### Solutions to the modified A’levels Questions

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

2012/P2/Q10

### Some TYS Questions worth looking at

Prelims Exams was scary. H2 Mathematics isn’t that easy.

Students that had difficulties finishing their prelims exams, should consider working on their time management. The best way to do it, practice 3 hour paper… in a single sitting. And students should note to modify their TYS slightly as several questions in each paper are out of syllabus. In general, we give ourselves 1.5min for every 1 mark.

So here, I’ll share a list of questions that Mr. Wee has compiled. Mr. Wee also wrote e-books recently on solving non-routine problems. They are very interesting and provides the learners a new perspective to solving problems.

Non-routine Problems (Click to link to the solutions)
N2016/P1/Q3
N2016/P1/Q8
N2016/P1/Q10(a)
N2015/P1/Q3
N2015/P1/Q11

Application Questions
N2016/P1/Q9
N2015/P1/Q8
N2014/P1/Q11
Specimen P1/Q9
Specimen P1/Q11
Specimen P2/Q9
Specimen P2/Q10

All the best for your revision!

### Making Use of this September Holidays

This is a little reminder and advice to students that are cheong-ing for their Prelims or A’levels…

For students who have not taken any H2 Math Paper 1 or 2, I strongly advise you start waking at up 730am and try some papers at 8am. I gave my own students similar advices and even hand them 4 sets of 3 hours practice papers. Students need to grind themselves to be able to handle the paper at 8am. It is really different. Not to mention, this September Holidays is probably your last chance to be able to give yourself timed practices.

For students who took H2 Math Paper 1, you might be stunned with the application questions that came out. For NJC, its Economics. For YJC, its LASER. For CJC, a wild dolphin appeared. And more. These application questions are possible, due to the inclusion of the problems in real world context in your syllabus. You can see the syllabus for yourself. I’ve attached the picture below. So for Paper 2, expect these application questions to be from statistics mainly, as suggested in your scheme of work below.

For students that have took H2 Math paper 1 & 2, and this is probably ACJC. The paper was slightly stressful, given the mark distributions, but most of the things tested are still technically “within syllabus”. For one, the directional cosine question, is a good reminder to students that they should not leave any pages un-highlighted. AC students should be able to properly identify their weaknesses and strengths this time round. If its time management, then start honing that skill this holidays – by having timed practice. A quick reminder that the TYS papers are not 3 hours, since some of the questions are out of H2 Mathematics 9758 syllabus. Students can consider the ratio of 1 mark to 1.5 min to gauge how much time they have for each paper.

R-Formulae seems to be popular about the prelims exams this time round, making waves in various schools. Perhaps it was because it appeared in the specimen paper, and if you’re keen on how it can be integrated or need a refresher. I did it recently here.

Lastly, for the students that are very concerned on application questions. Check the picture below. It contains some examples that SEAB has given. Students should also be clear about the difference between a contextual question and an application question.

With that, all the best to your revision! 🙂

### H2 Mathematics (9740) 2016 Prelim Papers

So many students have been asking for more practice. I’ll put up all the Prelim Papers for 2016 here. Do note that the syllabus is 9740 so students should practice discretion and skip questions that are out of syllabus. 🙂

Here are the Prelim Paper 2016. Have fun!

Here is the MF26.

### Thinking [email protected] #9

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found here

This is a standard summation question. I’m interested in the last part only.

The answer to (ii) is written there by the student. I’ll only do the solution to (iv).

### Checklist for Vectors

Many schools have been doing vectors recently. Thought I’ll share a little summary/ checklist I have done for my students.

Basic Concepts

• Operations on Vectors
• Scalar multiplication
• Dot Product (Scalar)
1. a • a = |a|2
2. If a ⊥ b, then a • b = 0
3. a • b = b • a
• Cross Product (Vector)
1. a × a = 0
2. a × b = − b × a
• Unit Vectors
• Parallel Vectors ( a = k)
• Collinear Vectors ( Parallel with a common point )
• Ratio Theorem ( Found in MF26)
• Midpoint Theorem
• Directional Cosines
• Angles between two Vectors
• Length of Projection
• Perpendicular Distance

Lines

• Equations
• Vector Form ( : r = a + λb, λ∈ ℜ )
• Parametric Form
• Cartesian Form
• Line & Line
• Parallel ( Directions are parallel to each other. )
• Same ( Same Equations )
• Intersecting ( There is a unique solution for λ and μ. )
• Skewed ( Not parallel AND not Intersecting. )
• Angle between two lines ( Angle between their directions )
• Point & Line
• Foot of Perpendicular
• Perpendicular (Shortest) distance
• Point on Line

Planes

• Equations
• Parametric Form ( π r = a + λb + μc, λ, μ ∈ ℜ )
• Scalar Product Form ( r • n = a • n  = d )
• Cartesian Form
• Point & Plane
• Foot of Perpendicular
• Perpendicular (Shortest) distance
• Distance from O to Plane
• Point on Plane
• Reflection of Point
• Line & Plane
• Relationships
1. Parallel
• Line intersects Plane entirely ( Infinite Solutions )
• Do not intersect ( No Solution )
2. Not Parallel
• Intersects at a point ( One Solution )
• Intersection Point
• Angle between Line & Plane
• Reflection of Line
• Plane & Plane
• Relationships
1. Parallel
• Same ( Infinite Solutions )
• Do not intersect ( No Solution )
2. Not Parallel
• Intersects at a line ( Infinite Solutions )
• Intersection Line ( Use of GC )
• Angle between two Planes ( Angle between their normals )

### Random Questions from 2016 Prelims #10

PJC P2 Q1

The complex numbers a and b are given by $2 + 3i$ and $-4-5i$ respectively.

(i) On a single Argand diagram, sketch the loci
(a) $|2z-a-b| = |a-b|$
(b) $0 \le \text{arg}(z-b) \le \text{arg}(a - b)$

(ii) Find the range of $\text{arg}(z)$ where $z$ is the complex number that satisfies the relationships in part (i)

### Random Questions from 2016 Prelims #9

HCI P1 Q2

Solve the inequality $\frac{2}{4(x+1)^2+1} > 1$

Hence find $\int_{-1}^{\frac{\sqrt{3}-2}{2}} |1 - \frac{2}{4(x+1)^2+1}| dx$, leaving your answer in exact form.

### Random Questions from 2016 Prelims #8

ACJC P2 Q3

The function g is defined by

$g: x \mapsto \begin{cases} 2x, & \text{for }0 \le x \le \frac{1}{2} \\ 2-2x, & \text{for } \frac{1}{2} \le x \le 1 \end{cases}$

(ii) Explain why the composite function $gg$ exist.

(iii) Sketch the graph of $gg(x)$.