4MA1/1HR Jan 2020, Question 23: Differentiating Polynomials
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
A particle's displacement is s = t³ + 4t² − 5t + 7 from fixed point O. Given velocity V ≥ −5 at time T, find T in terms of V in the form (−4 + √(k + mV))/3, finding integers k and m.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1Differentiate: v = ds/dt = 3t² + 8t − 5
- 2At time T the velocity is V, so 3T² + 8T − 5 = V
- 3Rearrange: 3T² + 8T − (5 + V) = 0
- 4Quadratic formula: T = (−8 ± √(64 + 12(5 + V)))/6
- 564 + 60 + 12V = 124 + 12V, and 124 + 12V = 4(31 + 3V)
- 6√(4(31 + 3V)) = 2√(31 + 3V), so T = (−8 ± 2√(31 + 3V))/6
- 7Divide through by 2: T = (−4 ± √(31 + 3V))/3
- 8T must be positive, so T = (−4 + √(31 + 3V))/3
Answer(−4 + √(31 + 3V))/3
Stuck on a step? Read the free lesson: Differentiating Polynomials
Practise more differentiating polynomials questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on differentiating polynomials
Also searched as: 4MA1 1HR January 2020 · 4MA1/1HR · 4ma1 jan20 1hr · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.