Mathematics 30 June 1999 Grade 12 Diploma Exam

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Use the following information to answer the next question. A student is given the partial graph of a third-degree polynomial function, y = P(x), as shown below. The x-intercepts of the graph are – 4, 0, and 2. y 35 <strong>30</strong> 25 20 15 10 5 –6 –5 –4 –3 –2 –1 –5 1 2 3 4 5 6 –10 –15 –20 –25 x 3. In order to determine the equation for P, the student will also require the A. range when x > 2 B. value of the y-intercept C. values of any additional x-intercepts D. coordinates of a point on the graph of y = P(x), such that y ≠ 0 4. A third-degree polynomial function is given by P(x) = (x – 2)(x + 3)(x + 4). If another polynomial function Q(x) = kP(x), k > 1, then the graph of y = Q(x) must have A. a y-intercept that is less than –24 B. a y-intercept that is greater than –24 C. k more x-intercepts than the graph of P(x) D. x-intercepts different from those of the graph of P(x) 2
Use the following information to answer the next question. The partial graph of the polynomial function P(x) = ax 3 + bx 2 + cx + d is shown below. The graph of y = Q(x) is the reflection of y = P(x) in the x-axis. y y = P(x) x y = Q(x) 5. According to this information, the equation of the polynomial function Q is A. Q(x) = ax 3 + bx 2 + cx – d B. Q(x) = –ax 3 + bx 2 + cx + d C. Q(x) = –ax 3 + bx 2 + cx – d D. Q(x) = –ax 3 – bx 2 – cx – d 3
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Page 3 and 4: Multiple Choice • Decide which of
Page 5: 1. The function f (x) = x 3 - 6 is
Page 9 and 10: Numerical Response 1. The polynomia
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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