Intermediate November 2019 Unit 2 Q10
10. A solution of the equation
\[x^3 - 3x = 37\]lies between 3 and 4.
Use the method of trial and improvement to find this solution correct to 1 decimal place.
You must show all your working. [4]
| Scheme | Marks | Comments | ||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| One correct evaluation 3 ≤ x ≤ 4 | B1 | Correct evaluation regarded as enough to identify if <37 or >37. If evaluations not seen accept ‘too high’ or ‘too low’. Look out for testing x3 − 3x – 37 = 0 | ||||||||||||||||||||||||||||||||||||||||||||||||
| 2 correct evaluations 3·55 ≤ x ≤ 3·75, one < 37, one > 37. | B1 | |||||||||||||||||||||||||||||||||||||||||||||||||
| 2 correct evaluations 3·55 ≤ x ≤ 3·65, one < 37, one > 37. | M1 | |||||||||||||||||||||||||||||||||||||||||||||||||
| x = 3·6 | A1 |
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