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

Plan for 11th June

Plan for 4th June

Plan for 28th May – 4th June

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

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

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

HW for 7th-14th May

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

HW for 30th April-7th May

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

Tentative HW for 23rd-30th April

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:

Google Drive

Google Drive I will be storing files in for this period of time:

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