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What is RCR

You can think of it like that I guess integral of sin(x)cos(x) integral of (x+2)/ (x^2 + 4x)

Well done. You are extremely close. What you have sort of done is said, (a+b)^2 = a^2 + b^2 # However this is not true since (a+b)^2 = a^2 + b^2 + 2ab. So what you should have as your integrand i.e. what your integrating is (2x^2 - 4x + 2)^2 # the square is because area circle...

Sometimes you just need to give the question a go. Sometimes when we are trying to solve, evaluate etc we may not know exactly what to do at first but if we try and give it a go we might get the answer. If that does not work Google will help, I believe v^2 = u^2 + 2as is common physics identity...

show your working out

def continuity if g(b) = lim (x-> b) g(b) then the function is continuous at point b. Note a(x^2 -9) / (x+3) = a(x-3) except x cannot equal -3 because that would result in division by zero. So now you need to find value value of a such that when x=-3, a(x-3) will equal 12

I think we can say at least this question is wrong. Not sure about the other math questions. In the future I might be useful to use emath calculator. That is quite advance, lot of features. There are also online calculators for integration and calculus with full steps.

I have not add complete look however you seem to be on the right track. You seem to have two points for x=1? I think they(Cambridge) messed up the factorisation.

bingo

sum_of_series = sigma 2^r + 2r -1 You can see part of the expression is compose of geometric and arithmetic series.

It seems oddly worded. I don't think terminology used is part of the cirriculum y = -4f[2(x+1)] -3 When y = 2 => 5/(-4) = f[2(x+1)] => x = (f^-1(5/-4) -2 )/ 2) # assuming the function has an inverse function.

"Thinking about your future self at university, what do you identify as the key challenges for you and how do you plan to manage these?" One of the key challenges will be learning how to learn on your own. Has I do not where to find resources and the materials provided by the lectures may not...

Use the theorem the expected value is given by np. This eliminates C/D. Now compute the probabilities through substitution to see if probability is around 0.2 for X=6

Use the theorem ln(f(x)) d/dx = f'(x)/f(x) # You can prove this through chain rule

So just do a partial screenshot of the histogram you make in excel. There are many YouTube videos regarding microsoft Excel.

Use the theorem cos(x) d/dx = -sin(x) in combination with chain rule. There dhould be a differentiation step by step calculator somewhere online

Was this in an exam? You would need to make use continuity correction approximate binomial distribution as a normal distribution. I would recommend reading Probability Statistic for Engineering Sciences by Jay L Devore. They should have some similar questions there or maybe try using google.

The Bernoulli would have n = 1.

binomial/bernoulli and normal distribution are completely different. normal distribution is probability density function (pdf). pdf is just fancy way of saying functions that models the probability of continuous random variable. binomial/bernoulli are probability mass function (pmf). pmf is...

For 19 a): we know px + qy + r = 0 (eq1) x^2 +y^2 = d^2 Notice that y is not i the equation of 19a). So to remove y make a substitution. Make y the subject in eq1 => y = (-r - px)/q Now substitute. A lot parametric equation have a similar format. Often just involving substitution.