### Transformations worksheet

### Plan for 28th June

- Recommended questions: CJC 2018 MYE
- Extra (optional). Q11 is hypothesis testing so we can skip that for now MJC 2018 MYE

### TPJC Paper Comments

Paper 1

- Q1,2: Good!
- Q3: Look for the line right after the “shown” line in your working. In the by parts step, when we differentiate the “$u^2$”, we should have “$2u$” so we’re missing a “2” in our working. All other steps look good.
- Q4(i). Add in these two key words: Since every
**horizontal**line $y=k$ cuts the graph of $y=f(x)$**at most**once, … - Q4(iii). For show questions good to give a bit more details. Your line $R_f \not \subseteq D_f$ is good, but even better if we start off by copying down what $R_f$ and $D_f$ is.
- Q5(ii) For qns that ask us for reason, good to give a short word statement: “Hence $\displaystyle \sum_{r=1}^\infty \frac{1}{4r^2-1}$ converges” after the $\frac{1}{4n+2}\to 0$ line.
- Q6(iii) Your answer is good: keep it up! If you want the most simplified answer, whenever we see a “big” power on our surds, we can further simplify it by taking out all even powers. For example $(\sqrt{3})^5 = (\sqrt{3})^4 \sqrt{3} = 9 \sqrt{3}$. So for our coordinates of $A$, we can further simplify $(\sqrt{\frac{2}{3}})^3$ into $\frac{2}{3}\sqrt{\frac{2}{3}}$.

A similar approach can be used for Q7(ii) to simplify $(\sqrt{8})^7$ into $1024 \sqrt{2}$. - Q9(iii) Careless at the last step. $\left | \begin{pmatrix} 6 \\ 2 \\ 4 \end{pmatrix} \right |$ is $\sqrt{56}$, not 56.
- Q10(a)(ii) Careless in the differentiation: the 13 should disappear after differentiation.

Paper 2

- Q1(a): For $y=3f(x)$, we are stretching parallel to the $y$-axis by factor $3$ (rather than $\frac{1}{3}$ for $x$-axis stretching like $y=f(3x)$). So final $y$-coordinate should be $3b$ rather than $\frac{b}{3}$.
- Q2(ii): Look for the line $an=3$ in your working. That step is correct. Careless in the next step where we had $a = \frac{n}{3}$ vs the correct step of $a = \frac{3}{n}$.
- Q4(ii):
- Q8(vi) Your answer is good! The short, mathematical way to phrase that will be that the event in part (iv) is a proper subset of the event in part (v).
- Q8(vii) You might want to double check your GC/table working. The answer should be 8 rather than 7 (all above steps look good).
- Q9(ii) Almost there. There’s an extra step of choosing which boys and girls to sit down. So we must further multiply by $\binom{5}{2} \times \binom{6}{3}$ to get the actual answer.
- Q9(iv): need an extra $\times 2!$ to account for the fact that either guys or girls could be first.

### TPJC Paper: Things to discuss together during class

Paper 1

- Q5(iii): use of “sum” vs “term” after the substitution step.
- Q7(iii): getting the 3 smallest positive integers for $n$ (using trial and error and the GC).
- Q8(iv)
- Q9(iii): Hence method
- Q10(a)(iii) Sketching
- Q10(b)

Paper 2

- Q4(iii) Recommendation in dealing with the modulus in DE questions.
- Q6(ii)
- Q9(iii)(a)
- Q10 (iii)

### Plan for 18th June

- Last week’s HW: Q1d, 5d. The rest are good.
- Sampling (no CLT) Worksheet
- TPJC 18 MYE
- TPJC 18 MYE Answers

### Plan for 11th June

- HW from last week: discuss presentation and 3(iii)
- Normal Summary Notes
- Q1, 5 Normal Basic Questions
- Past prelim questions (ignore the part with asterisks) Q1a,b,c, 3, 4, 5, 6, 9 S5_Normal

### Plan for 4th June

- Normal Summary Notes
- In this order: Q2(i),(ii),(iii), 3(i),(ii),(iii), 4, 6. Then Q1, 2(iv), 3(iv), 5,7,8,10,12 Normal Basic Questions
- Past prelim questions for next week S5_Normal

### Plan for 28th May – 4th June

- VJC 2018 MYE: Pure math 1 Q1-7. Stats Q8-11. (Q12 not yet)
- VJC 2018 MYE
- VJC 2018 MYE Answers

### 21st-28th May HW discussion

- Summation: CJC (i), (iii) (don’t need to redo MOD), DHS (replacement method), Q2(ii), NYJC (can use GC for 3), SAJC (replacement method)
- 2015 TYS: P1 Q10 (careless), Q11(iv), P2 Q3a (add $k\in\mathbb{R}$ and change ‘only’ to ‘at most’), Q4b (Set notation), Q4b (sign change when ‘flipping’), Q11(iv).

### HW for 21st-28th May

- Questions from CJC, DHS, NYJC Q2 (2nd question from NYJC, Page 6), SAJC, SRJC. 2017 Summation Questions Compilation

### 14th-21st May HW discussion

- To look at on your own
- Binomial Q9a) Just key the last line in your calculator again. Should get the answer behind. Working looks good.
- 2015 TYS: Q1: In your working you had this line: $-2.4 = \frac{a}{1.6^2} + b(1.6) + c$. To get to the next line, I think your multiplied throughout by $1.6^2$. But in doing that,
**every term**must be multiplied by $1.6^2$, including the guys behind with $b$ and $c$. So the correct equation (1) should be $-6.144 = a + 1.6^3 b + 1.6^2 c$.

Equation (2) the same mistake was made.

The rest of the question (equation (3)) and later parts) are all correct from ecf. - Q4: To get full marks for this question we’d also need to prove the the area we obtained is indeed a maximum.

- To discuss during class later
- Binomial Q7bi, 9b,d
- 2015 TYS: Q3, Q5(ii),(iii), Q7(iii), Q11 (set notation)

### Plan for 21st May

- Review questions from school/HW
- 2015 TYS: Q9a,10,11. HW: Paper 2: Q1-3,4b.
- Discuss summation: DHS, NYJC 2017 Summation Questions Compilation

### Plan for 14th May

- Review questions from school/HW
- DRV Q5b, 7, binomial presentation, binomial basic questions q1(ii), 4(iii),(iv), 5(i),(iii)
- Past prelim questions (tables, graphs, combinations with other topics, mode): Q1-4: S4_Binomial_2020
- Start on revision of earlier topics/other papers
- TYS P1 Q1-5 2015

### HW for 14th-21st May

- Binomial Past Prelim Questions (S4) Q6a,b, 8, 9

### Plan for 7th May

- Review questions from school/HW
- DRV Q8, 11 S3_DRV
- DRV Binomial Summary Notes
- Binomial basic questions (assumptions, problem sum and the template, pdf, cdf, switching): Q1-3,5-6 Binomial Basic Questions
- Past prelim questions (tables, graphs, combinations with other topics): Q1-4: S4_Binomial_2020

### HW for 7th-14th May

- TBD (DRV/Binomial/Past topics/Past papers).

### HW for 30th April-7th May

- Probability worksheet (adapted from TYS)T2020_9_Probability TYS

### Tentative plan for 30th April

- Review any questions from last week/school/tutorial
- DRV Q2-6, Q10: S3_DRV
- If time permits, start discussion on binomial
- Binomial Basic Questions
- Discuss holiday revision plan

### Tentative plan for 23rd April

- Review any questions from last week/school/tutorial
- Continue drill work on probability: Probability Worksheet
- Start discussion on DRV: DRV Binomial Summary Notes

### Tentative HW for 23rd-30th April

- Q1-3: HW_Prob_DRV

### Video for technique behind probability: Q2c

### Tentative plan for 16th April:

- Review any questions from last week/school/tutorial
- P&C Worksheet Q12b: Using Venn diagrams
- Continue with Probability work: discussions on conditional probability, independent events and mutually exclusive events. (we will do Q1 and Q2 below together)
- Continue on this worksheet: Probability Basic Questions
- P&C Worksheet Q14c: Use of conditional probability
- Start drill work on probability (past prelim questions): Probability Worksheet

### Tentative plan for 9th April:

- Review any questions from last week/school/tutorial
- Continue with P&C work: Q11-14
- Start discussion on probability: Probability Summary Notes
- Look at some probability questions together: Probability Basic Questions
- Tree diagram: Q1
- Venn diagram: Q3
- Independent events: Q2

### Tentative HW plan for 9th-16th April:

- Probability Basic Questions Q14-15 (P&C and probabilities)
- Probability Basic Questions Q4-8 (P&C and probabilities)

### Google Drive

Google Drive I will be storing files in for this period of time: https://drive.google.com/drive/folders/12mPA4orUqB3d098ZCfGR5qiwAWbOJHtB?usp=sharing

### Tentative HW plan: 2nd-9th April:

- P&C Worksheet: Q1-8

### Tentative plan for 2nd April:

- Review any questions from last week/school/tutorial
- Continue discussing P&C: I’d be using the handwritten notes and examples I passed you last week.
- Drill on P&C: Permutations and Combinations Worksheet