# Tips & Challenges

## Reflection of line about line

## Common error in area of periodic functions

## 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:

- 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.
- Solve inequality involving modulus in exact form.
- Secondary school syllabus like remainder theorem appear in N2017. R-formula appear in specimen paper.
- Using integration techniques to solve questions outside h2 maths syllabus: such as evaluate arc length given the formula. This is actually Further Maths.
- Applications of 1st order Differential equation: Motion with resistance proportional to velocity came out in N2017.
- 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.
- A differentiation question is actually disguised as a Differential Equation. 2018 P1 Q10.
- A lot of algebra manipulation. So students need to strengthen their algebra manipulation skills.
- 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

- Applications of integration such as arc length, surface area of revolution and centroid. Further applications of integration
- 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
- Applications of 2nd order DE such as vibrating springs and electric circuits 2nd order DE applicaions
- 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.

## How to graph X given Y

Example 1: Volume of revolution in 2017 alevel P2 4b

Let a=2 so we can visualise the shape of the graph

Example 2: Solution curve for Differential equation. 2014 alevel P1

This is solution for part iv.

It can be sketched without expressing the solution in the form x=f(t)

## How to sketch both cartesian and parametric graphs on the same diagram using GC

**Example 1**

DHS J1 2018 Aug Test

Suppose we want to sketch the curve C and the line y=-2x+2 on the same graph

Note how the line y-2x+2 is entered.

Adjust the Tmax to 1% more so the graph displays correctly.

**Example 2**

2011 alevel P1 Q11

## Finding sequence of transformation

Usually the sequence of transformation can be found by the replacement method. However, it can be tough to find the replacement for complicated functions. For such cases, we can use the general linear transformation c f(bx+a)+d to find the sequence.

**cf(bx+a)+d **= Translate by a units in the negative X direction, then scale by a factor of 1/b parallel to the X-axis, then scale by a factor of c parallel to the Y-axis, then translate by d units in the positive Y direction.

**Example**

**Solution**

## Rounding in Inequality

**Example 1: 2015 P1 8ii**

*Solution*

*Examiner’s report *

**Example 2: 2015 P1 2ii**

*Examiner’s report*

*Comments*

Graphical approach will yield x> 1.732. Notice Cambridge answer is not rounded to x>1.74 to satisfy the non-rounded inequality but rounded to 3 s.f.

*Conclusion*

Considering example 1 and example 2, we conclude that **in real life applications questions, when rounding off your answer to 3 s.f, round off such that the rounded off answer still satisfies the non-rounded off inequality.**

## InvNorm with Inequality Using TI 84 CE

## Vector distance formulas

Vector distance questions are common in alevel and carries 5 or 6 marks. Knowing the vector distance formulas can help to solve such questions easily and quickly.

**Practice Questions**