Higher June 2019 Paper 3 Q19
19 \(D = \dfrac{u^2}{2a}\)
\(u = 26.2\) correct to 3 significant figures
\(a = 4.3\) correct to 2 significant figures
(a) Calculate the upper bound for the value of \(D\).
Give your answer correct to 6 significant figures.
You must show all your working. (3)
Give your answer correct to 6 significant figures.
You must show all your working. (3)
The lower bound for the value of \(D\) is 78.6003 correct to 6 significant figures.
(b) By considering bounds, write down the value of \(D\) to a suitable degree of accuracy.
You must give a reason for your answer. (2)
You must give a reason for your answer. (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| 81.0662 | M1 | for one of 26.15 or 26.25 or 4.25 or 4.35 |
| M1 | for a correct process to find the upper bound for \(D\) [UB of \(u\)]\(^2 \div [2 \times\) LB of \(a\)] eg \(\dfrac{26.25^2}{2 \times 4.25}\) where \(26.2 \lt \) UB of \(u \leqslant 26.25\) and \(4.25 \leqslant\) LB of \(a \lt 4.3\) | |
| A1 | for answer given in the range 81.0661 to 81.0662 from correct working |
Additional guidance
Accept \(26.24\dot{9}\) for 26.25 and \(4.34\dot{9}\) for 4.35
Award for \(\dfrac{26.25^2}{4.25}\)
| Answer | Mark | Mark scheme |
|---|---|---|
| 80 explanation | B1 | for 80 ft answer to (a) with 78.6003 |
| C1 | for explanation relating to the upper bound found in (a) Acceptable examples bounds agree when rounded to 80 bounds agree to nearest 10 Not acceptable examples 80 79.83325 rounded to nearest tenth |