Mathematics 30 June 1999 Grade 12 Diploma Exam

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10. A student is investigating the effects of changing the values of the parameters a, b, c, and d in the equation y = a sin[b(θ + c)] + d. The graph of each of the following functions is plotted: f (θ )=sinθ g(θ) = 2 sinθ h(θ )=sin2θ k(θ)=sin(θ + 2) l(θ )=sinθ + 2 The equation whose graph will have the same θ -intercepts as the graph of y = f (θ ) is A. y = g(θ ) B. y = h(θ ) C. y = k(θ ) D. y = l(θ ) 11. ⎛3θ⎞ ⎛θ 3θ θ An equivalent expression for cos⎜ 2 ⎟ cos⎜ 2 sin 2 sin ⎝ ⎠ ⎝ ⎠ ⎟ + ⎛ ⎞ ⎛ ⎜ ⎟ ⎜ ⎞ ⎝ ⎠ ⎝2⎠ A. sin(2θ ) B. cos(2θ ) C. sin(θ ) D. cos(θ ) <strong>12</strong>. An equivalent expression for A. sin 2 x B. sin x C. cos 2 x D. cos x (sin x)(cos x) tan x is 6
13. If (π, –6) satisfies the equation h ( θ) = A sin ⎛ ⎞ ⎜θ + π − 4 2 ⎟ , then the value of A is ⎝ ⎠ A. 10 B. 6 C. 4 D. 2 Numerical Response 2. An arc of a circle with a radius of 100 cm subtends a central angle of 1.4 radians. The length of the arc, correct to the nearest centimetre, is __________ cm. (Record your answer in the numerical-response section on the answer sheet.) 7
Page 1 and 2: athematics 30 Mathematics 30 Mathem
Page 3 and 4: Multiple Choice • Decide which of
Page 5 and 6: 1. The function f (x) = x 3 - 6 is
Page 7 and 8: Use the following information to an
Page 9: Numerical Response 1. The polynomia
Page 13 and 14: 14. Given that log b 64 = 3 , the v
Page 17 and 18: Numerical Response 4. An exponentia
Page 21 and 22: 25. The foci of a hyperbola are F 1
Page 25 and 26: 32. If the sum of the first n terms
Page 27 and 28: 37. In the expansion of (x + 2y) 8
Page 31 and 32: • Write an expression for t n as
Page 33 and 34: • Assume that it becomes necessar
Page 35 and 36: • Identify the error that was mad
Page 37 and 38: Fold and tear along perforation. 0
Page 39 and 40: No marks will be given for work don
Page 41 and 42: Mathematics 30 Diploma Examination
Page 43 and 44: SAMPLE ANSWERS TO THE WRITTEN-RESPO
Page 45 and 46: • The store will lose money on th
Page 47 and 48: • Assume that it becomes necessar
Page 49 and 50: A POSSIBLE SOLUTION Student A Stude

Mathematics 30 June 1999 Grade 12 Diploma Exam

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