Questions (2) Flashcards
You got this wrong, because you skipped the important algebra steps in a rush. You also didn’t consider that Pascal’s triangle would have been a less messy and more convenient method over expanding each bracket.
In this case, you can completely avoid using factor Therom and instead just use factorising by inspection
To save time, do the scale factor method of triangle when tryna figure out distance /hypotenuse
The whole area top and bottom is usually considered not just a random small part of the
You got this wrong because of your mental arithmetic. 25% of 20 is 5, not 4
Use the 1 minus trick and imply between the lines
Learn this
Log change of base law
“Maximum possible “
A quintic is same shape as cubic
Manipulating equations to get better simultaneous solutions
Least possible value hints to TP. Use chain rule if applicable
Bare confusing
Write every working out step and don’t be lazy - trust it’s worth it
Remember and recognise the geometric sequence
Get better at sketching inequalities and finding counter examples
Know that “congruent “ means ASS, SSA, SSS and know that if sin (a) = sin (b), does not mean a=b
Try a find counter examples when it is sufficient
When asked about these questions draw the most wild, unsymmetrical graph ever
Similar triangles live in action
Notice how it says for sum. Draw the graphs
what does this mean?
Square the actual function before doing any integration
Square the function, then draw graph then do integral. To find a counter example of an if… then statement find one that first works for first part of statement and then one that doesn’t work for the second.
Start with plan, then front, then side
Practice integrating, esp be cautious of negative powers
Practice differentiating aswel
Always remember to measure angles when dealing with similar triangles
KNOW THE ARITHMETIC SERIES FORMULA
Say inequalities out loud if it helps
Just keep trying new values- it’s not supposed to be obvious!
Pushing graphs up by one creates a new rectangle and the bottom (when integrating with limits)
Don’t be scared to integrate
Stretch factors are actually represented as a fraction
Similar triangles!
It’s easier to manipulate numbers when they are written in term of prime factors sometimes as ir’s then easier to square or cube root
Manipulate (rationalise) without rationalising
Logic?
Rectangle formed after pushing same graph up, area trick
When it says which of the following “must” be true, come up with counter examples
To counter example an if… then first bit must be true and then false
A sufficient condition means that the values that it does hold are all true, but it doesn’t contain every single true possibility that exists.
A necessary and sufficient condition will contain every single possibility that can exist.
Negating statements
What graph can you draw the represent this?
Y = x
PRACTICE INTEGRATION AND GET COMFORTABLE WITH IT
Write out the factorial notation instead of the n choose r as it helps avoid mistakes
Start off simple by writing down what you know, then start trying to solve/ analyse. Don’t do it in your head cos you’ll probably get it wrong or make it more complicated than it needs to be
CHECK YOUR WORKING OUT FOR ANY NEGATIVE SUGNS THAT YOU MISSED
Coming up with counter examples
Draw the perpendicular bit before and then turn into a quadrilateral. Obviously the aim was to come up with an irregular quadrilateral
Notice how you can use the result to for, an arithmetic sequence
Always check for extra solutions, removing solutions or not looking for extra solutions when sin, cos and tan
Try using actual real life numbers
Negation statements. Basically you negate every single thing you can find
The error exists because they square rooted and this affects the inequality which they failed to acknowledge
Uniquely determines means one solution of the angle in given range
Be careful of small things like that. Coz Y intercept is positive, turininf point is still gonna be positive
Get to grips with the f(x) and x how it looks on a graph. ALSO if it says “necessary” start by looking at what the question has given as it is asking you what this given information implies.
What’s the unit circle ?
What are the two formula for the sum of the geometric sequence?
You got this wrong because of carelessness with working out (especially with negative numbers) and not having clear and neat working out. From now on: always draw a bold box around solutions so that it is easier to substitute in without mistakes. AND for each one of these questions can you please check your working out.
Think about bigger numbers in counter examples or even the same number: does this work?
Algebraic approach helped coming up with counter examples
How can you tell which bits of a curve are concave/ convex?
Concave is when it is going clockwise and convex is therefore anticlockwise
What does the trapezium rule say about convex and concave curves?
Convex= over estimate and concave = underestimate
What is the second derivative of concave and convex curves?
Think of how quickly the gradient is getting steep
Re write the logarithms in an easier way
Get better at graphing inequalities
When there is modulus, look at the cases where x is positive and the cases where x is negative
Factorise using surd method
Rationalising denominators
Need to know the red box thing
Kinda have make assumptions and infer
Hidden quadratics - logs edition
Trick question, make sure you acknowledge this is the graphs have different powers
Writing down a few numbers to test/ try the solution yourself is always helpful
Maybe it’s best to not always simplify until required. Also “solutions” may be a hint towards quadratic formula
A “sequence of translations” is equivalent to a translation in the x direction followed by a translation in the y direction (no stretches )
Another maximum possible area one
In what cases is the unlucky ASS actually congruent after all?
Considering ALL possible cases. A =1, a=0, a <1, a>1
Just because an algebraic expression is not factorisable doesn’t mean the number it represents doesn’t have any integer products
