Further maths

Question 1

2 trig identities

Answer 1

tanx = sinx / cosx
sin²x + cos²x =1

Question 2

Binomial expansion
Rows of Pascal’s triangle?

Answer 2

First row = brackets to power of 0
Second row = brackets to power of 1
Third row = brackets to power of 2

Question 3

Differentiation 2 steps

Answer 3

Multiply by power
Subtract 1 from power

Question 4

How to work out the matrix transformations on the spot?

Answer 4

Use identity matrix and draw a the square on a graph. Use each of the two columns as co-ordinates, then transform the points. The end co-ordinates make the transformation matrix.

Question 5

Matrix transformation for enlargement around the origin?

Answer 5

(k 0)
(0 k)

Question 6

Matrix transformation for rotation 90 degrees clockwise around origin?

Answer 6

(0 1)
(-1 0)

Question 7

Matrix transformation for rotation 90 degrees anticlockwise around the origin?

Answer 7

(0 -1)
(1 0)

Question 8

Matrix transformation for rotation 180 degrees around the origin?

Answer 8

(-1 0)
(0 -1)

Question 9

Matrix transformation for reflection in the x axis?

Answer 9

(1 0)
(0 -1)

Question 10

Matrix transformation for reflection in the y axis?

Answer 10

(-1 0
(0 1)

Question 11

Matrix transformation for reflection in the line y=x?

Answer 11

(0 1)
(1 0)

Question 12

Matrix transformation for reflection in the line y= -x?

Answer 12

(0 -1)
(-1 0)

Question 13

Key rule when combining matrix transformations?

Answer 13

Do them in the reverse order e.g transformation A followed by B is BA