Numeracy Higher November 2022 Unit 1 Q8
8. Emma wants to know how much water is in a pond near her house.
She has taken width measurements of the pond every 3 m along its length.
These width measurements are shown on the plan view of the pond below.
Diagram not drawn to scale
Emma has used these width measurements to sketch the following graph.
Diagram not drawn to scale
Emma knows that the pond has a uniform depth of 1·2 m.
Use the trapezium rule with 4 strips to calculate an estimate for the volume of water in the pond. [5]
Estimate of the volume of water in the pond = …………… m3
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\)
| Scheme | Marks | Comments |
|---|---|---|
| (Area =) \(\dfrac{1}{2}\) × 3 × (1 + 3.4 + 2(3.2 + 5.4 + 6.2)) | M2 | M1 for 1 slip in substitution of width values |
| = 51 (m2) | A1 | FT from M1 |
| (Volume of water =) 51 × 1.2 | m1 | FT ‘their 51’ provided M1 or M2 previously awarded Condone further multiplication by 2 for m1A0 |
| = 61.2 (m3) | A1 |
Alternative method for the first 3 marks:
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{(1 + 3.2)}{2}\)×3 + \(\dfrac{(3.2 + 5.4)}{2}\)×3 + \(\dfrac{(5.4 + 6.2)}{2}\)×3 + \(\dfrac{(6.2 + 3.4)}{2}\)×3 or equivalent [6.3 + 12.9 + 17.4 + 14.4] | M2 | M1 for the sum of these 4 areas with one error (may be repeated) in the substitution of width values |
| = 51 (m2) | A1 | FT from M1 |