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Hi, we tried to rush it out. This might not be the most appropriate suggested solutions. Feel free to comment and discuss. Let me know if I make mistakes. Thanks!
Also, we might not respond too fast as we will be trying to do the paper 2 for h2 math later too.
ERRATA:
4(ii) I made a silly mistake substituting the equations back in. You should get (4, 18) and (8,6) as the answers.
Many thanks to those who point out my mistakes.
Suggested answers to GCE O Level 2014 A. Math (4047) Paper 2
1(i) When t = 0, 20 + A = 80, so A must be equal to 60.
1(ii) k = 0.288 (to 3 SF)
1(iii) Since t > 3.82, it is safe to give the food 4 min after removal from the microwave.
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2(i) Remainder = – 12
2 (ii) f(-2) = 0, so (x+2) is a factor of f(x). Solving f(x) = 0, x = -2, 1/2 or 3.
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3(i) Length of rectangle = 9/2 + Sqrt(3)/6
3(ii) c = -1
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4(I) 2.25 4
(ii) 8x^2 + 5x + 64 = 0
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5(a) x^2 – 8x + 32 = 0. No real solution because discriminant is less than 0.
5(b) y = 1/x^2
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6(I) Use the fact that triangle ACE is isosceles and the alternate-segment theorem to state that angle ACE = angle ABC. Angle DEF = angle ECA + angle EAC.
6(ii) angle DFE = 2 x angle ACB.
6(iii) Use the fact that angle BAC = 180 deg – (angle BAF + angle CAE).
So 2 x (angle BAC) = 360 deg – 2(angle BAF + angle CAE).
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7(I) p = 3 and q = 2
7(ii) (a) increasing
7(ii) (b) decreasing
7(iii) It is a maximum point
7(iv) 0
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To be continued
Suggested answers to GCE O Level 2014 A. Math (4047) Paper 1
1. k = -2
2. sqrt(26)/26
3. 1.75
4. -3/x – 2/x^2 + 4/(x-2)
5(i) v = 0.263
5(ii) around v = 0.231
5(iii) around f = 0.120
6. (i) Remember that when there is a mixture of trigo functions which cannot fit into a single trigo identity, convert all the given trigo functions into sine and cosine. Start with the LHS, the more complicated expression. You will reach the key stage where
LHS = 1 / [(1 – sin^2@)/(sin@cos@)] = 1/ (cos^2@/sin@cos@) = 1/(cos@/sin@) = tan@
6(ii) acute angle, so @ = 1.05.
7(i) A = (h, 2h); B = (7h/4, 2h); C = (h, h/2)
7(ii) Area of trapezium = 21 sqr units.
8. Integrate f'(x) to get f(x) with a +c. Use f(pi/2) = 0 to get c = 1/4. Differentiate f'(x) to get f”(x)= 4cos4x + 2sin2x. Proceed to add f”(x) to 4f(x) to get the RHS.
9(i) Pure inequality question. Solve 2x^2 + 5x – 12 > 0 by sketching a quadratic graph. Ans: {x : x < -4 U x > 3/2}
9(ii) Show that the (b^2 – 4ac) of (4x^2 + 4x + 1 = 0) is zero.
9(iii) a = -1.
To be continued ….
Suggested answers to GCE O Level 2014 Math (4016) Paper 2
Related links:
-
O-LEVEL E. MATH TOPICAL CRASH COURSE
-
O-LEVEL A. MATH TOPICAL CRASH COURSE
-
O-LEVEL PHYSICS TOPICAL CRASH COURSE
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1(a) x < 1/2
1(b)(i) W = 126
1(b)(ii) u = +- Sqrt(v^2 – 2W/m)
1(c) 2x / (x – 4y)
1(d) x = 7 or -1
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2(a) 4.12 x 10^10 kWh
2(b) 40.5% (to 3 SF)
2(c) 1439 kWh (to the nearest kWh)
2(d) 26.2% (to 3 SF)
2(e) 5725 GWh (to the nearest GWh)
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3(a) p = 11.4
3(b) cubic graph
3(c) Near exact answers are x = -1.54, 3.84 or 1.69 (examiners accept answers within a small range)
3(d) Exact answer for the gradient is -5.2 (examiners accept answers within a small range).
3(e) (i) straight line with positive gradient intersects the curve at one point.
3(e)(ii) Near exact answer is (4.24, 0.83) (examiners accept answers within a small range)
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4(a) 83 deg
4(b) Use AA property
4(c) Triangle EAB
4(d)(I) 5:3
4(d)(ii) 82.62 cm squared
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5(a)(I) (-6, -7) in vertical form (2×1 matrix)
5(a)(ii) 9.22 units
5(a)(iii) (4, 8.5)
5(b)(I) 4y + 3x = 16
5(b)(ii) (-2, 5.5)
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To be continued …….
Suggested answers to GCE O Level 2014 Math (4016) Paper 1 (via crowdanswering)
NEW!
MOCK EXAMS FOR SCIENCE PRACTICAL
O-LEVEL PRACTICAL TRAINING
PRACTICAL CRASH COURSES
1) sqrt (0.48), 0.702, 27/38, 0.61
2) 3.90 swiss francs
3a) 629.25
3b) 630
4) 47.9 deg or 132.1 deg (or 0.836 rad or 2.31 rad)
5) zero hours not offered; the choices given for the intervals for the number of hours spent are not continuous; time limit, such as per day or per week, not set.
6) – 1/3 (corrected)
7) 112
8) 79.4%
9a) 1000
9b) 200%
10a) 32 sec
10b) 7.5 sec
11) $78.50
12) x = 3 cm, y = 5 cm, z = 15 cm
13) $7500
14a) 1/3 (b – a)
14b) vector DC cannot be expressed as k(vector OA), so vectors DC and OA are not parallel.
15a) Two circles overlapping
15b) {4,6,7,8,9,10,11}
16a) 3b^5/2a
16b) (8x-5)/(x-3)^2
17a) a = 5, b = 19, c = 26
17b) 7n – 2
c) There is no integer value of n such that 7n-2 = 109
18a) 8 11/18 m/s
18b) 9 min 43 sec
19a) graph curves upwards, passes thru origin
19b) s = 2.25 t^2
19c) 2.98 sec
20a) 1/4
20b) 1/16
20c) 55/64
21ai) (2.6 4.3 6.8) as in 3×1 matrix
21aii) E = (151.4 135.4) as in 2×1 matrix
21aiii) It represents the masses of the coins saved by Lin and Hadi respectively
21b) (10 20 100) as in 3×1 matrix
22) $644.17
23a) 314 cm^2
23b) 5 cm by 7 cm by 11 cm
23c) 42
24a) 9(x-1)
24b) 57 cm
24c) 196 cm^2
Ad hoc O Level Math or Physics Tuition from 20 Oct to 26 Oct 2014
Suggested answers to GCE O Level 2014 Math (4016) Paper 2
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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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TUITION CLASSES:
_______________________________________________________________
EDUCATIONAL SERVICES:
______________________________________________________________
By EX-MOE TEACHERS & EXPERIENCED TUTORS
@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.
Sec Math Textbook Solutions
If you are looking for fully-worked solutions to problems found in commonly used mathematics (Additional or Elementary) textbooks in Singapore, you can check out this wonderful website created by Lee Chu Keong, a lecturer at the Nanyang Technological University: http://www.openlysolved.org
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