## Good 2020 prelim to do and difficulty rating

Level 1 (Similar to 2019 alevel standard)

1. YIJC (Recommended)
2. JPJC stats (Recommended)
3. MI
4. TMJC
5. CJC

Level 2 (Harder than 2019 alevel, similar to 2018 alevel standard)

1. EJC (Recommended)
2. DHS
3. RI
4. RVHS

Level 2+ (Questions similar to alevel style but harder)

1. NYJC (Recommended)
2. NJC
3. SAJC

Level 2++

1. ACJC (Recommended, many good contextual questions)
2. HCI stats (Recommended)
3. TJC P1 (Recommended)
4. VJC Pure maths (Recommended)
5. ASR stats (Recommended)

## Value added by tuition: A better way to gauge

As alevel is easier than school internal exams, students often improve by 2 to 3 grades from their prelim results even without tuition.

So how to better gauge the value-added by tuition? Using percentile improvement is one way.

Below are some illustrations based on my students’ 2019 alevel results:

 1 Student scored 16 percentile in school internal exams before joining tuition. Her school distinction rate in 2018 is 68%. So to be on track for distinction, she has to improve to at least 32 percentile to get A in alevel Student got A in alevel. So there is value add of at least 16 percentile. 2 Student scored S grade in J2 MYE before joining tuition. S grade is around 20 percentile in her school. Her school distinction rate in 2019 is 65.5%. So to get A, she must have improved to at least 34.5 percentile. Student got A in alevel. So there is value add of at least 14 percentile.

Percentile improvement is not easy to achieve. Imagine running the alevel marathon, one has to overtake more than 16% of people along the journey to get A.

Side note: 100% of students who joined my tuition since J1 get A or B in 2019 alevel.

## H1 or H2 maths?

If student don’t have amaths background, or score B3 or below in amaths, it is better to take H1 maths. Over the years, I have observed these 2 group of students mostly getting U throughout their school internal exams.

More than 50% of students get distinction in O level amaths. The average student taking h2 maths got distinction in amaths. If student don’t have amaths background, or score B3 or below in amaths, it is very difficult for them to compete against other students in the national exams.

In general,

• Those who got A in H2 maths in Alevel had achieved amaths A1. Some students who got A1 in addtional maths merely by drilling will not get A in H2 maths, because H2 maths require understanding and application.
• Those that get B3 or below in amaths get B or below in H2 maths alevel
• Those without Amaths background get C or below in H2 maths alevel.

If student don’t have amaths background, or score B3 or below in amaths, better to take H1 maths and get A for it, rather than struggle to cope with H2 maths and likely end up with B or below.

If student score B3 or below in amaths and want to take h2 maths, revise differentiation and integration and work very hard. It is still possible to do well in h2 maths like the example below:

## Good 2019 prelim to do

After their school prelim exams, students should do 2017 and 2018 alevel. Then attempt the following 2019 prelim to prepare for alevel.

Good papers to do post prelim

1. JPJC
2. YIJC
3. TMJC
4. MI
5. CJC
6. EJC
7. RI
8. TJC P1

Good questions to do post prelim

1. HCI P1: 4,9,10,11,12
2. HCI P2: 1, 2,3,5,7,8,10
3. ACJC P1: 3,6,7,8,12
4. ACJC P2: 3
5. ASRJC P1: 6,7,9
6. DHS P1: 5a, 10c,11,12
7. DHS P2: 7, 10
8. NJC P2: 3
9. NYJC P1: 12
10. NYJC P2: 2,3,4,5,6,7,9
11. SAJC P1: 1,2,9ii,10
12. SAJC P2: 1,3,4,8
13. VJC P1: 9
14. VJC P2: 8,10

Students can get the papers from their school.

## 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:

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.
2. Applications of 1st order DE such as motion, population growth, orthogonal trajectories, mixture problems, Torricelli’s Law, Newton’s Law of cooling.
3. Applications of 2nd order DE such as vibrating springs and electric circuits
4. Odd/even functions, floor/ceiling functions

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

Example 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. ## 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 