1. System of linear equations / Graphing techniques
(i) a = -3.953 , b = -5.187 , c = 7.303
(ii) x = -0.589
(iii) y = 5.19x + 7.3
2. Graphing techniques / Inequalities
i)
(ii) -1.73 < x < 0.414 or x > 1.73
3. Integration
(i) When n→∞ , sum of area of rectangles ≈ area of function
(ii) 3/4
4. Application of differentiation
Maximum area = (1/32) d²
5. Graphing techniques / Transformation
(i) Translation of +3 units parallel to the x-axis,
Scaling by scale factor of 1/4 parallel to the y-axis
ii)
iii)
6. Maclaurin’s series / Binomial expansion
(i) 2x – 2x² + (8x³/3)
(ii) -(104/27)
7. Vectors
(i) OC = (3/5)a
OD = (5/11)b
(ii) line BC : r = (3/5)λa + (1 – λ)b
line AD : r = (1 – μ)a + (5/11)μb
(iii) AE : ED = 11:9
8. AP/GP
(i) T = { T∈R : 59 ≤ T ≤ 77 }
(ii) t = { t∈R : 63.8 ≤ t ≤ 74.5 }
9. Complex numbers
a) w = a ± (a/√3)i
b)(i) z = 2e^(-π/10) , 2e^(3π/10) , 2e^(-π/2) , 2e^(7π/10) , 2e^(-9π/10)
(ii) 4 sin ( π/5)
10. Application of integration
i) A1/A2 = (2-√2)/(√2 -1)
= √2
iii) Volume = (π³/16√2) + (π²/2√2) – √2 π
11. Application of differentiation and integration
i) dy/dx = (-3sin³Θ + 6sinΘ cos²Θ)/(3sin²Θ cosΘ)
= 2 cot Θ – tan Θ (shown)
ii) ( (2√2)/(3√3) , ( 2 /√3 ) ) maximum point
iii) Area ≈ 0.884
iv) a = (3√2)/(2)
A-LEVEL H2 MATH JUNE HOLIDAYS INTENSIVE REVISION
A-LEVEL H2 PHYSICS JUNE HOLIDAYS INTENSIVE REVISION
JUNIOR COLLEGE / A-LEVEL TUITION:
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Suggested Answers to 2014 A Level H2 Math 9740 PAPER 2
NEW!
H2 PHYSICS PRACTICAL
H2 CHEMISTRY PRACTICAL
H2 BIOLOGY PRACTICAL
The following is a suggested solution by our H2 and H1 Math Tutor, Mr. Teng. Please note that it is a suggested solutions and was rushed out. Mr. Teng omitted several presentation steps out of convenience. There might be alternative solutions at times too. Feel free to comment and discuss. Please let us know if there are mistakes too. Thanks in advance.
PLEASE NOTE THAT STUDENTS ARE EXPECTED TO WRITE STATE YOUR DISTRIBUTIONS CLEARLY. We omitted for convenience.
Disclaimer: This suggested solutions is provided free by Mr. Teng & Singapore Learner. Both parties do not profit from this. We simply believe that this will help current students and future students to learn from the mistakes of others. Thanks.
ERRATA & Remarks:
6(ii) I miscounted and was careless.
Case 1: A plays midfield, B sits out of attacker =>3c1 x 8c4 x 4c1 x 5c4
Case 2: A sits out midfield, B plays attacker => 3c1 x 8c4 x 4c2 x 5c3
Case 1 + Case 2 =1 6800
(iii) I doubled counted indeed. Thanks for pointing out. Should be
Case 1: Midfielder A plays midfield => 8c4 x 3c1
Case 2: Midfielder A plays defender => 8c3 x 3c2
Case 3: Midfielder A sits out => 8c4 x 3c2
3c1 x 5c4 x (8c4 x 3c1 + 8c3 x 3c2 + 8c4 x 3c2) = 8820
8ai. I drew the left side of the quadratic. It should be the right side. my bad.
9. I initially used Z-Test for this question. But T-test is definitely more appropriate as we are given as unknown population variance. I changed it to T-test in the following solutions, but understand that some teachers consider Z-Test to be acceptable too. I should highlight that nobody has access to the actual answer scheme; we only see the marker’s report.
(ii), (iii) Set notations should be used. {t>3.48} and {0<k^2<0.423}
11. Please take note that I used CLT here, so cc is not required.
– I understand some students misunderstand that CLT is used to find the mean of any distribution. This is a terrible misconception. CLT is a limiting theorem, and we apply it to approximate a non-normal distribution to a normal distribution, given n is sufficient. And they can be sum of independent random variables, sample sum, or sample mean. You can read more from the link below.
– Why I used CLT approximation instead of poisson approximation (Poisson approximation is not incorrect either): I used continuity correction in qn 7 alr, so given examiner psychology, I would think they want to be impressed with something different. That’s why I picked CLT approximation. Do note that this does not mean that doing poisson approximation is wrong; so long as you perform cc precisely.
I do hope this clarifies, and I’m sorry it came late as I was ill and had jc1 classes yesterday too.
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Suggested Answers to 2014 A Level H2 Math 9740 Paper 1
MOCK EXAMS FOR SCIENCE PRACTICAL
The following is a suggested solution by our H2 and H1 Math Tutor, Mr. Teng. Please note that it is a suggested solutions and was rushed out. Mr. Teng omitted several presentation steps out of convenience. There might be alternative solutions at times too. Feel free to comment and discuss. We will try our best to answer.
Errata:
Qn3 I misread it. Answer should be 2/3 and need not be evaluated.
Qn5i I copied wrongly off GC. answer should -3+4i. It shouldn’t affect the back parts.
Qn7 I copied wrongly off GC. So rounding off, the answers should α=1.885(3dp)
Advice and tips from Mr Teng for H2 Math exam 2014 paper 2
Please focus on tomorrow’s paper 2 and not let paper 1 affect you too much.
Errata:
Qn3 I misread it. Answer should be 2/3 and need not be evaluated.
Qn5i I copied wrongly off GC. answer should -3+4i. It shouldn’t affect the back parts.
Qn7 I copied wrongly off GC. So rounding off, the answers should α=1.885(3dp)
Much thanks for those that point it out.
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Suggested Answers to 2013 A Level H2 Math 9740 Paper 2
NEW! H2 MATH TOPICAL CRASH COURSE (Sign Up Now!)
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The above solutions had been worked out by Mr Teng.
Errata:
For qn 3(I) line 7, the denominator of the third derivative of f(x) should be of power 4 instead of 2.
For qn 4(I), was some scanning error. The answer is 40.4.
For qn11(III), I made a terrible mistake and forgot the third case for which exactly three letters same AND two digits same. The permutation for that will be (26×9).
11(iv) I made the mistake of double counting and arranged after using the permute function. The following is the full solutions
Case 1: Exactly one vowel and 2 different consonants and exactly one even digit
(5C1)(21C2)(3!)(4C1)(5C1)(2!) =252000
Case 2: Exactly one vowel and 2 same consonants and exactly one even digit
(5C1)(21C1)(3!/2!)(4C1)(5C1)(
P(exactly one vowel & exactly one even digit) = (252000+12600)/(26^3*9^2) = 0.186 (3SF)
Disclaimer: We welcome fair comments and discussion. The answers were rushed out and done while Mr Teng was in between classes too. So there are errors definitely, so many thanks for all who point them out. 🙂
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Suggested Answers to 2013 A Level H2 Math 9740 Paper 1 (11 Nov)
MOCK EXAMS FOR SCIENCE PRACTICAL
END OF PAPER
Note: The above answers had been hurriedly worked out by Mr Teng, our H2 Math tutor.
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Errata: question 7(iii)
This question is really confusing due to the word “before”. However, after much discussions, Mr Teng concludes that he is wrong. The answer should be n=12. If you put the emphasis on how many MUST be cut off, 12 will be the correct answer. If you’re my student, you will know that my English is terrible. Haha.
Question 6(iii)) should λ = 8μ/7.
Question 9(iii) due to the lousy app should be 24n.
Disclaimer: Question 3
The line y=1 was drawn as part of my solution to (ii). So long as the diagram is clearly labeled, there should be no issues.
Any more issues, please let me know. Lastly, big thank-you to all the j1 and j2s who helped me clarify and explain the English behind the statement. And do watch out this space for P2!
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(1) What to do if your A-level results are bad …
(2) A-Level Results: What to do if you get BAD or DEAD, i.e., the ‘middle class’
(3) Beware the critical years in math education …
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