SPM Mathematics Tips
by Bobby Ng
Mathematics (is also known as Modern Maths) and Additional Mathematics are categorized as thinking subjects which you take your time thinking rather than memorizing facts. The formula will be given at the front page of the examination paper. Additional Maths is notably 4 times harder than Modern Maths. It’s like if students think Maths is shit, then take Add Maths. If you get 90% marks in Maths, you may have potential to get 40% marks in Add Maths. It’s near to impossible for someone who get A1 in Add Maths fail in Math. Well it’s not important. What I’m going to discuss at here is Mathematics.
In SPM, mathematics is considered as compulsory subject. You must pass this subject in order to get the certificates along with Malay language. Malay language test takes a lot of time and your hand hurts like hell after writing so many words. It’s not simple either. However, the percentage of students fail in Mathematics is higher than Malay Language in real SPM, which is ridiculous. It is told that Mathematics is quite ‘difficult’ among Art students in seminar SPM, which I can’t believe my eyes either.
In my opinion, Mathematics is the easiest subject in SPM for Science students. I believe PMR students can even do with their PMR standard knowledge because some questions like volume of solid and area and perimeter of a circle being test in SPM. It’s not being taught in SPM therefore you can only depend on your past knowledge in Form 2. Although the questions are a lot easier than Add Maths, There are still some pupils having difficulties in Maths.
I see some students leave the ‘haven’t done’ answers after they get the formulae to be applied in the questions, which they didn’t really answer the questions. Some of them don’t understand the questions’ needs. Therefore, exercises and guidance from teachers are essential for improvement.
The questions are so direct and mostly the answers will less likely to appear in decimal. You need a little bit of logic compare to Add maths. Besides that, even if you do well in monthly test, you might end up tilting head during SPM examination hall. It’s because monthly tests don’t follow the real format of SPM. Like Intervention 1 for KL state this year, there’s no chance in hell this question is coming out in real SPM.
Based on SPM Maths, it consists of 2 papers
- 1 ¼ hors
- 40 questions
- 40 marks
- 2 ½ hours
- working steps must be done
- Section A
= 52 marks
= 11 questions
- Section B
= 48 marks
= 5 questions (answer 4 of out 5)
Every chapter will be tested in Paper 1. The questions will be tested from Form 1 until Form 5. Since you have already mastered the some basics in PMR, these shouldn’t be a problem. Do past year objective questions will strengthen your basic.
In paper 2, there are only certain chapters that will be tested in SPM maths. That’s why I will concentrate more on paper 2. The whole paper 2 format based on past year questions in random order with brief tips below
Confirmed to be tested every year
Paper 2 (Section A)
1) Volume of solids (which was taught in form 2)
- most of the formula given are for this question
- make sure the formula are used correctly
- combined solid is sum of volume of the solids
- remaining solid is the subtraction of bigger solid and smaller solid
2) Angles of elevation and depression
-using trigonometry rule
3) Mathematical reasoning
- statement ‘and’ and ‘or’
- If p, then q. If q, then p.
4) Simultaneous linear equation
- equalize the same unknown and take out
Example : 4p – 2q = 15
(2p + 4q = 19) x2 (times 2 to make unknown 4p same)
- don’t use Add Math method, answers will be different.
5) The straight line
- y = mx + c
- gradient, gradient….
- What is c? c (y-intercept) is the point where the line touches the y-axis.
6) Quadratic expressions and equations
- ‘solve the equation’ is to find the unknown
- change the equation of the question into this form
- factorise by your own or using calculator
- must state x = ?, x = ?, there will be 2 answers
- will mostly ask inverse matrix
- if you’re not sure about the answer, check if the whole outcome is identical to the inverse matrix in the question.
- the answer in a) is related to b)
8) Area and perimeter of circles (same as number 1)
- 2πr (perimeter or circumference) and πr2 (area)
- (angle/360 degree) x the formula above for the area or perimeter of certain part
- the formula given are plain useless
- final answer is never less than 0 or more than 1, 1 > answer > 0
10) Gradient and area under a graph
- based on speed/ time graph
= distance is area of the graph
= rate of change of velocity is gradient of the graph
= speed is based on the graph (seldom being asked)
- beware of total distance and total speed
Can be varied each year
1) Sets (2004 and 2006)
- shading based on the questions (intersection or union)
- beware of the complement such as A’
2) Graph of functions (2005 and 2007)
- the inequalities (upper line is >, lower line is <)
- if slanted line, you can imagine it into horizontal straight line. Same concept as above.
What’s the conclusion? 2008 will be ‘Sets’! How about 2010 ? Wow, I can predict what will come out in this year’s SPM.
Paper 2 (Section B) Answer 4 questions
1) Graph of functions
- Linear functions (less likely to come out as it’s a straight line after plotted)
- Quadratic functions (2004 and 2005)
- Cubic functions (2007)
- Reciprocal functions (2006)
= this question is easy because you can detect the type of graph after you plot it.
= elastic ruler is recommended
= x-axis and y-axis should be stated in the graph
- Enlargement ( careful with the word ‘to’ and ‘from’ because it determines the image would be smaller or bigger)
= combination of transformation like VT
-do T before V. It’s some kind of law.
- Histogram ( 2004 and 2005)
= x-axis the upper boundary with an additional lower boundary at the front of the graph
= y-axis is frequency
- Frequency Polygon (2006)
= x-axis is midpoint
= y-axis is frequency
- Ogive (2007)
= x-axis is upper boundary
= y-axis is cumulative frequency
= additional upper boundary should be added to the table
= x-axis and y-axis should be stated in the graph
My school hasn’t come to these chapters below, but I will try my best to explain it.
4) Plans and elevations
-well I’m not sure but what I can see is you must be able to imagine the solid from every side
-plan is looked from above
-elevation is looked from the side of the solid
-the length and the edge (ABCD) should be stated correctly
-similar to a chapter of the living skills in PMR
5) Earth as a sphere
-no comment because I’m not going to explain something that I’m not sure
-latitude is vertical and longitude is horizontal of the sphere
If you concentrate on these chapters and do a lot of past year questions, I’m sure getting A1 in Maths is not a matter for you. Choose the 4 questions that you’re confident in section B paper 2. Do all questions if you think you have much time to spend for taking a nap. Why study more if you know what kind of questions will come out?
1) You know doesn’t mean you can get correct, try to make less careless mistakes in each paper.
2) See through the questions word by word as there will be some tricky part in the questions, especially ‘to’ and ‘from’ in enlargement.
3) Don’t be sad if you do badly in trial SPM because the odd might come to you/