Tricksidk

Question 1

Sum of cubes vs difference of cubes

Answer 1

(a+b)(a^2-ab+b^2) - sum

(a-b)(a^2+ab+b^2) - diff

same sign at start if that makes sense

Question 2

Reflection matrix

Answer 2

[ cos2θ sin2θ ]
[ sin2θ -cos2θ ]

in the line y = (tanθ )x

θ is line between axis of reflection and x axis

Question 3

Rotation matrix

Answer 3

[ cosθ -sinθ]
[sinθ cosθ ]

θ measured from x axis anticlockwise

Question 4

Reflection in y axis

Answer 4

[ -1 0 ]
[0 1 ]

Question 5

Reflection in x axis

Answer 5

[ 1 0]
[ 0 -1]

Question 6

Reflection in y = x

Answer 6

[ 0 1]
[ 1 0 ]

Question 7

Reflection in y = -x

Answer 7

[ 0 -1]
[ -1 0]

Question 8

Properties of dot product

Answer 8

Commutative - a.b = b.a

Distributive - a. (b+c) = a.b + a.c

xa .b = x(a.b) = a.xb where x is a scalar

a.a = modA all squared

Question 9

Rule for perpendicular and parallel vectors a and b

Answer 9

a.b = 0 - ppd
a.b = moda modb - parallel

Question 10

Determinant of reflections and rotations

Answer 10

Reflections = -1
Rotations = 1