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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 ….
What’s new in the new exam syllabus for A. Math?
Express-stream students taking the O-levels in 2o14 for the first time will do A. Math 4047, whereas those repeating their A. Math O-level exam in 2014 will do A. Math 4038. A. Math 4047 is likely to stay around for the next five years.
So what is the difference between A. Math syllabus 4047 and A. Math 4038? The difference is technically not much, but makes a world of difference for students and teachers. Here are the differences:
(1) Students no longer need to know the inverse matrix method of solving simultaneous equations.
(2) Students now need to memorize two new formulae:
(i) a^3 + b^3 = (a+b)(a^2 – ab + b^2)
(ii) a^3 – b^3 = (a-b)(a^2 + ab + b^2)
(3) For Trigonometry, students no longer need to know the Factor Formula or its reverse, the Product Formula. Thank God. (But for JC H2 Math, the Product Formula is useful in the integration of some trigonometric functions)
(4) For Plane Geometry, students no longer need to know the Intercept, Intersecting and Tangent-Secant theorems. Thank God. (Many IP schools skip this topic anyway).
In summary, the new syllabus has less sub-topics than the old one. This is good news for both students and teachers of our content-heavy math curriculum.
Rgds,
Ilyasa (hp: 97860411)