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