June 2022 Paper 1 Q5

Notes

(a)(i)

M1: Indicate horizontal translation (in either direction) in some way with magnitude of 4 (‘units’ not required)
B1 for \(\begin{pmatrix}4\\0\end{pmatrix}\)
Condone informal language as long as intent is clear eg ‘left’ (or even ‘right’, as either direction allowed)
M0 if ambiguous eg ‘in’ or ‘on’ the \(x\)-axis

A1: B2 for \(\begin{pmatrix}-4\\0\end{pmatrix}\)
Must now be correct language so A0 for eg ‘along’ the \(x\)-axis or ‘left’
Allow ‘parallel to the \(x\)-axis’ or ‘horizontal’

(a)(ii)

B1: Identify direction - correct language needed
Allow ‘\(x\)-axis invariant’, ‘parallel to the \(y\)-axis’ or ‘vertical’
Condone ‘positive’ \(y\)-direction (as given function > 0)

B1: ‘scale factor’ or ‘factor’ needed (condone ‘stretch’ factor)
Not dep on previous B1, but must have indicated vertical stretch in some way, including informal language such as ‘upwards’
Cannot be ambiguous language, such as ‘in’, ‘on’, ‘across’ the \(y\)-axis

Notes

M1: Correctly combine two correct log terms
Or \(\log_2(8x) = \log_2\frac{2}{1-x}\)
Or \(3 + \log_2(x(1 - x)) = 1\)
Or \(\log_2(4x(1 - x)) = 0\)
OR use indices base 2 on both sides (ie \(8x = 2^{1 - \log_2(1-x)}\)) and use rules of indices to split eg \(8x = 2 \times 2^{-\log_2(1-x)}\)

M1: Correct method to remove logs
Correctly used on equation of form \(\log_2\mathrm{f}(x) = \log_2\mathrm{g}(x)\) or \(\log_2\mathrm{f}(x) = k\)
OR correct method to deal with log term – expect \(8x = \frac{2}{1-x}\)

A1: Any correct equation not involving logarithms
Could still contain brackets and / or fractions

A1: Obtain \(x = 0.5\)
A0 if additional solutions

DR so no credit for answer only