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