A-LevelMathematicsNumerical methods9709/23 · Oct/Nov 2024 · Q58 Marks
It is given that ∫_a^(a³) (10 / (2x+1)) dx = 7, where a is a constant greater than 1.
- (a)Show that a = ³√(0.5e^(1.4) (2a+1) - 0.5).[5]
- (b)Use an iterative formula, based on the equation in part (a), to find the value of a correct to 3 significant figures. Use an initial value of 2 and give the result of each iteration to 5 significant figures.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [5] Obtain integral of form kln(2x+1) *M1
- Obtain correct 5ln(2x+1) A1
- Apply limits correctly and equate to 7 DM1
- Apply appropriate logarithm property to reach at least a³ =... DM1
- Confirm a = 0.5e^1.4 (2a+1) - 0.5 A1 AG – necessary detail needed.
- [3] Use iterative process correctly at least once M1
- Obtain final answer 2.18 A1 Answer required to exactly 3 sf.
- Show sufficient iterations to 5 sf to justify answer or show a sign change in the interval [2.175, 2.185] A1
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