## How to prepare for H2 maths from 2019 onwards

Many students commented that 2018 alevel is very difficult. There are many non-routine questions that require students to think on their feet.

Trends from 2017 and 2018 alevel:

1. Solving in terms of a and b. Students need to know how to generalize a solution when the question is not given numbers. Need to know how to sketch graph in terms of a and b.
2. Solve inequality involving modulus in exact form.
3. Secondary school syllabus like remainder theorem appear in N2017. R-formula appear in specimen paper.
4. Using integration techniques to solve questions outside h2 maths syllabus: such as evaluate arc length given the formula. This is actually Further Maths.
5. Applications of 1st order Differential equation: Motion with resistance proportional to velocity came out in N2017.
6. Applications of 2nd order Differential equation: Electric circuits came out in N2018. This is again Further Maths. That’s why further maths students have advantage in 2018 alevel.
7. A differentiation question is actually disguised as a Differential Equation. 2018 P1 Q10.
8. A lot of algebra manipulation. So students need to strengthen their algebra manipulation skills.
9. Application questions are packaged. More wordings. Students need to understand what concept the question is testing. Peel away the outer layer of packaging and is the same as the old syllabus 9740.

Recommended Learning to familiarize

1. Applications of integration such as arc length, surface area of revolution and centroid. Further applications of integration
2. Applications of 1st order DE such as motion, population growth, orthogonal trajectories, mixture problems, Torricelli’s Law, Newton’s Law of cooling. 1st order DE applications
3. Applications of 2nd order DE such as vibrating springs and electric circuits 2nd order DE applicaions
4. Odd/even functions, floor/ceiling functions Odd and even functions
Floor and ceiling function

Drilling ten year series is no longer enough to get A in alevel. Students need to think on their feet to solve non-routine questions. To train their problem solving skills, students should train to solve non-routine questions. If they are stuck on a problem, do not look at the solution immediately. Sleep over it. Let the subconscious work on it. Give yourself two days to solve a problem. After that, if still stuck, can glance at the solution for hints. Once understand how to do, close the solution and solve the question. And then try a similar problem. Problem solving skills and speed will improve and eventually students can solve non-routine questions in exams.

Don’t have to worry about the paper getting more difficult. The grade boundaries for A will be lowered accordingly. Easy paper requires 75 to 80 to get A. In 2018, the grade required to get A is lowered to around 72. % of students getting A remains the same about 1 in 2. To get A, students need to make sure they are in the better half of the whole cohort taking the national exams.

A good way to predict grades is percentile. For example, since about 68% of VJC students get A in alevel, if a VJC student get above 32 percentile in major school exams, that student is on track for alevel distinction. So if student is below that “A percentile”, work hard and/or get a tutor to improve to be on track for alevel distinction.

## Spotting for 2016 P2

These are the likely topics for the pure maths portion of 2016 Paper 2

• Techniques and applications of integration (area, volume)
• Application of differentiation (max/min, rate of change)
• Complex numbers (loci, de Moivre’s theorem, calcuation of modulus and argument)
• Binomial theorem and small angle approximation
• System of linear equations

Practice questions

JJC 2016 Prelim P1 Q1

JJC 2016 Prelim P1 Q3

JJC 2016 Prelim P2 Q3

PJC 2016 P1 Q11

TPJC 2016 P1 Q7

TPJC 2016 P2 Q4

IJC 2016 P1 Q3

Rate of change problem

Solutions

## Interpretation of sum to infinity 2015 question

Some students interpret the following question (2015 paper 2, 4 biii) wrongly.

In the examiner’s report, it was commented that “most were able to state or imply the sum to infinity correctly, but some did not interpret correctly the phrase ‘within 10−3 of the sum to infinity.”

Examples of correct interpretation from past Cambridge papers

Example 1

Correct interpretation

Example 2

## Highlights of alevel examiner report

These are the important highlights for h2 maths (9740) alevel examiner report (2007 to 2015). Take note of the common mistakes.

## Analysis of 2015 Alevel paper

This is the breakdown of H2 math 2015 Alevel paper 1 and 2:

Many students feel that paper 1 is tough and paper 2 is easy.

2015 H2 math paper 1 question 10i and 10ii are exactly the same as the N2003 question.

Many students viewed Paper 1, question 3 as the top killer question.

Based on 2015 alevel examiner’s report, these are the questions that were poorly done:

2015 P1: 3, 5 iii, 7iii, 9b ii, 11 ii explain why is maximum, 11 iii

2015 P2: 1 ii, 2ii, 3b, 4b iii (some students interpret wrongly), 7i, 7iii, 9 ii, 9 iii, 10 iv, 11 iv

## Spotting for 2015 H2 math P2

Based on 2013 and 2014 combined marks allocation and the topics already assessed in 2015 P1, this is my prediction for 2015 H2 math paper 2 pure math questions:

For stats, the challenging questions are likely to be on P&C or probability. 2015 H2 math paper 1 question 10i and 10ii are exactly the same as the N2003 question. So it might be good to practice questions more than 10 years ago.

## Analysis of 2014 A level paper

This is the breakdown of 2014 A level H2 math paper 1 and 2.

 Pure Maths Marks Percentage Differentiation and its applications 27 13.5% Complex numbers 20 10.0% Vectors 18 9.0% Integration & its applications 15 7.5% Differential equations 13 6.5% APGP 11 5.5% Functions (Inverse, composite, even function) 9 4.5% Graphing techniques 7 3.5% Sequence and series, sigma notation 7 3.5% Mathematical Induction 5 2.5% Maclaurin’s series 4 2.0% Binomial expansion 4 2.0% Subtotal 140 70.0%
 Statistics Marks Percentage Poisson distribution 11 5.5% Probability 10 5.0% Approximation of distribution 9 4.5% Hypothesis testing 9 4.5% Permuations and combinations 8 4.0% Correlation and regression 8 4.0% Sampling 4 2.0% Binomial distribution 1 0.5% Subtotal 60 30.0%

As usual, these are the four important modules:

 Module Percentage Calculus (Differentiation, integration, differential eqn, maclaurin) 29.5% Sequence and series (Including APGP, MI, Binomial expansion) 13.5% Complex numbers 10.0% Vectors 9.0% Subtotal for 4 major modules 62.0%

Paper 1 is easy.

Paper 2 challenging questions are question 6ii, 6iii (Permutation and combination) and question 9 ii, 9 iii (Hypothesis testing).

## Challenging H2 math topics

These are the topics that most students find challenging:

• Vectors
• Complex Numbers
• Sequence and Series
• Integration techniques
• Volume of revolution
• Tangents and normals
• Transformation of graphs
• Functions
• Probability
• Discrete random variables

## Analysis of 2013 A level paper

This is the breakdown of 2013 A level H2 math paper 1 and 2

 Pure Maths Marks Percentage Vectors 25 12.5% Differentiation and its applications 20 10.0% Complex numbers 17 8.5% Differential equations 13 6.5% Graphing techniques 12 6.0% Maclaurin’s series 12 6.0% Integration & its applications 11 5.5% Arithmetic and Geometric series 9 4.5% Sequences and Method of Differences 8 4.0% Functions 6 3.0% Mathematical Induction 5 2.5% Inequalities 2 1.0% Subtotal 140 70.0%
 Statistics Marks Percentage Permuations and combinations (question set as probability) 12 6.0% Correlation and regression 9 4.5% Poisson distribution 8 4.0% Approximation of distribution 7 3.5% Hypothesis testing 7 3.5% Probability 6 3.0% Sampling 4 2.0% Normal distribution 4 2.0% Binomial distribution 3 1.5% Subtotal 60 30.0%

Paper 1 is easy. Questions are routine. No challenging questions.

Challenging questions are in paper 2.

 Challenging questions in Paper 2 Marks Percentage Q4 (iii) on Vectors 6 3.0% Q8 (ii) and (iii) on Probability 5 2.5% Q11 (ii) to (iv) Permutation and combinations 10 5.0% Subtotal 21 10.5%

These challenging questions make up around 10%, which will distinguish the students who deserve distinction.

As usual, these are the 4 most important topics in H2 math.

 Calculus 28.0% Vectors 12.5% Sequences and Series (Including Mathematical Induction) 11.0% Complex numbers 8.5% Subtotal for 4 major topics 60.0%

These 4 topics make up more than half of the total marks. So students should put more emphasis in these 4 pure math topics.

The topics that are important in Statistics seem to be different in each year. Fortunately, statistics questions are usually straight forward, except for probability, permutations and combinations which can be challenging.