Higher June 2025 Paper 3 Q23
23 A roller coaster starts at ground level.
The height above ground level, \(h\), in metres, of the roller coaster is given by
\[h = -(t - 7)^2 + 49\]where \(t\) is the time in seconds after the roller coaster starts.
Sam draws a graph of \(h\) against \(t\) for \(\quad 0 \leqslant t \leqslant 14\)
Make two criticisms of Sam’s graph. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Any two from valid criticism about the \(h\)-intercept or valid criticism about the maximum point or valid criticism about the non-linear scaling on the horizontal axis | B2 | eg graph should go through (0, 0) graph should intercept when \(h = 0\) \(y\)-intercept should be 0 eg the maximum point should be (7, 49) at \(t = 7\), \(h\) should be 49 eg 0, 7 and 14 should be evenly spaced B1 any one valid criticism |
Additional guidance
Allow use of \(y\) for \(h\) or use of \(x\) for \(t\)
Each criticism may be implied by a correct, unambiguous graph drawn
Examples of valid criticisms
The intersection of the \(y\)-axis is wrong
The height at the beginning should not be 49
It should start at zero/ground level
The maximum/turning point is wrong
Goes higher than 49
Spacing of numbers on the \(x\)-axis is not equal
Examples of invalid criticisms
The \(y\)-axis is wrong
Wrong graph
Should be more symmetrical
The maximum point not labelled correctly
The coordinates are wrong
Needs more labels
The labels on the \(t\)-axis are wrong
Scales not easy to read