for first step to change the subject of \(y = \dfrac{5x - 3}{4}\) or \(x = \dfrac{5y - 3}{4}\) eg \(4y = 5x - 3\) or \(4x = 5y - 3\)
A1
oe
Additional guidance
Answer of \(\dfrac{4y + 3}{5}\) gets M1A0
Mark scheme (b)
Answer
Mark
Mark scheme
100
M1
for \(\mathrm{h}(5) = 1 - 2 \times 5\ (= -9)\) and a clear intention to find \(\mathrm{g}(\text{``}{-}9\text{''})\) or for \(((1 - 2 \times 5) - 1)^2\) or for stating \(\mathrm{gh}(x)\), eg \((1 - 2x - 1)^2\) oe
When \(\quad x = 5 \quad y = 13\) and when \(\quad x = 10 \quad y = 28\)
Complete the number machine. [2 marks]
Mark scheme (a)
Answer
Mark
Comments
40 in correct position in number machine
B1
Mark scheme (b)
Answer
Mark
Comments
\(+\,11\) in correct position in number machine
B1
oe operation to reach 18 eg \(-\,-11\) or \(\times\,\dfrac{18}{7}\)
Mark scheme (c)
Answer
Mark
Comments
3 and 2 in correct positions in number machine
B2
B1 correct operations for input 5, output 13 or correct operations for input 10, output 28
Additional guidance
B1 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts
Examples of correct operations for input 5, output 13 include \(\times\,2.6\) and \(-\,0\) or \(\times\,4\) and \(-\,7\) or \(\times\,5\) and \(-\,12\)
B1
Examples of correct operations for input 10, output 28 include \(\times\,2.8\) and \(-\,0\) or \(\times\,4\) and \(-\,12\) or \(\times\,5\) and \(-\,22\)
(a) \(\mathrm{h}(x) = \sqrt[3]{x} \qquad\) for all values of \(x\)
On the grid, draw the graph of the inverse function \(\;y = \mathrm{h}^{-1}(x) \quad\) for \(\;-2 \leqslant x \leqslant 2\) [2 marks]
(b) For all values of \(x\)
\(\mathrm{f}(x) = \sin x\)
\(\mathrm{g}(x) = x + 90\)
On the grid, draw the graph of the composite function \(\;y = \mathrm{fg}(x) \quad\) for \(\;0^\circ \leqslant x \leqslant 360^\circ\) [2 marks]
Mark scheme (a)
Answer
Mark
Comments
Fully correct graph passing through \((-2, -8)\ (-1, -1)\ (0, 0)\ (1, 1)\) and (2, 8)
B2
B1 \(x^3\) or \(y^3 = x\) or at least 4 points from \((-2, -8)\ (-1, -1)\ (0, 0)\ (1, 1)\) and \((2, 8)\) plotted or seen in a table Tolerance of \(\pm 1\) small square Points can be implied by graph passing through them
Additional guidance
Tolerance of \(\pm 1\) small square means it is on the edges of or within the shaded area
Ignore graph drawn outside of \(\;-2 \leqslant x \leqslant 2\)
B1 \(\sin (x + 90)\) or \(\cos x\) or at least 4 points from \((0, 1)\ (90, 0)\ (180, -1)\ (270, 0)\) and \((360, 1)\) plotted or seen in a table Mark intention
Additional guidance
Ignore graph drawn outside of \(\;0^\circ \leqslant x \leqslant 360^\circ\)
