4MA0 Higher January 2018 Paper 4R Q14
14 \(P\) is directly proportional to the square of \(Q\).
\(P = 180\) when \(Q = 12\)
(a) Find a formula for \(P\) in terms of \(Q\). (3)
(b) Find the value of \(P\) when \(Q = 30\) (1)
| Scheme | Marks |
|---|---|
| \(P = kQ^2\) or \(P \propto kQ^2\) | M1 |
| Eg \(180 = k \times 12^2\) or \(180 \propto k \times 12^2\) | M1 |
| \(P = 1.25Q^2\) | A1 |
| (3) |
Notes
M1: Allow \(Q^2 = kP\) or \(Q^2 \propto kP\)
M1: For a correct substitution into a correct equation
Implies first M1
Award M2 if \(k = 1.25\) oe stated unambiguously in (a) or (b)
A1: oe
Only award if \(P\) is the subject.
M2A1 for \(P = kQ^2\) on answer line if \(k = 1.25\) oe seen in part (a) or (b)
| Scheme | Marks |
|---|---|
| 1125 | B1 |
| (1) | |
| (4 marks) |
Notes
B1: Ft if (a) in form \(P = kQ^2\)