C4

Question 1

How would a partial factor which has a (x-1)(x^2+4) denominatior be written ?

Answer 1

A/(x-1) + (Bx-c)/(x^2+4)

Question 2

If when doing the general binomial expansion and the constant is not 1 how can it be written?

Answer 2

(a+b)^n = a^n × (1+(b÷a))^n

Question 3

What is cosec

Answer 3

1÷ sin

Question 4

What is sec

Answer 4

1÷cos

Question 5

What is cot

Answer 5

1÷tan

Question 6

What are the inverse trig identities to know?

Answer 6

Tan^2 +1 = sec^2

Cot^2+1=cosec^2

Question 7

Sin2x=

Answer 7

2sinxcosx

Question 8

What does cos(2x) equal

Answer 8

Cos^2 -sin^2
1-2sin^2
2cos^2 -1

Question 9

How would you write sin(75) in surd form

Answer 9

write is as sin(30+45), then expand and simplify.

Question 10

write 5cosσ-12sinσ in the form Rcos(σ+θ)

Answer 10

R(cosσcosθ-sinσsinθ)
Rcosθ=5                   Rsinθ=12
θ=67.4
R=the root of 5^2 plus 12^2 which is 13
13cos(θ+67.4)

Question 11

How do you differentiate a parametric equation?

Answer 11

Differentiate the different parts and use the chain rule to find dy/dx.
It is usually the differential of y divided by the differential of x.

Question 12

what is the formula for the volume of revolution around the x axis?

Answer 12

intergrate pi*(y^2) for x axis

Use pi*(x^2) for the y axis.

Question 13

in the formula booklet for the plane going through a point, what does the a and n mean?

Answer 13

a is a point that is on the plane. n is a normal to the plane.
the coefficeints of the plane are the values of the perpendicular.

Question 14

how can you tell that two planes are parallel?

Answer 14

The coefficients will be the same.

Question 15

how do you find the angle between 2 vectors?

Answer 15

cos theta = (a dot b) / |a||b|

Question 16

what does the cross product give?

Answer 16

a vector that is perpendicular to 2 different vectors.

Question 17

What is the parametric equation of a circle?

Answer 17

X= a+rcos⊝
Y= b+rsin⊝
r is the radius and the centre is (a,b)

Question 18

How would the fraction with denominatior (x-1)(x+2)² be written in partial fractions?

Answer 18

A/(x-1) + B/(x+2) + C/(x+2)²

Question 19

For what values of x are binomial expansions valid?

Answer 19

For (1+x)ª |x|

Question 20

What is a vector perpendicular to a plane?

Answer 20

One with the same coefficients of the plane.

Question 21

How do you find the angle between two planes?

Answer 21

Angle between the normals