A2 October 2021 Paper 2 Q4
4 In this question you must show detailed reasoning.
Determine the value of \(\displaystyle\sum_{r=1}^{100}(2r + 3)^2\). [3]
| Scheme | Marks | AO |
|---|---|---|
| DR \(\displaystyle\sum_{r=1}^{100}(2r + 3)^2 = 4\displaystyle\sum_{r=1}^{100}r^2 + 12\displaystyle\sum_{r=1}^{100}r + 9\displaystyle\sum_{r=1}^{100}1\) | B1 | 3.1a |
| \(\displaystyle\sum_{r=1}^{100}r^2 = \dfrac{1}{6} \times 100(100 + 1)(2 \times 100 + 1)\) | M1 | 1.1a |
| \(4 \times 338350 + 12 \times \tfrac{1}{2} \times 100 \times 101 + 900 = 1414900\) | A1 | 1.1 |
| [3] |
Notes
B1: Expanding and separating
M1: Use of formula for \(\displaystyle\sum_{r=1}^{100}r^2\)