(a) Sketch the graph of \(y = 8^x\). Indicate any values where the graph crosses the axes. [2]
(b) Sketch the graph of \(y = \cos x\) for \(0^\circ \leqslant x \leqslant 360^\circ\). Indicate any values where the graph crosses the \(x\)-axis. [2]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Correct sketch with \(y\) – intercept 1 indicated
2
B1 for increasing exponential curve with no ruled sections
or for any sketch with a single \(y\) – intercept at 1
For 2 marks, condone curve touching but not crossing \(x\)- axis For 2 marks or B1 mark intention For 2 marks no ruled sections
See AG
Additional guidance: Question 22(a)
Example A
Correct shape, mark intention passes through \(y = 1\) 2 marks
Example B
Correct shape B1
Example C
\(y\) – intercept at 1 B1
Example D
Ruled wrong shape B0
Mark scheme (b)
Answer
Marks
Part marks and guidance
Correct sketch of \(y = \cos x\) with 90 and 270 indicated and starting at 1 on \(y\)-axis
2
B1 for cos shape graph with period 360 starting at (0, \(k\)), \(k \gt 0\) and amplitude \(k\) Or for cos shape graph starting at (0, 1) with amplitude 1 and with a period a factor of 360 Or for cos shape graph with period 360 with 90 and 270 indicated where graph crosses \(x\) - axis
For 2 marks mark intention
e.g. \(y = 2\cos x\) For B1 allow poor curvature, mark intention
