Paper 2 Logic

Question 1

why must you always check before taking the logarithm of both sides?

Answer 1

• taking logs can loose/ add solutions
• Always make domain resitricts as to check that the value is positive ( cannot be = 0 either)

Question 2

Answer 2

Question 3

Answer 3

Loging and squaring can both introduce extra solutions. The substitution trick is neat

Question 4

Answer 4

Necessary but not sufficient means you can deduce the outcome from what you are given. BUT you can’t go the other way round (outcome to condition)

Question 5

Answer 5

Question 6

Answer 6

If a part of the inequality is true for all values of x, you can drop the inequality

Question 7

Answer 7

Simple notation

Question 8

Answer 8

Question 9

Answer 9

For a sufficient condition to be true, must be affirmative (100%) no maybes

Question 10

Answer 10

Question 11

Answer 11

Recognise that recurring means sum to infinity

Question 12

What is 2nd approach to this question

Answer 12

Question 13

Answer 13

They always want you to think in term of geometric series sums

Question 14

Answer 14

Question 15

What can you infer about stationary points given the number of roots?

Answer 15

Number of stationary points = at least (number of roots -1) between every root.
BUT may also be more stationary points between these pairs of values or before the first or after the last value. eg

Question 16

Answer 16

Might be more efficient to have a yes no prime section to avoid misses

Question 17

Answer 17

Question 18

what is the simplest way to rationalise surd?

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

What does this mean?

Answer 22

Question 23

What is a way to view the modulus function

Answer 23

The positive distance of x from 3

Question 24

Draw the graph of

Answer 24

(One to one function)
Bear in mind. It is just assumed the input values will always be positive and zero. Also when they give square root it is also just assumed it is the positive square root.

Question 25

Answer 25

Reflect whatever is below the x axis

Question 26

what must you be aware of with the recurance relationship type questions?

Answer 26

always makes sure you write out enough terms | do till at least 10

Question 27

what are common mistakes when doing binomial expansion?

Answer 27

1. not putting a bracket around the whole thing. eg: 2x^7 instead of (2x)^7 2. forgetting about the minus sign. eg: (3x)^5 instead of (-3x)^5

Question 28

What is another way to write

Answer 28

Question 29

How many terms are in the sum

Answer 29

n - m + 1

Question 30

Alternate method of finding the smallest distance

Answer 30

Question 31

why does the sin rule used in triangles give an ambigious result?

Answer 31

sin A can given 2 values below 180

Question 32

what are some limit/ things to keep in mind of the following rule?

Answer 32

* We only take logs with a positive base number: so 𝑎 > 0 [but 𝑎 ≠ 1] * We can only take the logs of positive numbers: so 𝑐 > 0 * The log of a number can be negative: so 𝑏 can be any number [even 0]

Question 33

Sketch

Answer 33

Question 34

Draw the graph of What are some things to note?

Answer 34

* the graph is only defined for 𝑥 > 0

Question 35

What is

Answer 35

Question 36

Where does this formula come from?

Answer 36

Question 37

what does it mean for a cubic graph to have no stationary points?

Answer 37

it only has one point of inflection. This is because when you differenciate, the quadratic has no real solutions

Question 38

What does the following imply?

Answer 38

Question 39

Why is this true?

Answer 39

Question 40

When are functions defined as strictly increasing or strictly decreasing?

Answer 40

Question 41

When is this true

Answer 41

Function is symmetrical about the y axis

Question 42

When is this true?

Answer 42

Question 43

What are all of the following?

Answer 43

Question 44

Wrong

Question 45

What is another way of writing?

Answer 45

Question 46

What can this also be written as?

Answer 46

Question 47

What does this rule essentially mean?

Answer 47

Question 48

What is the trapezium rule formula ?

Answer 48

Question 49

When is the trapezium rule an overestimate /underestimate / useless?

Answer 49

Question 50

Answer 50

Question 51

Answer 51

Question 52

What is the effect on the graph of a vertical stretch by a scale factor ‘a’?

Answer 52

Question 53

Summarise these transformations

Answer 53

Question 54

Answer 54

Question 55

How firm do sufficient / only if statements have to be?

Answer 55

ROCK SOLID

Question 56

Answer 56

Question 57

Answer 57

Question 58

Memorise table on shapes

Answer 58

Question 59

Draw a vent diagram including trapeziums, parallelograms, rectangles, squares, rhombi and kites. Also include which ones have equal diagonals, perpendicular diagonals, symmetry around diagonals and bisecting diagonals

Answer 59

Question 60

Answer 60

Question 61

Answer 61

Question 62

Answer 62

Question 63

What is the statement negation table ?

Answer 63

Question 64

Answer 64

Question 65

Answer 65

Question 66

Answer 66

Get to grips with manipulating the function notation

Question 67

Answer 67

Question 68

Answer 68

Question 69

Answer 69

Question 70

Answer 70

Question 71

Answer 71

Question 72

Answer 72

To be sufficient not necessary the statement must be true, but there are other cases apart from the condition where it is also true

Question 73

Answer 73

Question 74

Answer 74

Question 75

Answer 75

Question 76

Answer 76

Question 77

Answer 77

Question 78

What is the definition of a polynomial?

Answer 78

Continuous smooth curve. With non-negative integer powers

Question 79

Answer 79

Question 80

Answer 80

Question 81

Answer 81

Question 82

Answer 82

Necessary and sufficient means logically equivalent statement

Question 83

Answer 83

Question 84

Answer 84

Question 85

Answer 85

Question 86

What must you do when it asks which of the following conditions (options) are necessary for statement?

Answer 86

To show that a condition is not fully necessary, find an example of a function for which the main statement is true but the condition is not.

Question 87

Answer 87

Question 88

Answer 88

Question 89

Answer 89

Question 90

Answer 90

Question 91

Answer 91

Question 92

Answer 92

Question 93

Answer 93

Question 94

Answer 94