Edexcel IALGeneralGeneral Applications8 Marks

(a) Sketch the graph of `y = |4x-3|`, showing the coordinates of the points where the graph meets the coordinate axes. (b) Solve the equation `|4x-3| = 2x+1`.

(a)Sketch the graph of `y = |4x-3|`, showing the coordinates of the points where the graph meets the coordinate axes.[3]
(b)Solve the equation `|4x-3| = 2x+1`.[5]

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

B1 for V-shape, either cusp on x-axis or minimum at `(3/4, 0)`.
B1 for `(0, 3)` (stated or shown on graph).
B1 for `(3/4, 0)` (stated or shown on graph).
M1 for considering both `4x-3 = 2x+1` and `-(4x-3) = 2x+1` (or equivalent e.g. squaring both sides).
A1 for `2x = 4 \Rightarrow x=2`.
A1 for `-4x+3 = 2x+1 \Rightarrow 6x=2 \Rightarrow x=1/3`.
B1 for concluding both `x=2` and `x=1/3` are valid solutions (e.g., by checking them or graphical interpretation).
M1 for squaring both sides `(4x-3)^2 = (2x+1)^2`.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.