Скачать или смотреть Numerical Methods - Iteration (Q9 A2 P1 Edexcel 2025)

In this video, Lee Guffick — former Head of Mathematics and A-Level Examiner — walks through Question 9 from Edexcel A Level Maths Paper 1 (2025) on kinematics, differentiation, and numerical methods.
You’ll learn how to:
✅ Solve for the time when a car’s velocity first returns to zero.
✅ Differentiate to find where maximum speed occurs and show that
𝑡
=
5
ln
⁡
 ⁣
(
75
5
−
𝑡
)
t=5ln(
5−t
75
​

).
✅ Apply the iteration formula to calculate
𝑡
3
t
3
​

and the converged time for maximum speed.
✅ Understand how exponential terms and recursive iteration connect across calculus and modelling topics.

Perfect for students aiming for A/A* in Edexcel A Level Maths 2025, this problem combines exponential equations, the product rule, and Chapter 10 iteration techniques — a true mixed-topic exam test.

⏱️ TIMESTAMPS:
00:00 – Understanding the velocity model
00:26 – Finding t when v = 0 (13.5 s)
01:55 – Differentiating v using the product rule
04:19 – Rearranging to derive
𝑡
=
5
ln
⁡
 ⁣
(
75
5
−
𝑡
)
t=5ln(
5−t
75
​

)
06:24 – Setting up the iteration formula
07:49 – Calculating
𝑡
2
t
2
​

and
𝑡
3
t
3
​

with a Casio calculator
08:37 – Repeated iteration → converging to
𝑡
=
8.55
 
s
t=8.55s
09:49 – Final answers and exam recap

✏️ TOPICS COVERED:

Exponential motion modelling

Differentiation (product rule)

Natural logarithms and rearrangement

Iterative methods and recursion

Numerical methods (Chapter 10)

Edexcel A Level Maths Paper 1 (2025)

💯 EXAM TIPS:

Factorise first to spot trivial solutions quickly.

Always state “
𝑑
𝑣
/
𝑑
𝑡
=
0
dv/dt=0” before finding max speed.

Check calculator modes and iteration syntax carefully.

Continue iteration until two successive values match to 3 s.f.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a premium online maths tutor, former Head of Mathematics, and A-Level Examiner, helping students achieve A/A grades* and secure places at Oxford, Cambridge, and Ivy League universities.

📅 JOIN OUR PROGRAMME:
→ 1:1 Tutoring: https://www.gufficktuition.com/tutoring

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📱 CONNECT WITH LEE:
→ Instagram: @leeguffick

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→ Email: [email protected]

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