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# Maths notes for 4038 and 4016 paper

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### Maths notes for 4038 and 4016 paper

1. 1. Notes for Additional and Elementary Mathematics and Supplementary Questions<br />
2. 2. Dear user of this note,<br />This note is to supplement what you will receive in your 4 years of secondary school education. These are my experience of learning maths and my tips for you. I definitely tell you that by spotting ques is for you to make sure a pass in exam only. However, I do have to remind you if you have the ability to ace it, please do your best and not spotting ques. (Sounds like a paradox ah). I wish you all the best in your O levels after using this note. I hope it brushes up your fundamental skills of mathematics argumentations and presentation. Also a reminder, this paper is not the usual O level style as my ques are half difficult and half easy. You might not be able to answer all ques as o level is usually 70-80% easy and 20-30% difficult only.<br />Best wishes,<br />Creator of this note<br />Fabian<br />
3. 3. AM (4038) 2009 O LvlStatistics<br />27.8% of AM paper is on differentiation and integration which mean that it will determine a quarter of your marks. You would therefore have to be very good in it. In addition, Trigo will decide another 18.4% of your marks. This means that you need this 3 chapter to almost pass your AM which I presume is easier for you guys to focus on.<br />TRIGO: 18.4%<br />DIFF & INT: 27.8%<br />EXP & LOG & MODULUS & POLYNOMIAL & DISCRIMINANT: 12.8%<br />BIONOMIAL: 5%<br />CIRCLE: 5.6%<br />
4. 4. AM (4038) 2009 O LvlStatistics<br />LINEAR LAW: 5%<br />THIS 11/18 chapters give you 74.6 % of your AM paper hence these Chapters are what you should focus on when you have no time during an exam. Although it varies yearly, but I believe it will still give you a min of 62% even if it changes a lot. This will allow you to pass with more than what you have now. However, if you do have the time to finish studying all, please do so. Use Allen’s Tips although I don’t really trust what he said but I have to admit it is still 60% useful.<br />Usually the most commonly asked question by anyone would be how do I predict questions. This can be done by reviewing all the chapters that you have study. <br />After doing paper 1, those chapter that did not come out will come out for paper 2<br />
5. 5. Other than trigo which will come out more than 1 ques, the rest of the chapters will be tested for1 ques.<br />1 ques on maxima and minima, 1 ques on area under graph, 1 ques on kinematics and 1 ques on linear law will definitely be tested.<br />Also, for quad and inequality, usually they will ask find alpha3-beta3 or alpha4-beta4<br />(Statistics of 4038 paper quoted from pass with distinction by topics)<br />AM (4038) 2009 O LvlStatistics<br />
6. 6. Quad Func & Inequalities<br />If the roots of the quad Eqn 2x2-5x-1=0 are α and β, find the value of (β3+(1/ α3))( α3+(1/β3)).<br />A quad func y=f(x) attains its min value 11/3 at x=4/3 and y=5 when x=2. Find an expression, in terms of x, for y.<br />Show that, if x is real, the values of the expression (x2-3x+1)/(2x2-3x+2) can only lie btw -1 and 5/7 inclusive.<br />
7. 7. Logarithm, Indices and Surds<br />Rationalise (4+2√5)/(1+√2+√5)<br />Find the Exact Value of x if 27x=(√(3√27))<br />Given that ((9n+2 – 3n+2)/25 )= 2a3b, where a and b are Z, find the value of a and express b in terms of n.<br />Exact form of (lnx)lnx=x<br />If a˃b˃1 and , find the value of <br /> without the use of calculator.<br />
8. 8. Trigonometry(Factor Formula, Basic identities, Double angle, Integration, Sketch)<br />For all Trigonometry identities question, Start solving from the more complicated side to the less complicated side. If you are stucked halfway, please also try solving from the other side. Then, merge the answer as one by making one side writing the steps from the bottom.<br />A trigonometry proving may be a mixture of usually 1-2 type of trigonometry equations.<br />If they asked you to solve questions for eg, given that sinx=(3/5) and 180˂x˂270, give the value of cosx. This ques you have to draw triangle to ans. What I would suggest is that u don’t use the Cartesian plane method if u will confuse with the angle quadrant. <br />