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A Level Maths Edexcel > Pure Year 2 > Flashcards

Flashcards in Pure Year 2 Deck (49)
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1

What is an improper algebraic fraction?

One whose numerator has a degree equal to or larger than the denominator

2

What is a mapping? (Functions)

A function if every input has a distinct output.

3

What counts as a function and what doesn't?

One-to-one functions
Many-to-one functions
But One-to-many is not a function!

4

What is the relationship between the graph of f(x) and f⁻¹(x)?

f⁻¹(x) is a reflection of f(x) in the line y=x

5

Describe the transformation f(x+a)

Horizontal translation of -a

6

Describe the transformation f(x) + a

Vertical translation of a

7

Describe the transformation f(ax)

Horizontal stretch of scale factor 1/a

8

Describe the transformation af(x)

Vertical stretch of scale factor a

9

Describe the transformation -f(x)

Reflects f(x) in the x-axis

10

Describe the transformation f(-x)

Reflects f(x) in the y-axis

11

What is the formula for the nth term of an arithmetic sequence?

uₙ = a + (n-1) d

12

What is the formula for the nth term of an geometric sequence?

uₙ = arⁿ⁻¹

13

What is the sum to infinity formula for a geometric series? What is the condition?

Series must be converging, |r|<1
S∞ = a /(1-r)

14

What is the sum of series formula for arithmetic series?

Sₙ = 0.5n(2a + (n-1)d)
or
Sₙ = 0.5n (a + l)

15

What is the sum of series formula for geometric series?

Sₙ = a(1-r ⁿ)/(1-r)

16

When is a sequence increasing?

If uₙ₊₁ > uₙ

17

When is a sequence decreasing?

If uₙ₊₁ < uₙ

18

When is a sequence periodic? What is the order of a periodic sequence?

If the terms repeat in a cycle. For a periodic sequence there is an integer k such that uₙ₊ₖ = uₙ for all n ε ℕ. The value k is the order of the sequence

19

When is the binomial expansion f (1+bx)ⁿ valid, when n is negative or a fraction?

|bx| < 1
or |x| < 1/ |b|

20

When is the binomial expansion f (a+bx)ⁿ valid, when n is negative or a fraction?

|ba/x| < 1
or |x| < |a/b|

21

What is a sector? A segment? (of a circle)

Sector is like a pizza slice
A segment is the area of the circle when the circle is cut by a chord

22

What is the formula for the area of a segment?

A = 0.5 r² (θ - sinθ)

23

What are the small angle approximations?

sinθ ≈ θ
tanθ ≈ θ
cosθ ≈ 1 - θ²/2

24

What does the graph of y = sec x look like? What is the domain and range? Period?

Symmetrical about y-axis
u and n shapes. Asymptotes at π/2, 3π/2 etc.
Domain: all real values of x. Except x ≠ π/2, 3π/2, ... or any odd multiple of π/2
Range y ≤ -1, y ≥ 1
Period: 2π

25

What does the graph of y = cosec x look like? What is the domain and range? Period?

u and n shapes. Asymptotes at π, 2π etc.
Domain: all real values of x. Except x ≠ π, 2π, ... or any integer multiple of π
Range y ≤ -1, y ≥ 1
Period: 2π

26

What does the graph of y = cot x look like? What is the domain and range? Period?

Period of π rads. Vertical asymptotes at 0, π, 2π etc.
Domain: All real values of x. Except x ≠ π, 2π, ... or any integer multiple of π
Range: All real values of y

27

State the identity including tan and 1

1 + tan²x ≡ sec²x

28

State the identity including cot and 1

1 + cot²x ≡ cosec²x

29

What is the domain and range of y = arcsin x?

Domain: -1 ≤ x ≤ 1
Range: -π/2 ≤ arcsin x ≤ π/2

30

What is the domain and range of y = arccos x?

Domain: -1 ≤ x ≤ 1
Range: 0 ≤ arccos x ≤ π