This question was posted by a student at Singapore JC maths.

**Solution for Part ii**

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# Category: Challenging questions

## Challenging graphing technique question 1

## Challenging Method of difference question 1

## Challenging System of Linear Equations Problem 2

## Challenging Alevel questions

## Challenging Probability problem 6

## Challenging Vector problem 4

## Dividing people or distinct objects into groups

## Challenging Differential equation problem 1

## Distinguish X1+X2 from 2X

## Challenging Normal Distribution problem 3

This question was posted by a student at Singapore JC maths.

**Solution for Part ii**

Solution for the Hence portion:

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

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 6^{th} week is the second busy week, given that there is at most one busy week in the first four weeks.

Ans: 0.166

**Solution**

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?

When dividing people or distinct objects into groups, if ** p groups** are

**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?

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

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

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:

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:

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