How to improve Add Math?
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Hi guys.
i am currently at Sec 3. Are there any way to improve my Add Math effectively without burning a hole in my pocket? My parents aren't rich so they cannot afford expensive tuition (more than $120/monthly).
Also, besides consistent practising, are there any other ways?
Sometimes when i practise, i will be stressed up whenever my answers were wrong, then i feel very demoralised. How can i overcome this kind of situation?
Help appreciated :D
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Originally posted by chifan:
Hi guys.
i am currently at Sec 3. Are there any way to improve my Add Math effectively without burning a hole in my pocket? My parents aren't rich so they cannot afford expensive tuition (more than $120/monthly).
Also, besides consistent practising, are there any other ways?
Sometimes when i practise, i will be stressed up whenever my answers were wrong, then i feel very demoralised. How can i overcome this kind of situation?
Help appreciated :D
A maths qn style is more fixed so i would say practice is really 1 of the most effective way to do well in it. Its not impossible to do well if you are willing to put in alot of hard work. I went from D7 in Sec 3 term 1 to A1 in O's without needing a tuition teacher so just presevere and work hard.
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I am also struggling with Add Maths.
Differentiation and Intergration.
Haiz.
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Add maths used to be very difficult for me... but then i realise Add maths is all about formula. So you just need to practice and practice. No need for practice. It is apply formula and input the figures and get the results.
E maths need more thinking instead..
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Originally posted by chifan:
Hi guys.
i am currently at Sec 3. Are there any way to improve my Add Math effectively without burning a hole in my pocket? My parents aren't rich so they cannot afford expensive tuition (more than $120/monthly).
Also, besides consistent practising, are there any other ways?
Sometimes when i practise, i will be stressed up whenever my answers were wrong, then i feel very demoralised. How can i overcome this kind of situation?
Help appreciated :D
1st thing you should know is that the distinction rate for AM and EM at 50+% is the easiest subject to ace.
Consistency (which come from practise) is a must but at Sec 3 you should focus on concepts and techniques 1st, merely passing at Sec 3 mean you will generally perform well if you work hard in Sec 4.
Stressed because of wrong answers? You are trying to resolve too many issues at the same time. Generally, the different objectives in order of resolving should be concepts, sequences, accuracy, checking and then pace. In Sec 3, your focus should be on concepts and sequences. If these are not a problem, then you have plenty of time in Sec 4 to resolve accuracy, checking and pacing. You eat pizza you eat it piece by piece not the whole pizza, maths also sama sama.
Personally, I ask that my Sec 3 students give me 65% ( even if lower by a bit I won't mind) in their school exams. Why is that so? I do not want them to worry unnecessarily on exams techniques (accuracy, checking and pace). Don't fail can liao.
Then when it come to Sec 4, all you have to do ( if you manage to pass your Sec 3 AM exams) is to make sure those guys behind you don't catch you loh. Sec 3 AM is at least 1/2 fail one. Someone who passed is already in the correct position to gear up or maintain his/her position.
To gear up (if you believe you are in A2 position and want A1), simply work harder ( and hopefully smarter) than your rivals.
To maintain (if you are top 20% or settling for A2), track your exams results vs your rivals. Tests don't count.
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By practising, of course.
Quantitative subjects are nothing but practising and practising, work on a formula long enough and you will know how to apply it. Work on various questions long enough, and you know when to apply what.
Think of it as foot drill, if you aren't working your legs, you aren't learning shit
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Originally posted by chifan:
Hi guys.
i am currently at Sec 3. Are there any way to improve my Add Math effectively without burning a hole in my pocket? My parents aren't rich so they cannot afford expensive tuition (more than $120/monthly).
Also, besides consistent practising, are there any other ways?
Sometimes when i practise, i will be stressed up whenever my answers were wrong, then i feel very demoralised. How can i overcome this kind of situation?
Help appreciated :D
Hi,
You are stressed probably because you 'fight' with the mistakes and feel guilty for making them. See and respect mistakes for what they are...milestones to help you improve further and become a better mathematics student, rather than letting them lower your self-esteem and deflate your self-confidence. Remember that you are not a poor mathematics student, but rather a person who has done poorly on isolated occasions. Making mistakes is fantastic when you are practising because it means that you may be much better during the 'real thing', provided that you have been monitoring carefully where you have gone wrong and rectified them proactively. Laugh at your mistakes because it helps to relieve uneasiness. I do that often enough in class sessions when I make silly mistakes in front of my students (both in tuition and in university) and we all have a good laugh! Rather than let the world laugh at you, have it laugh with you :)
Thus, one practical way to overcome is to change your response to mistakes.
Thanks!
Cheers,
Wen Shih -
A Maths questions don't need to think at all, they are all dead, compared to E maths. Its always the same old thing. Just need to practice doing the same sums over and over again, it will become so routine, you will start doing the sums even before you finish reading it.
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Hi,
Another practical and smart approach to ace maths is to analyse deeply the concepts and skills which are often assessed.
Look at some exam papers (Cambridge and school) and make a checklist of concepts and skills. You may model the style I have adopted for A-level maths:
http://www.freewebs.com/weews/Pure%20Mathematics%20Checklist.pdf
Thanks!
P.S. If I may find time, I'll compile such a list for Additional Mathematics later.Cheers,
Wen Shih -
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Hi,
Let me start a humble list (after referring to a school exam paper) which could be improved upon by other visitors with more detailed input.
1. Trigonometry
- Prove identities.
- Solve equations (sometimes after proving an identity).
- Find min/max of an expression using the R-sine or R-cosine result.
- Find values of trigonometric expressions, given trigonometric ratios.
- Sketch trigonometric graphs (directly or after some transformations) and show appreciation of period and amplitude.
- Transformations include these forms: y = f(ax), y = f(x) + a, y = |f(x)| and combinations.
- Determine the number of roots of given equations, where their graphs need to be sketched and checked for the number of intersections.
- Find trigonometric ratios of specific angles without using calculator.
- Know about radian and degree modes.2. Surds and indices
- Form expressions using surds.
- Rationalise surds.
- Solve equations involving indices.3. Logarithmic and exponential functions
- Solve logarithmic equations.
- Solve real-life problems involving exponential functions (e.g. radioactive decay of a substance).
- Simplify and evaluate, without using calculator, using laws of logarithm.
- Sketch logarithmic and exponential curves.4. Modulus functions
- Sketch graphs of modulus functions.
- Solve equations and/or inequalities (by graphical approach) involving modulus functions.5. Circles
- Find equations of circles and show appreciation of radius and centre.
- Find new equations given some transformation (e.g. reflected about x-axis).6. Quadratic equations
- Appreciate the nature of roots (real, equal, imaginary) for graphs which are always above/below the x-axis, for graphs that do not intersect, for graphs that are tangent to each other and the like.
- Form new quadratic equations via sum and product of roots.
- Solve quadratic inequalities.7. Binomial expansion
- Expand.
- Find terms independent of x or terms with certain powers.
- Approximate values by suitable substitutions.
- Know how to expand nCr where n is an unknown.8. Linearisation of non-linear expressions
- Express a non-linear equation by manipulation to become Y = mX + c.
- Find slopes and intercepts in order to find unknowns in the original non-linear form.
- Find values from graphs.
- Interpretations of linear graphs.
- Draw another graph to find the number of roots of an equation.Part 2 coming soon...
Thanks!
Cheers,
Wen Shih
P.S. I have added a few more points (in red) from my teacher friend. -
Hi guys. Thanks for all the constructive comments.
Looks like practising is the key for scoring in amath. i will work hard and hopefully able to do amath questions with more confidence. Thank you wee_ws for your checklist. Mikethm, are you a teacher? your advice is very helpful, thank you.
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Hi,
Here is part 2.
9. Differentiation and its applications
- Differentiation techniques, especially the use of product rule, quotient rule and differentiation of composite functions like cos (3/x).
- Tangents and normals
(i) find gradients of tangents and normals;
(ii) find equations of tangents and normals;
(iii) find axial intercepts of tangents and normals.
- Rates of change via the chain rule.
- Maxima and minima
(i) form an expression based on the given information;
(ii) carry out differentiation, set the derivative to zero, find the stationary value(s);
(iii) determine the nature of stationary value via first or second derivative test.
- Curve sketching
(i) find axial intercepts.
(ii) carry out differentiation, set the derivative to zero, find the stationary values;
(iii) determine the nature of stationary points via first or second derivative test.10. Integration and its applications
- Integration of standard functions.
- Integration via partial fractions.
- Find areas of regions via integration.
- Given known definite integrals, evaluate some other integrals.11. Applications involving both differentiation and integration
- Motion (involving displacement, velocity, acceleration).
- Applying the derivative of a given expression to find the integral of a related one, e.g. differentiate x ln x, then find the definite integral of ln x.12. Coordinate geometry
- Find gradients or equations of lines (parallel to or perpendicular to given lines).
- Find points of intersections.
- Find areas.
- Apply known geometrical properties of quadrilaterals.
- Find mid-points.
- Prove collinearity.
13. Remainder and factor theorems
- Factorise completely some expression and find its solutions.
- Form simultaneous equations based on given information and solve for unknowns.
- Use the fact that polynomial = quotient * divisor + remainder to solve problems.
- Carry out long division of polynomials.
- Three types of partial fractions.14. Geometrical proofs
- Prove congruency and similarity.
- Prove results by applying mid-point and intercept theorems for triangles.
- Prove results by applying tangent-chord, intersecting-chord and tangent-secant theorems for circles.
- Know and apply angle properties and symmetric properties of circles.
- Know and apply alternate segment theorem.15. Simultaneous equations in two unknowns
- Both linear.
- One linear, the other non-linear.
- Solve via substitution or inverse matrix method.Hope I have covered all topics. Thanks!
Cheers,
Wen Shih
P.S. The additions in red are points from my teacher friend. -
Originally posted by wee_ws:
Hi Mr Wee,
Thanks for the recommendation.
Regards,
ahm97sic
PS : You have summarised the patterns for each topic of the new Syllabus of Add Maths in this thread for TS. It will be very useful for TS to study and revise them.
May I suggest that you put this in your Add Maths TYS too ie each topic will begin with the different types of questions asked followed by one worked example for each type of question and next arrange all the past TYS questions under each type of question for each topic ?
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Hi,
Thanks, I will speak with the publisher about your suggestion in the next TYS release.
Cheers,
Wen Shih -
good idea than the major classified...but try to follow MOE syllabus points...btw, ww_ws, which publisher TYS you providing answer???