Maths

Question 1

Remember for trig questions for min angle, and cos and sun, what should you ALWAYS DO

Answer 1

find the negative values,mbevause adding might give a smaller value

Always fir cos , find cast, -2pi or use even function prorpty

Question 2

Remember for transformations,
It each transformation into brackets

Answer 2

Therefore don’t make mistakes multiplying something by 2 when shiukdnt

Question 3

Fucntioms

Answer 3

Are many to Ken or one to on mapping

For an inverse function to be true the function must be one to one so restrict , as inverse of many to one is one to many which is not a fucntiom

The domain and ranges of inverse functions are swapped , but there maybe other thingd too
% find inverse by making y the subject

Question 4

Inequalities, remember dotted and two inewuakitedfor shaded regions

Question 5

WHATS A PERIODIC SEQUENCE

Answer 5

One thst keeps repeating st regular intervals, and the period is the number of terms thst repewt

Question 6

DIFFERENC e between series and seweucney

Answer 6

Sequence is just a det numbers ina Given order

A series is the sum of the sequence

Question 7

Divergent vs convergent

Answer 7

Diverges means infinity, converged means arrive at a liktm

If b is -1 this will diverge

I’d b is 1 this will converge si it can’t be 1 but it can be -1

Any values outside it will diverge!

Converge between -1 and 1, including 1

Question 8

Take care for tangent and normal

Answer 8

If they want exact working might be better to sue y- y1 = m (x-x1)

Question 9

How to solve fraud triangle in semi circle questions with diameter

Answer 9

Never use diameter , use distance from each end of diameter to point in semi circle as yiu can slash find this and do 1/@BH

Question 10

Path of the particles is what
Motions of particle is what

Answer 10

Oath is dispalcment
Motion is velocity

And Remmeber ti make Cartesian det oath to x and y and parametric t

Question 11

Bruv don’t be stupid snd remember product rule when there is and x outside bracket s

Answer 11

So when diff twice be wary!

Question 12

IF VELOCLITY IS NEGATIVE at a time, or whatever how to tell if SPEED IS INCREASING

Answer 12

find the rate if change if velocity so the acceleration

If the accerlwtion is negative, and it already is negative, it’s getting negativer so it’s speed is actually increasing

However if accerlwtion is positbe and it’s negative it’s slowing down

Vice verbs too!

Question 13

How to show a line is a tangent to a vorfiel

Answer 13

Sub in and discriminatory should be repeated 0 means one solution

Question 14

How to prove two things are perpendicular again

Answer 14

Make sure brsdients multiply to minus 1!

Show initsl angles

Show that they perpendicular so everything is 90, ,sans a rectangle

Now show two oppsite sides bith hsve the same length so must be sqaure

Question 15

Why can Unterste bunimial expansionnonly

Answer 15

If the limits of the integral are completely in the renege in which the model is vs,id for

And the limits are not not in the domain!

Question 16

Accerlwtion better modle now before v goes CONSTSNT?

Answer 16

Because acceleration is “ just ss it goes CONSTSNT, which mesns it rwsches max speed without suddenly changing accerlwtion

Question 17

How to prove infinitely primes

Answer 17

Ssume there is a if it’s list of primes from p1 to pn

Let P be the number p1 x p2 to n +1

If P is prime, this is not in the list, so contracidts

If p I nit prime, by number theory, it must be able to have a prime factor

But this means the prime factor must be a factor of 1 too,
Which js impossible
Thus the prime number thst csn divide it is not in the lidt

And thus this contradicts the original statement

And there are ifnintiley number of prime

Question 18

Changing binomial up cna you Stil approximate same baleu

Answer 18

NO CHECK THE NEW RANGE KF VS,IFITY

Question 19

See transformation, look if it eokesfor zTop and BOTTOM

Question 20

If CONSTSNT snd trig, what can you don

Answer 20

Jsut keep ti in same form and act like Su using cast

Question 21

For k CONSTSNT questions and they give you a range how to calculate

Answer 21

Use the maximum and minimum values of range, so you know it will lie here

Do calc

See if it was a sqaure number or something snd msde a difference

Question 22

Remember if you get equation and answer one looks right consider rest of graph might be diff stick with unstick well done!

Question 23

Equating effeicmt wackzino

Answer 23

Yeah in this case equate the coeffeicnt that ARE SUPPOSED TO BE THERE

THE REESSON THIS IS 9 BEVSUSE IT SNOT SUPOOSED TO BE THERd