2018 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

JC Mathematics

Post will be updated again on 9th November 2018.

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Question 9:
Question 10:

Relevant materials

MF26

KS Comments

2018 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

JC Mathematics, Mathematics

Post will be updated again on 14th November 2018.

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Question 9:
Question 10:

Relevant materials

MF26

KS Comments

Modal value & Expected value

Modal value & Expected value

JC Mathematics

Let us look at the difference between modal value and expected value. We shall start by saying they are different, albeit close.

Modal value refers to the mode, that is, the value that has the highest probability (chance) of occurring.

Expected value refers to the value, we expect to have, on average.

Before we start, I’ll do a fast recap on Binomial Distribution, X \sim \text{B}(n, p) by flashing the formulae that we can find on MF26.

\text{P}(X = x) = ^n C_x (p)^x (1-p)^{n-x}

\mathbb{E}(X) = np

\text{Var}(X) = np(1-p)

The expected value is simply given by \mathbb{E}(X).

Now to find the modal value, we have to go through a slightly nasty and long working. You may click and find out.

We have that \frac{\text{P}(X = r + 1)}{\text{P}(X = r)} = \frac{(n-r)}{(r+1)}  \frac{p}{1-p}. This is what we call the recurrence formula. We consider this to give us the ratio between successive probabilities. And to illustrate how this works, nothing beats an example question.

Consider candies are packed in packets of 20. On average the proportion of candies that are blue-colored is p. It is know that the most common number of blue-colored candies in a packet is 6. Use this information to find exactly the range of values that p can take.

First, most common number is the same as saying the modal/ highest frequency.

This means that \text{P}(X=6) is the highest/ largest probability… Let us turn our attention to the recurrence formula now. If \text{P}(X=6) is the largest, then it means that \text{P}(X=6) \textgreater \text{P}(X=7) and also \text{P}(X=6) \textgreater \text{P}(X=5).

Lets start by looking at the first one… \text{P}(X=6) \textgreater \text{P}(X=7)

\text{P}(X=6) \textgreater \text{P}(X=7)

1 > \frac{\text{P}(X=7)}{\text{P}(X=6)}

\frac{\text{P}(X=7)}{\text{P}(X=6)} \textless 1

But hold on! This looks like the recurrence formula. (ok, in exams, its either you use the recurrence formula or derive on the spot. Both works!)

Now I’ll advice you try the second one (before clicking on answer) on your own, that is, \text{P}(X=6) > \text{P}(X=5).

Now, if the question simply says that the expected number of blue-colored candies in a packet of 20 is 6. Then

\mathbb{E}(X) = 6

(20)p = 6

p = \frac{3}{10}

We observe that this value actually falls in the range of p we found.

Scatter Diagrams

JC Mathematics

I was teaching scatter diagram to some of my students the other day. A few of them are a bit confused with correlation and causation. I gave them the typical ice cream and murder rates example, which I shared here when I discussed about the r-value.

Think of correlation like a trend, it simply can be upwards, downwards or no trend. And since we only discuss about LINEAR correlation here, strong and weak simply is with respect to how linear it is, that means how close your scatter points can be close to a line.

Since A’levels, do ask students to draw certain scatter during exams to illustrate correlation. Here is a handy guide.

Scatter Diagrams
Credits: pythagorasandthat.co.uk
Solutions to Set B

Solutions to Set B

JC Mathematics, Mathematics

Hopefully, you guys have started on the Set B. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂

If you do have any questions, please WhatsApp me. 🙂

Relevant Materials: MF26

Solutions to Set A

Solutions to Set A

JC Mathematics, Mathematics

Hopefully, you guys have started on the Set A. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂

If you do have any questions, please WhatsApp me. 🙂

Relevant Materials: MF26

Thoughts on the H2 Mathematics (9758) Papers 2017

Thoughts on the H2 Mathematics (9758) Papers 2017

JC Mathematics, Mathematics

Solutions can be found here.

Personal Thoughts: The paper isn’t tedious. Students can do them so long as they know their stuffs. There are several generalising of questions, like question 6 of paper 1. We also saw how conditional probability was actually tested subtly, this tests students’ abilities to reason with guidance (not sure if after this first trial year, will they still guide the students.) Application questions were not tough and well guided. Students can solve it easily if they read it well. Statistics was well crafted and neat.

To be blunt, I’ll give credit to the 9740 H2 Mathematics paper that run concurrently, since it is too tough to set two sets of papers. Its easy to acknowledge that the 9740 (2016) paper was way harder than 9740 (2017). Next year won’t be the same.

Advice: Students should be careful when you revise, make sure you learn, and not do. Understand what you’re doing. The 2017 paper was an inquisitive paper, examiners were watching closely if you pay attention to details, and know your definitions well.

I’ll do an analysis for the paper, you can click on the individual question and read. For students that took the paper, I hope it doesn’t demoralise you.

Paper 1

Paper 2

 

 

2017 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

2017 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

JC Mathematics, Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6: \mu = 1.69, \sigma^2 = 0.0121
Question 7: 0.254; 0.194; 0.908
Question 8: 40320; 0.0142; \frac{1}{4}
Question 9: \text{r}=0.978; a=0.182, b=2.56; $293
Question 10: 0.0336; \bar{y}=0.64, s^2 = 0.0400; Sufficient evidence.
Question 11: \frac{48+x}{80+x}, \frac{32+x}{80+x}; x= 16; \frac{25}{32}; \frac{7}{16}; \frac{341}{8930}
Question 12: 0.773; 0.0514; 0.866; 0.362

 

Relevant materials

MF26

KS Comments