Cultivating Champions, Moulding Success
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here
This is a standard summation question. I’m interested in the last part only.
The answer to (ii) is written there by the student. I’ll only do the solution to (iv).
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here
This is a interesting Complex Number Question.
The complex number 
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here
This is an application question for hypothesis testing from the 9758 H2 Mathematics Specimen Paper 2 Question 10.
The average time required for the manufacture of a certain type of electronic control panel is 17 hours. An alternative manufacturing process is trialled, and the time taken, 
The Production Manager wishes to test whether the average time taken for the manufacture of a control panel is different using the alternative process, by carrying out a hypothesis test.
(i) Explain whether the Production Manager should use a 1-tail or a 2-tail test.
(ii) Explain why the Production Manager is able to carry out a hypothesis test without knowing anything about the distribution of the times taken to manufacture the control panels.
(iii) Find unbiased estimates of the population mean and variance, and carry out the test at the 10% level of significance for the Production Manager.
(iv) Suggest a reason why the Production Manager might be prepared to use an alternative process that takes a longer average time than the original process.
The Finance Manager wishes to test whether the average time taken for the manufacture of a control panel is shorter using the alternative process. The Finance Manger finds that the average time taken for the manufacture of each of the 40 randomly chosen control panels, using the alternative process, is 16.7 hours. He carries out a hypothesis test at 10% level of significance.
(v) Explain, with justification, how the population variance of the times will affect the conclusion made by the Finance Manager.
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here
This is a very interesting vectors question from a recent JC BT
Shown in the diagram is a methane molecule consisting of a carbon atom, G, with four hydrogen atoms, A, B, C, and D, symmetrically placed around it in three dimensions, such that the four hydrogen atoms form the vertices of a regular tetrahedron.
Treat A, B, C, D, and G as points. The coordinates of A, B, C, and D are given by (5, -2, 5), (5, 4, -1), (-1, -2, -1) and (-1, 4, 5) respectively, By considering the line DG and the symmetrical properties of methane, find the bond angle of methane, that is, 
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here.
This is a question from 1993 Paper 1.
The positive integers, starting at 1, are grouped into sets containing 
(i) Write down the expressions, in terms of 
(a) the number of integers in the 
(b) the first integer in the
(c) the last integer in the
(ii) Given that the integer 
(iii) The sum of all the integers in the 
Hence, evaluate 
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here.
This is a question from 1976 A’levels Paper 2. I thought it is pretty interesting to discuss the question with a little extension.
(a) In how many ways can 5 copies of a book be distributed among 10 people, if no-one gets more than one copy?
(b) In how many ways can 5 different books be distributed among 10 people if each person can get any number of books?
So now, let us modify it a bit.
(c) In how many ways can 5 copies of a book be distributed among 10 people if each person can get any number of books?
Notice that the difference between (b) and (c) is that the book distributed is not identical. So for (c), we are pretty much distributing 
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here.
(i) Find the two possible values of 
(ii) Hence or otherwise, find the exact roots of the equation
[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.
Thinking [email protected] is curated by KS. More of him can be found here.
Each card in a deck of cards bear a single number from 1 to 5 such that there are 
(i) Find the probability distribution of
(ii) Show that 
Andrew draws one card from the deck, notes the number and replaces it. The deck is shuffled and Beth also draws on card from the deck and notes the number. Andrew’s score is 
A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears 
. This is to make the term in the summation similar, disregarding the lower and upper limit.
while upper limit is 
.
appear. 
by 
directly. It will affect our RHS.
. 
.
— (1)
— (2)
into (1)
or 
(rej since 
)
, find the approximate percentage change in 
when 
increases from 2 by 2%.
