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Answer ALL the questions. Write your answers in the spaces provided. Leave blank 1 a) Give n tha t f(x ) = x 3 – 4x 2 – 3x + 7, find f '(x ). (2) b) Hence find the values of x for which f(x) is a decreasing function, giving your answer in the form {x : x > a}  {x : x < b} where a and b are real numbers to be found. (3) 2 A helicopter flies between 3 locations, A, B and C, which are positioned such that AB = 9 km, AC = 5 km and angle ABC = ...

2.1 The Linear Second-Order Equation 1. It is a routine exercise in differentiation to show that y1 (x) and y2 (x) are solutions of the homogeneous equation, while yp (x) is a solution of the nonhomogeneous equation. The Wronskian of y1 (x) and y2 (x) is W (x) = sin(6x) cos(6x) = −6 sin2 (x) − 6 sin2 (x) = −6, 6 cos(6x) −6 sin(6x) and this is nonzero for all x, so these solutions are linearly independent on the real line. ...

1.Mr. Davis is 52 years old and has recently been diagnosed with end-stage renal disease (ESRD) and will soon begin dialysis. He is wondering if he can obtain coverage under Medicare. What should you tell him? correct answersHe may sign-up for Medicare at any time however coverage usually begins on the fourth month after dialysis treatments start. 2.Juan Perez, who is turning age 65 next month, intends to work for several more years at Smallcap, Incorporated. Smallcap has a workforce o...

Question Scheme Marks AOs 1 (a) 1 Area(R)  ×0.5 × 1 + 2(e0.05 + e0.2 + e0.45 ) + e0.8  B1 1.1b 2   M1 1.1b    1 10.... =2.... =2.73 (2dp) = ×  4   A1 1.1b (3) (b)(i)  2 1 x2  ∫4 + e 5 d x=4(2) +"2.73" =10.73 (2dp)    0  B1ft 2.2a (b)(ii)  3 1 ( x- 1)2  ∫e5 dx ="2.73" (2 dp)  1  B1ft 2.2a (...

Section A(1) (46 marks) 1. (a) Find the L.C.M. of 20, 24 and 36. (b) Find the H.C.F. 50, 80 and 240. (4 marks) Solution: (a) By short division, 20 12 18 10 5 2 2 3 5 2 3 1M ∴ L.C.M. = 2  2  3  5  2  3 =360 1A (b) By short division, 50 40 120 25 2 5 5 8 24 1M ∴ H.C.F. = 2  5 =10 1A 2. Assume that +8000 dollars re...

(a) A function, f say, is a set of ordered pairs in which no two distinct elements have the same first entry. If A is a source set of f and B is a codomain of f then we use the notation f : A→B marks 1 2 1(c) (i) The Modulus or Absolute Value function mod ( x )≡∣x∣ f : R→R mod ( x ) or ∣x∣= x x >0 0 x=0 −x x ∈0 4 1 marks Properties y (i) ∣x∣>0 (ii) ∣...

1. In the marking scheme, marks are classified into 3 categories: ‘M’ marks awarded for correct methods being used ‘A’ marks awarded for the accuracy of the answers Marks without ‘M’ or ‘A’ awarded for completing a proof or arriving at an answer given in a question 2. The meanings of the abbreviations and notations are stated below: r.t. accepting answers can be rounded off f.t. follow through Shaded area steps can be skipped alternative methods ...

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