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