Higher November 2024 Paper 1 Q14
14 \(B\) is inversely proportional to the square of \(d\)
\(B = 0.25\) when \(d = 12\)
Find a formula for \(B\) in terms of \(d\)
(3)
| Scheme | Marks |
|---|---|
\(B = \dfrac{k}{d^2}\) oe or \(Bk = \dfrac{1}{d^2}\) oe | M1 |
\(0.25 = \dfrac{k}{12^2}\) oe or \(0.25 = \dfrac{k}{144}\) oe or \(k = 36\) or \(0.25 \times k = \dfrac{1}{12^2}\) oe or \(0.25 \times k = \dfrac{1}{144}\) oe or \(k = \dfrac{1}{36}\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(B = \dfrac{36}{d^2}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: (NB Not for \(B = \dfrac{1}{d^2}\))
Constant of proportionality must be a symbol such as \(k\)
Allow \(D\) or \(b\)
M1: for substitution of \(B\) and \(d\) into a correct formula
A1: e.g \(B = 36 \times \dfrac{1}{d^2}\) or \(B = 36 \times d^{-2}\)
Award 3 marks if answer is \(B = \dfrac{k}{d^2}\) on the answer line and \(k = 36\) clearly given in the body of working of the script
M2A0 for \(Bd^2 = 36\) or \(d = \dfrac{6}{\sqrt{B}}\) or \(d^2 = \dfrac{36}{B}\)
M2 for
\(0.25 = \dfrac{k}{12^2}\) oe or
\(0.25 \times k = \dfrac{1}{12^2}\) oe or