^2-c^2)

Question 9

Important properties of a circle

Answer 9

Any line drawn from the centre of a circle to any chord, is a perpendicular bisector of the chord

Angles subtended on the diameter are 90 degrees

Question 10

Formula for the area of a triangle

Answer 10

1/2 * a*b sin c

Question 11

sin(90-x)=?

Answer 11

cosx

Question 12

How to solve or sketch functions of the form asinx + bcosx

Answer 12

Equate to any of the expressions Rsin(x+y) or Rcos(x+y) given in the equations, and then cancel out like terms

Question 13

The higher the power of a proper fraction?

Answer 13

The lower the result

Question 14

How to prove that a line is a tangent of a circle

Answer 14

Simultaneously solve both equations (circle and line). One answer indicates that the line is a tangent

Question 15

What’s the formula for the volume of a region when rotated about the x-axis?

Answer 15

integral of pi * (y)^2 dx

Question 16

What’s the formula for the volume of a region when rotated about the y-axis?

Answer 16

integral of pi * (x)^2 dy