Mathematics 30 June 1999 Grade 12 Diploma Exam

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Use the following information to answer the next question. A mathematics class was asked to solve the equation 3 x + 2 = 6 x The attempts of two students to solve the equation are shown below. Each student made one error that led to an incorrect solution. Student A Student B 3 x + 2 =6 x 3 x + 2 =6 x 3 x + 2 =3 2x log 3 x + 2 = log 6 x x + 2 = 2x x + 2 log 3 = x log 6 2=2x – x 2 log 3 = –x + x log 6 x =2 2 log 3=x(–1 + log 6) 2log3 ( −1 + log6) = x x is approximately – 4.3 Written Response—10% 3. • Show that neither x = 2 nor x = – 4.3 satisfies the equation 3 x + 2 = 6 x . <strong>30</strong>
• Identify the error that was made by each student and state why each error leads to an incorrect answer. • Algebraically solve the equation 3 x + 2 = 6 x and give the solution, correct to the nearest hundredth. You have now completed the examination. If you have time, you may wish to check your answers. 31
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 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 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: • Assume that it becomes necessar
Page 37 and 38: Fold and tear along perforation. 0
Page 39 and 40: No marks will be given for work don
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Page 43 and 44: SAMPLE ANSWERS TO THE WRITTEN-RESPO
Page 45 and 46: • The store will lose money on th
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Page 49 and 50: A POSSIBLE SOLUTION Student A Stude

Mathematics 30 June 1999 Grade 12 Diploma Exam

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