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 . 8
A POSSIBLE SOLUTION Student A Student B 3 x + 2 =6 x 3 x + 2 =6 x 3 x + 2 6 x 3 x + 2 6 x 3 2 + 2 6 2 3 –4.3 + 2 6 –4.3 81 36 3 –2.3 6 –4.3 ≈ 0.0799 ≈ 0.00045 LHS ≠ RHS ∴ x = 2 is not a correct solution LHS ≠ RHS ∴ x = – 4.3 is not a correct solution • Identify the error that was made by each student and state why each error leads to an incorrect answer. A POSSIBLE SOLUTION Student A Student A stated that 6 x = 3 2x which would indicate that 6 = 3 2 which is obviously not correct. Student B In the third line of their work the student did not realize that log 3 was multiplied by (x + 2), so that in line 4 they incorrectly subtracted x. 9
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Mathematics 30 June 1999 Grade 12 Diploma Exam

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