Challenging Alevel questions

These are the more challenging alevel questions

2018 P1: 6,9 iii, 10, 11

2018 P2: 6,7,9v

2017 P1: 5ii, 6, 7ii, 8, 9c, 11 iii

2017 P2: 1 ii, 2 ii, 3a, 4b, 7i, 9v, 9 vi

2016 P1: 3, 4, 6 iii, 7, 8 iii, 10 bii, 11 b

2016 P2: 2a ii, , 2b,  4bii, 7 iv, 9a

2015 P1: 3, 5 iii, 7iii, 11 ii explain why is maximum, 11 iii

2015 P2: 1 ii, 2ii, 3b, 4b iii (some students interpret wrongly), 9 ii, 9 iii, 10 iv, 11 iv

2014 P1: 2, 3, 4ii, 6 (a) (ii), 6 (b) (ii), 7 iii, 7 iv, 8 iii, 9 iii, 10 ii, 10 iv, 11 iii, 11 iv

2014 P2: 1 ii, 3 ii,  4 b ii, 6 ii, 6 iii, 10 ii

2013 P1: 2, 5, 6i, 6 iii, 8 i, 9 ii, 9 iii, 10 i, 10 iii, 11 ii, 11 iv

2013 P2: 1 ii,  2, 3 iii, 4iii, 6, 7 i, 8 iii, 9 i, 10 i, 11

2012 P1: 4, 5, 6 iii, 7 iii, 8 iii, 9 iii, 10, 11

2012 P2: 1 b, 3 ii, 3 v, 4, 6ii, 7 iii to v, 8 iii, 8  vii

2011 P1: 1, 3 iii, 4 i, 5 iii, 7 ii b, 8 c, 9 ii, 10 ii

2011 P2: 2 ii, 3 ii, 3 iii,  8 i, 9ii b, 10 iii, 11 ii

2010 P1: 1 ii, 6 iii, 6 iv, 7,  9, 10 i, 11 ii, 11 iii

2010 P2: 1 ii, 3 iii,  4v, 7iv, 7v,  8ii, 8iii, 10 iv

2009 P1: 1 ii, 2, 4, 10 iii, 11 iv

2009 P2: 1 i, 1 iii, 2 iii, 2 iv, 3, 4,  6 ii, 6 iii, 6 iv, 7, 8iii, 8iv, 9 iv, 11 i, 11 ii, 11 v

2008 P1: 1, 5 ii, 6a,  9 ii, 10 ii a, 10 ii b,

2008 P2: 1 iv, 2, 7, 8iii, 8 iv, 10 , 11 last part

2007 P1: 1, 2 i,  5 (hence part), 7i, 10 iii, 11

2007 P2: 2 iii, 2 iv, 3 iii, 4 ii b,  7 last part, 8, 9 (i) (b), 9 (ii) (c), 11

Challenging Probability problem 6

The owner of a restaurant counts the number of banquets received by the restaurant at the end of each week. The probability that the restaurant receives at least two banquets in a randomly chosen week is 0.3. A week is considered busy if the restaurant receives at least two wedding banquets in the week.

Calculate the probability that in a period of 6 consecutive weeks, the 6th week is the second busy week, given that there is at most one busy week in the first four weeks.

Ans: 0.166

Solution

1

2

Dividing people or distinct objects into groups

Calculating number of ways of dividing people or distinct objects into groups of the same size often pose difficulty to students.

Hopefully these examples will help students understand the concept.

Basic Example

How many ways can 10 children be divided into two groups of 5?

1

When dividing people or distinct objects into groups, if p groups are indistinguishable, we need to divide by p! to avoid double counting.

Challenging example 1 

At a particular reception, 9 guests are to stand at 3 identical round tables. How many ways can this be done if there are at least two people at each table?

3

Challenging example 2 (SAJC 2011/MYCT/2/6)

2

Distinguish X1+X2 from 2X

This challenging question on normal distribution was posted in Edusnap by a student.

Screenshot_2015-05-27-13-52-49

There were two mistakes made:

1) Interpreting the distribution of 2 large hampers and n small hampers as 2L + nS.

2) Calculation of variance

Here is the correct solution:

hamper

1

2

Smallest possible value of n = 9

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When the question mentions n items, the distribution is X1+X2+…Xn.  When the question asks for “n times of a randomly chosen..”, then the distribution is nX.

Students also need to be familiar with calculating the expectation and variance of the sum or difference of normal distribution using the formula:

form

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