Small angle approximation questions

If they ask you to use a specific one, use that

Remember the sec identity exists

Correct usage of A given B' when given value in Q

Use the formula to help get info from it

Events A and B in earlier part of Q now have event C added

All the probabilities from before are the same (in total). i.e. the regions enclosed by A and B will still be 0.9, so tells us the section of C not in A and B is the remainder of their union Do Q10c again. P(C) = 0.35

'probability H0 is incorrectly rejected'

BOTH tails (using critical values)

Test statistic mean and standard deviation

Can be worked out with sigma(x) and n. The sigma for the normal test is the s/sqrt(n), where s is calculated from the sigmax and sigmax^2

Q14 - do it again (answers: 6/2/26)

Say what mu is - population vs sample mean important. mu for hypotheses is population Don't need to standardise

Employment figures for large data set

Specifically mention 'the large data set'. Only 16 - 64, not 70 yr olds

'Explain why this expression has no solutions'

Either: Sketch graphs to show no intersect. Otherwise just reasoning - gradient of straight line smaller than gradient of positive part of modulus graph etc etc Or the mathematical working from 2/2/26

Factorise to get the roots don't just skip it

Careful to remove bottom from top

Check pictures 2/2/26. Trying to remove the r^2 to get to the answer so rewrite as sqrt(r^4) For part b, more working between step 1 and step 2 needed rlly

Finding integer value of x for which matrix (4/1/x) magnitude is an integer

All squared = 17 + x^2 17 + x^2 = n^2 n^2 - x^2 = 17 (n-x)(n+x) = 17 n-x = 1 and n+x = 17 AND n-x = -1 and n+x = -17 So x = +- 8

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Maths Y13 Mock

Maths Summer Y13

Question	Answer
Small angle approximation questions	If they ask you to use a specific one, use that
Lost working marks to dividing by cos	Factorise instead
Redo Q8 probably	Remember the sec identity exists
Correct usage of A given B' when given value in Q	Use the formula to help get info from it
How to show not mutually exclusive	P(AnB) = 0.2 0.2 =/= 0
Events A and B in earlier part of Q now have event C added	All the probabilities from before are the same (in total). i.e. the regions enclosed by A and B will still be 0.9, so tells us the section of C not in A and B is the remainder of their union Do Q10c again. P(C) = 0.35
Hypothesis test	Use the word 'suggest'
'probability H0 is incorrectly rejected'	BOTH tails (using critical values)
Test statistic mean and standard deviation	Can be worked out with sigma(x) and n. The sigma for the normal test is the s/sqrt(n), where s is calculated from the sigmax and sigmax^2
Q14 - do it again (answers: 6/2/26)	Say what mu is - population vs sample mean important. mu for hypotheses is population Don't need to standardise
Employment figures for large data set	Specifically mention 'the large data set'. Only 16 - 64, not 70 yr olds
'Solve'	Not coordinates
'Explain why this expression has no solutions'	Either: Sketch graphs to show no intersect. Otherwise just reasoning - gradient of straight line smaller than gradient of positive part of modulus graph etc etc Or the mathematical working from 2/2/26
Rationalising	Useful tool to remember
Graph labelling	y intercept
Detailed reasoning	Factorise to get the roots don't just skip it
Area between 2 lines	Careful to remove bottom from top
Quotient rule	Careful not to add them
Read Q defining bounds of x
Normal not tangent
Q11a - do it again	Check pictures 2/2/26. Trying to remove the r^2 to get to the answer so rewrite as sqrt(r^4) For part b, more working between step 1 and step 2 needed rlly
Finding integer value of x for which matrix (4/1/x) magnitude is an integer	All squared = 17 + x^2 17 + x^2 = n^2 n^2 - x^2 = 17 (n-x)(n+x) = 17 n-x = 1 and n+x = 17 AND n-x = -1 and n+x = -17 So x = +- 8
Don't get acceleration direction wrong, and check if Q says velocity changes partway through

Created by: Pyrogearos2

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