Pure Chapters 8-14

Question 1

nCr = ?

Answer 1

n! / r!(n-r)!

Question 2

What is the general term in the expansion of (a+b)^n

Answer 2

(n r) a^(n-r) b^r

Question 3

Which row of Pascal’s triangle gives the coefficients in the expansion of (a+b)^n

Answer 3

(n+1)th row

Question 4

What is the cosine rule?

Answer 4

a^2 = b^2 + c^2 -2bc cos(A)

Question 5

What is the sine rule?

Answer 5

a / sin(A) = b / sin(B) = c / sin(C)

Question 6

How do you find the two possible angles from the sine rule?

Answer 6

sinθ = sin(180-θ)

Question 7

What is the area of a triangle?

Answer 7

1/2 ab sin(C)

Question 8

What is a periodic graph?

Answer 8

One that repeats itself after a certain interval

Question 9

Which trigonometric ratios are positive in the first quadrant?

Answer 9

sin θ - positive
cos θ - positive
tan θ - positive

Question 10

Which trigonometric ratios are positive in the second quadrant?

Answer 10

sin θ - positive
cos θ - negative
tan θ - negative

Question 11

Which trigonometric ratios are positive in the third quadrant?

Answer 11

sin θ - negative
cos θ - negative
tan θ - positive

Question 12

Which trigonometric ratios are positive in the fourth quadrant?

Answer 12

sin θ - negative
cos θ - positive
tan θ - negative

Question 13

Trigonometric Ratios - sin 30°

Answer 13

1/2

Question 14

Trigonometric Ratios - sin 45°

Answer 14

1/✔️2

Or ✔️2 / 2

Question 15

Trigonometric Ratios - sin 60°

Answer 15

✔️3 / 2

Question 16

Trigonometric Ratios - cos 30°

Answer 16

✔️3 / 2

Question 17

Trigonometric Ratios - cos 45°

Answer 17

1 / ✔️2

Or ✔️2 / 2

Question 18

Trigonometric Ratios - cos 60°

Answer 18

1/2

Question 19

Trigonometric Ratios - tan 30°

Answer 19

1 / ✔️3

Or ✔️3 / 3

Question 20

Trigonometric Ratios - tan 45°

Answer 20

1

Question 21

Trigonometric Ratios - tan 60°

Answer 21

✔️3

Question 22

What are the two trigonometric identities? (2)

Answer 22

sin^2(θ) + cos^2(θ) = 1

tan θ = sin θ / cos θ

Question 23

For what values of k do solutions for sin θ = k and cos θ = k exist?

Answer 23

-1 < k < 1

Question 24

For what values of p do solutions for tan θ = p exist?

Answer 24

All values of p

Question 25

What is the principal value?

Answer 25

The angle you get from your calculator when using inverse trigonometric functions

Question 26

If PQ = RS, what can be said for the line segments PQ and RS? (2)

Answer 26

Equal in length

Parallel

Question 27

Why does AB = -BA? (3)

Answer 27

AB is equal in length to BA
AB and BA are parallel
AB is in the opposite direction to BA

Question 28

What is the triangle law for vector addition in terms of AB, AC and BC?

Answer 28

AB + BC = AC

Question 29

What is the equivalent to subtracting a vector?

Answer 29

Add the negative vector

a - b = a + (-b)

Question 30

PQ + QP = ?

Answer 30

0

Question 31

How can a parallel vector be written?

Answer 31

Any vector parallel to a can be written as λa where λ is a non-zero scalar

Question 32

How do you find the magnitude of a vector (x y)?

Answer 32

|a| = ✔️(x^2 + y^2)

Question 33

How can a unit vector in the direction of a be written?

Answer 33

a / |a|

Question 34

If a and b are two non-parallel vectors and pa + qb = ra + sb, What can be said for p, q, r and s? (2)

Answer 34

p = r
q = s

Question 35

What can the gradient function be used for?

Answer 35

Finding the gradient of the curve for any value of x

Question 36

When is the function f(x) increasing?

Answer 36

On the interval [a,b] if f’(x) >/ 0 where a < x < b

Question 37

When is the function f(x) decreasing?

Answer 37

On the interval [a,b] if f’(x) < 0 where a < x < b

Question 38

What is a stationary point?

Answer 38

Any point on the curve y = f(x) where f’(x) = 0

Question 39

How does f”(a) show the nature of a stationary point? (3)

Answer 39

If f”(a) > 0 - local minimum
If f”(a) < 0 - local maximum
If f”(a) = 0, the point is either a local minimum, maximum or point of inflection

Question 40

Sketching gradient functions - maximum or minimum on y = f(x)

Answer 40

y = f’(x) - cuts the x-axis

Question 41

Sketching gradient functions - point of inflection on y = f(x)

Answer 41

y = f’(x) - touches the x-axis

Question 42

Sketching gradient functions - positive gradient on y = f(x)

Answer 42

y = f’(x) - above the x-axis

Question 43

Sketching gradient functions - negative gradient on y = f(x)

Answer 43

y = f’(x) - below the x-axis

Question 44

Sketching gradient functions - vertical asymptote on y = f(x)

Answer 44

y = f’(x) - vertical asymptote

Question 45

Sketching gradient functions - horizontal asymptote on y = f(x)

Answer 45

y = f’(x) - horizontal asymptote at the x-axis