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 H2 Mathematics (9758) 2017 Paper 1

Thoughts on H2 Mathematics (9758) 2017 Paper 1

JC Mathematics, Mathematics

This is a new syllabus and this is the first time it will be tested. Personally, I don’t think it will be easy and students should not underestimate this upcoming A’levels. And I’m referring to the A’levels, on the whole. We saw how the Science Paper 4 were… unexpected.

The new H2 Mathematics (9758) syllabus has several topics removed, and these were mostly topics that were “drill-able”, aside from complex numbers. The new syllabus added in mainly, new integration forms, focus on parametric Equations with Cartesian equations, and of course, Discrete R.V. But let us leave the statistics out.

Students should familiarise themselves with the trigonometry Formulae in MF26. There are several topics that can be linked up with trigonometry, makes me wonder why it isn’t a chapter by itself. Complex numbers has a trigonometry form too, so make sure students know how to manipulate it, given the trigonometry Formulae.

Next, students should understand the use of Maclaurin’s. What does it mean for x to be small, and the implications when they say h is small compared to R… And also finding the general term of a Maclaurin’s Expansion.

It won’t hurt to review how to find the Area using Shoe-lace method. And not forgetting our Sine Rule and Cosine Rule.

Do know how to prove a one-one function… Non-graphically. (i.e. not using the Horizontal Line Test)

Do know that the oblique asymptote of f(x) becomes y=0 when we do the y = \frac{1}{f(x)} transformation too.

Lastly, students must READ really carefully and discern every information. Having marked many scripts, many students do not read carefully and lose marks here and there. And they do add up… Be alert and read, take note of the forms that they want. Here are 10 little things to take note when you read the question.

  1. Cartesian/ Polar/ Exponential for complex
  2. Scalar/ Parametric/ Cartesian for vectors
  3. Set/ range/ interval of values
  4. Algebraically => show all the workings without a GC.. usually discriminant, completing the square or maybe some differentiation will be involved.
  5. Without using a calculator => show your workings and check with a GC (secretly)
  6. Decimal places, etc…
  7. Rounding off when you’re dealing with an inequality
  8. Units used in the questions, (ten thousands, etc)
  9. Rate of change; leaking means the rate is negative…
  10. All answers should be in 3 SF UNLESS OTHERWISE STATED. Degrees to 1 DP. RADIANS to 3 SF.

Have fun and all the best!

2017 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

2017 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

JC Mathematics, Mathematics

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

This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1: 2 \sqrt{15}; xy=6
Question 2: d = 1.5;~ r \approx 1.21 \text{~or~} r \approx -1.45;~n=42
Question 3: (\frac{1}{2}a, 0), (0,b);~ (a+1, 0,);~ (\frac{a+1}{2}, 0);~ (0, a), (b, 0);~ a = 1;~ gg(x) = x, x \in \mathbb{R}, x \neq 1  , ~ g^{-1}(x) = 1 - \frac{1}{1-x}, x \in \mathbb{R}, x \neq 1;~b= 2 \text{~or~}0
Question 4: 15.1875;~ \frac{\pi}{2a(a-1)};~ b = \frac{1}{2} + \frac{1}{2}\sqrt{1-a+a^2}
Question 5: 0.647;~ 0.349;~k=2.56
Question 6: 955514880;~ 1567641600;~ \frac{1001}{3876}
Question 7: 31.8075, 0.245;~ p = 0.0139; Do not reject h_0, Not necessary.
Question 8: Model (D); a \approx 4.18, b \approx 74.0;~ r \approx 0.981
Question 9: 0.632;~ 1.04 \times 10^{-4};~ 0.472;~ 0.421;~ 0.9408
Question 10: 0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7

Relevant materials

MF26

KS Comments

2017 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

2017 A-level H2 Mathematics (9740) 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.

This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1: ax + (2a - \frac{a^2}{2})x^2 + (\frac{a^3}{3} + 2a - a^2) x^3; a = 4
Question 2: x \textgreater \frac{1}{\sqrt{b}} + a or x \textless a
Question 3: 2
Question 4: a = 4, b =1; translate the graph 4 units in negative y-direction and translate the graph 2 units in positive x-direction.
Question 5: a = -1.5, b = 1.5, c = 7; x \approx -1.33; x \approx -0.145 or x \approx 1.15
Question 6: r = a + (\frac{d - a \cdot n}{b \cdot n}) b
Question 7: (\frac{1}{a}, \frac{1}{ae}); \frac{1}{a^2}
Question 8: z = -1 + 2i or z = 2 - i; p =-6, q=-66; (w^2 - 2w+2)(w^2-4w+29)
Question 9: U_n = 2An - A +B; A = 3, B =-9; k=4; \frac{1}{4} (n^4 + 2n^3 + n^2) ; e^x
Question 10: a = -4.4; R(1.5, 0.5, -1); \frac{1}{2}\sqrt{10}
Question 11: \frac{dv}{dt}=c; v = 10t +4; v = \frac{1}{k}(10- 10 e^{-kt})

 

Relevant materials

MF26

KS Comments

To be honest, this paper is really the same as the H2 Mathematics (9758). They just rephrased everything. You can see for yourself here.

Solutions to the modified A’levels Questions

Solutions to the modified A’levels Questions

JC Mathematics

Students of mine who have been diligently doing the modified TYS I sent them, and have difficulties with the questions that were added in to make the paper a full 3 hour paper, will find the following solutions helpful. Please try to do them in a single 3 hour seating, these are modified to cater to the 9758 syllabus…

The rest of the solutions (that are questions from the original TYS) can be found here.

2012/P1/Q10

2012/P2/Q2

20112/P2/Q7

2012/P2/Q7

2017 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

2017 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

JC Mathematics, Mathematics

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

This is answers for H2 Mathematics (9740). H2 Mathematics (9740), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1: 2 \sqrt{15}; xy=6
Question 2: d = 1.5;~ r \approx 1.21 \text{~or~} r \approx -1.45;~n=42
Question 3: (\frac{1}{2}a, 0), (0,b);~ (a+1, 0,);~ (\frac{a+1}{2}, 0);~ (0, a), (b, 0);~ a = 1;~ gg(x) = x, x \in \mathbb{R}, x \neq 1  , ~ g^{-1}(x) = 1 - \frac{1}{1-x}, x \in \mathbb{R}, x \neq 1;~b= 2 \text{~or~}0
Question 4: 15.1875;~ \frac{\pi}{2a(a-1)};~ b = \frac{1}{2} + \frac{1}{2}\sqrt{1-a+a^2}
Question 5: \frac{5}{12}, \frac{5}{14}, \frac{5}{28}, \frac{1}{21};~ \mathbb{E}(T) = \frac{20}{7}, \text{Var}(T) = \frac{75}{98};~ 0.238
Question 6: 955514880;~ 1567641600;~ \frac{1001}{3876}
Question 7: 31.8075, 0.245;~ p = 0.0139; Do not reject h_0, Not necessary.
Question 8: Model (D); a \approx 4.18, b \approx 74.0;~ r \approx 0.981
Question 9: 0.632;~ 1.04 \times 10^{-4};~ 0.458;~ 0.421;~ 0.9408
Question 10: 0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7

 

Relevant materials

MF26

KS Comments