Mathematics 30 June 1999 Grade 12 Diploma Exam

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Use the following information to answer the next question. The partial graph of a cubic polynomial function, y = P(x), is shown below. y 6 5 4 3 2 1 –3 –2 –1 –1 1 2 3 –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –<strong>12</strong> –13 –14 –15 x 6. When P(x) is divided by (x + 2), the remainder is A. negative B. zero C. positive D. undefined 7. If the factored form of 3x 3 – 2x 2 – 17x – <strong>12</strong> is (x – 3)(x + 1)(ax + b), then (ax + b) is A. 3x – 4 B. 3x + 4 C. –3x + 4 D. –3x – 4 4
Numerical Response 1. The polynomial function P(x) = 4x 3 – 18x 2 – x – 45 is divided by D(x) = x – 5. The quotient is of the form Q(x) = ax 2 + bx + c. Determine the values of a, b, and c, where a, b, and c ∈ N. a is ___________ (Record in the first column.) b is ___________ (Record in the second column.) c is ___________ (Record in the third column.) (Record your answer in the numerical-response section on the answer sheet.) 8. An angle of A. 52° B. 39° C. 26° D. 13° 13π 90 radians, expressed in degrees, is 9. If 2 sinθ cosθ – cosθ = 0, 0 ≤ θ < 2π, then the values of θ are A. B. C. D. 0, π , π, and 5π 3 3 0, π , 5π , and 3π 3 6 2 π , π , π, and 5π 6 2 3 π , π , 5π , and 3π 6 2 6 2 5
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: Use the following information to an
Page 11 and 12: 13. If (π, -6) satisfies the equat
Page 13 and 14: 14. Given that log b 64 = 3 , the v
Page 15 and 16: Use the following information to an
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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