# Samiya

### Plan for 28th June

• Regarding your DE question over whatsapp on 21st June, most of the steps are actually good. Small careless mistake. In the first step of by parts integration, the first term should be $\frac{x}{2-x}$ (without the negative) because integrating $(2-x)^{-2}$ gives us $\frac{(2-x)^{-1}}{-1(-1)}$ (the second negative one from chain rule).
That aside, you were on the right track. We can find $c$ to be $-\ln 2$ so our particular solution is $y= (2-x) \left ( \frac{x}{2-x} + \ln (2-x) - \ln 2 \right )$.
• Recommended questions: Start with stats Q8-10. Then pure math Q2-5,7 CJC 2018 MYE
• Extra (optional). Stats Q7-10, pure math Q2,5,6MJC 2018 MYE

### Plan for 18th June

• Review of last week's work:
• Questions to look at on your own:
Paper 1 Q4(ii): for $f^{-1}(x)$ formula, remember to change $y$s back to $x$s at the last step.
Paper 2 Q5: have a look at the question and your tree: I think you swapped the 0.35 and 0.65 around. The other steps throughout your working looks good otherwise
• Questions we'd discuss together: Paper 1 Q4, Paper 2 Q4(ii), 6, 7e, 9cii,d, 10
• Other questions not mentioned are done well: keep it up!
• TPJC 18 MYE: Paper 1 Q1,3,6,7,9, Paper 2 Q1,3
• I've compiled the answers (first draft, so high chance of typos and mistakes so immediately ask me if any of your answers don't match up) TPJC 18 MYE Answers

### Plan for 11th June

• Recommended questions Paper 2 Q4-9 TPJC 18 MYE
• Next Week: Paper 1 Q3,4,6,7,9, Paper 2 Q1-3

### Plan for 21st May

• Mixed distributions HW discussion: Q4, 1, 2b,f,3c,d
• Complex 2017 Complex questions compilation
• General algebra: use of conjugates, quadratic formula, simultaneous equations, compare real and imaginary: ACJC 1(a), CJC (a), HCI 2, PJC
• Conjugate root theorem AJC: 2, IJC 1, RI (a)
• Conversion between 3 forms, purely real/imaginary, Argand diagram: CJC (c), HCI 1, MI (b), NJC (b)
• The half angle trick: DHS (c)
• More complex problems: 4. Module 5 Complex Numbers

### Tentative plan for 7th May

• Review any questions from last week/school/tutorial
• Normal past prelim questions: Q2,4,5,6 S5_Normal
• Start discussion on sampling. Attempt Q8d from normal worksheet together.
• Sampling discussion Sampling Discussion Questions
• If $X$ is normally distributed,
• Sum, $X_1 + \ldots + X_n \sim N(n \mu, n \sigma^2)$, Average/sample mean $\overline{X} \sim N\left( \mu, \frac{\sigma^2}{n} \right)$
• If $X$ is not normally distributed (unknown, DRV, binomial), CLT (if $n$ is large)
• Concepts about population, sample, population mean, population variance, sample mean, unbiased estimate of population mean, unbiased estimate of population variance
• Mixed distributions worksheet: QSS Random Variables

### School Test Review

• Q2(ii) To get easier cancellation, it's useful to put our fractions in either ascending/descending order
• Q2(iii) How to use (ii): Splitting up the summation by changing limits
• Q3(i) Q3(i) discussion post
• Q7 First order test presentation
• Q8(ii) Using GC
• Q10(i) Use GC to get $\theta$
• Q10(ii) Continuation after the show part to find exact area $A$

### Google Drive

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

For the probability worksheet, the questions with asterisks (**) are from the next topic of DRV. Q2c is a tough question. I've explained the technique in tackling these sort of questions in two TYS examples in the following youtube videos. You can either look at those videos or ask me to explain to you directly.

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

• Probability Worksheet: Q1-6, 12-15