Tiêu đề P3 SAMPLE WRITTEN MS.pdf ✅

Leave blank 4 *S59757A0435* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. f(x) = x3 + 3 2 + 4x – 12 (a) Show that the equation f(x) = 0 can be written as x = 4 3 3 ( ) ( ) − + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ x x x –3 (3) The equation x3 + 3 2 + 4x – 12 = 0 has a single root which is between 1 and 2 (b) Use the iteration formula xn + 1 = 4 3 3 ( ) ( ) − + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ x x n n n . 0 with x0 = 1 to find, to 2 decimal places, the value of x1 , x2 and x3 (3) The root of f(x) = 0 is Į. (c) By choosing a suitable interval, prove that Į = 1.272 to 3 decimal places. (2) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Leave blank 5 *S59757A0535* Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 90 Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and Pure Mathematics – Sample Assessment Materials (SAMs) – Issue 3 – June 2018 © Pearson Education Limited 2018 www.mymathscloud.com www.mymathscloud.com www.mymathscloud.com
Leave blank 4 *S59757A0435* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. f(x) = x3 + 3 2 + 4x – 12 (a) Show that the equation f(x) = 0 can be written as x = 4 3 3 ( ) ( ) − + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ x x x –3 (3) The equation x3 + 3 2 + 4x – 12 = 0 has a single root which is between 1 and 2 (b) Use the iteration formula xn + 1 = 4 3 3 ( ) ( ) − + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ x x n n n . 0 with x0 = 1 to find, to 2 decimal places, the value of x1 , x2 and x3 (3) The root of f(x) = 0 is Į. (c) By choosing a suitable interval, prove that Į = 1.272 to 3 decimal places. (2) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Leave blank 5 *S59757A0535* Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 91 Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and Pure Mathematics – Sample Assessment Materials (SAMs) – Issue 3 – June 2018 © Pearson Education Limited 2018 www.mymathscloud.com www.mymathscloud.com www.mymathscloud.com