First Order Differential Equations (Edexcel A Level Further Maths: Core Pure)

Exam Questions

34 mins3 questions

4 marks

A pond initially contains 1000 litres of unpolluted water.

The pond is leaking at a constant rate of 20 litres per day.

It is suspected that contaminated water flows into the pond at a constant rate of 25 litres per day and that the contaminated water contains 2 grams of pollutant in every litre of water.

It is assumed that the pollutant instantly dissolves throughout the pond upon entry.

Given that there are $x$ grams of the pollutant in the pond after $t$ days,

(a)

show that the situation can be modelled by the differential equation,

$\frac{d x}{d t} = 50 - \frac{4 x}{200 + t}$

How did you do?

5 marks

(b)

Hence find the number of grams of pollutant in the pond after 8 days.

How did you do?

1 mark

(c)

Explain how the model could be refined.

How did you do?

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First Order Differential Equations (Edexcel A Level Further Maths: Core Pure)

Exam Questions

1. Complex Numbers

1.1 Complex Numbers & Argand Diagrams

1.2 Exponential Form & de Moivre's Theorem

2. Matrices

2.1 Properties of Matrices

2.2 Transformations using Matrices

3. Further Algebra & Functions

3.1 Roots of Polynomials

3.2 Series

3.3 Maclaurin Series

4. Hyperbolic Functions

4.1 Hyperbolic Functions

5. Further Calculus

5.1 Volumes of Revolution

5.2 Methods in Calculus

6. Further Vectors

6.1 Vector Lines

6.2 Vector Planes

7. Polar Coordinates

7.1 Polar Coordinates

8. Differential Equations

8.1 First Order Differential Equations

8.2 Second Order Differential Equations

8.3 Simple Harmonic Motion

9. Proof

9.1 Proof by Induction