Higher June 2023 Paper 2 Q16
16 \(Q\) is directly proportional to \(\sqrt{t}\)
The graph shows the relationship between \(Q\) and \(t\) for \(0 \lt t \lt 8\)
(a) Find a formula for \(Q\) in terms of \(t\) (3)
\(Q\) is increased by 20%
(b) Find the percentage increase in \(t\) (2)
| Scheme | Marks |
|---|---|
| \(Q = k\sqrt{t}\) | M1 |
| eg \(6 = k\sqrt{4}\) or \(3 = k\sqrt{1}\) or \(k = 3\) | M1 |
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(Q = 3\sqrt{t}\) | A1 |
| (3) |
Notes
M1: for linking \(Q\) and \(t\) correctly
(must have constant eg \(k\)) (allow \(Q \propto k\sqrt{t}\) )
M1: for substituting a suitable pair of values or finding \(k = 3\) (allow \(\propto\) sign)
A1: oe allow \(q\) for \(Q\) (must have =) allow 2.95 – 3.05 for \(k\) if method clearly shown and readings correct ±0.5 small square
allow an answer of \(Q = k\sqrt{t}\) with \(k = 3\) clearly stated
| Scheme | Marks |
|---|---|
\(1.2^2\) or 1.44 or 144 could be within a calculation eg \(\left(\dfrac{3 \times 1.2}{3}\right)^2\) (= 1.44) or \(\left(\dfrac{6 \times 1.2}{3}\right)^2\) (= 5.76) eg \(\left(\dfrac{6 \times 1.2}{\text{``}{3}\text{''}}\right)^2 \div 4\) (= 1.44) or \(\left(\dfrac{6 \times 1.2}{3}\right)^2 - 4\) (= 1.76) eg 6 × 1.2 = 7.2 and reading from \(Q\) = 7.2 to \(t\) axis and calculates \(t\) value ÷ 4 (or 0.04) | M1ft |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 44 | A1 |
| (2) | |
| (5 marks) |
Notes
M1ft: ft for an equation in the correct form
Stating the multiplier \(1.2^2\) or 1.44 or 144
or
showing the multiplier within a calculation
or
for using a pair of values and showing a correct calculation for the increase in \(t\), ft their \(k\) from (a)
or
correct calculation and use of graph
A1: allow 43 – 45 as long as not from incorrect working