Paper 2 Logic Flashcards
why must you always check before taking the logarithm of both sides?
- taking logs can loose/ add solutions
- Always make domain resitricts as to check that the value is positive ( cannot be = 0 either)
Loging and squaring can both introduce extra solutions. The substitution trick is neat
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)
If a part of the inequality is true for all values of x, you can drop the inequality
Simple notation
For a sufficient condition to be true, must be affirmative (100%) no maybes
Recognise that recurring means sum to infinity
What is 2nd approach to this question
They always want you to think in term of geometric series sums
What can you infer about stationary points given the number of roots?
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
Might be more efficient to have a yes no prime section to avoid misses
what is the simplest way to rationalise surd?
What does this mean?
What is a way to view the modulus function
The positive distance of x from 3
Draw the graph of
(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.
Reflect whatever is below the x axis
what must you be aware of with the recurance relationship type questions?
always makes sure you write out enough terms
do till at least 10
what are common mistakes when doing binomial expansion?
- not putting a bracket around the whole thing. eg: 2x^7 instead of (2x)^7
- forgetting about the minus sign. eg: (3x)^5 instead of (-3x)^5
What is another way to write
How many terms are in the sum
n - m + 1
Alternate method of finding the smallest distance
why does the sin rule used in triangles give an ambigious result?
sin A can given 2 values below 180
what are some limit/ things to keep in mind of the following rule?
- 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]
Sketch
Draw the graph of
What are some things to note?
- the graph is only defined for 𝑥 > 0
What is
Where does this formula come from?
what does it mean for a cubic graph to have no stationary points?
it only has one point of inflection. This is because when you differenciate, the quadratic has no real solutions
What does the following imply?
Why is this true?
When are functions defined as strictly increasing or strictly decreasing?
When is this true
Function is symmetrical about the y axis
When is this true?
What are all of the following?
Wrong
What is another way of writing?
What can this also be written as?
What does this rule essentially mean?
What is the trapezium rule formula ?
When is the trapezium rule an overestimate /underestimate / useless?
What is the effect on the graph of a vertical stretch by a scale factor ‘a’?
Summarise these transformations
How firm do sufficient / only if statements have to be?
ROCK SOLID
Memorise table on shapes
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
What is the statement negation table ?
Get to grips with manipulating the function notation
To be sufficient not necessary the statement must be true, but there are other cases apart from the condition where it is also true
What is the definition of a polynomial?
Continuous smooth curve. With non-negative integer powers
Necessary and sufficient means logically equivalent statement
What must you do when it asks which of the following conditions (options) are necessary for statement?
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.
