Pure Chapters 8-14 Flashcards Preview

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Flashcards in Pure Chapters 8-14 Deck (45)
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1
Q

nCr = ?

A

n! / r!(n-r)!

2
Q

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

A

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

3
Q

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

A

(n+1)th row

4
Q

What is the cosine rule?

A

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

5
Q

What is the sine rule?

A

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

6
Q

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

A

sinθ = sin(180-θ)

7
Q

What is the area of a triangle?

A

1/2 ab sin(C)

8
Q

What is a periodic graph?

A

One that repeats itself after a certain interval

9
Q

Which trigonometric ratios are positive in the first quadrant?

A

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

10
Q

Which trigonometric ratios are positive in the second quadrant?

A

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

11
Q

Which trigonometric ratios are positive in the third quadrant?

A

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

12
Q

Which trigonometric ratios are positive in the fourth quadrant?

A

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

13
Q

Trigonometric Ratios - sin 30°

A

1/2

14
Q

Trigonometric Ratios - sin 45°

A

1/✔️2

Or ✔️2 / 2

15
Q

Trigonometric Ratios - sin 60°

A

✔️3 / 2

16
Q

Trigonometric Ratios - cos 30°

A

✔️3 / 2

17
Q

Trigonometric Ratios - cos 45°

A

1 / ✔️2

Or ✔️2 / 2

18
Q

Trigonometric Ratios - cos 60°

A

1/2

19
Q

Trigonometric Ratios - tan 30°

A

1 / ✔️3

Or ✔️3 / 3

20
Q

Trigonometric Ratios - tan 45°

A

1

21
Q

Trigonometric Ratios - tan 60°

A

✔️3

22
Q

What are the two trigonometric identities? (2)

A

sin^2(θ) + cos^2(θ) = 1

tan θ = sin θ / cos θ

23
Q

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

A

-1 < k < 1

24
Q

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

A

All values of p

25
Q

What is the principal value?

A

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

26
Q

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

A

Equal in length

Parallel

27
Q

Why does AB = -BA? (3)

A

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

28
Q

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

A

AB + BC = AC

29
Q

What is the equivalent to subtracting a vector?

A

Add the negative vector

a - b = a + (-b)

30
Q

PQ + QP = ?

A

0

31
Q

How can a parallel vector be written?

A

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

32
Q

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

A

|a| = ✔️(x^2 + y^2)

33
Q

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

A

a / |a|

34
Q

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)

A
p = r
q = s
35
Q

What can the gradient function be used for?

A

Finding the gradient of the curve for any value of x

36
Q

When is the function f(x) increasing?

A

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

37
Q

When is the function f(x) decreasing?

A

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

38
Q

What is a stationary point?

A

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

39
Q

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

A

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

40
Q

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

A

y = f’(x) - cuts the x-axis

41
Q

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

A

y = f’(x) - touches the x-axis

42
Q

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

A

y = f’(x) - above the x-axis

43
Q

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

A

y = f’(x) - below the x-axis

44
Q

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

A

y = f’(x) - vertical asymptote

45
Q

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

A

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