Date | May 2018 | Marks available | 3 | Reference code | 18M.1.hl.TZ2.2 |
Level | HL only | Paper | 1 | Time zone | TZ2 |
Command term | Sketch | Question number | 2 | Adapted from | N/A |
Question
Sketch the graphs of \(y = \frac{x}{2} + 1\) and \(y = \left| {x - 2} \right|\) on the following axes.
Solve the equation \(\frac{x}{2} + 1 = \left| {x - 2} \right|\).
Markscheme
straight line graph with correct axis intercepts A1
modulus graph: V shape in upper half plane A1
modulus graph having correct vertex and y-intercept A1
[3 marks]
METHOD 1
attempt to solve \(\frac{x}{2} + 1 = x - 2\) (M1)
\(x = 6\) A1
Note: Accept \(x = 6\) using the graph.
attempt to solve (algebraically) \(\frac{x}{2} + 1 = 2 - x\) M1
\(x = \frac{2}{3}\) A1
[4 marks]
METHOD 2
\({\left( {\frac{x}{2} + 1} \right)^2} = {\left( {x - 2} \right)^2}\) M1
\(\frac{{{x^2}}}{4} + x + 1 = {x^2} - 4x + 4\)
\(0 = \frac{{3{x^2}}}{4} - 5x + 3\)
\(3{x^2} - 20x + 12 = 0\)
attempt to factorise (or equivalent) M1
\(\left( {3x - 2} \right)\left( {x - 6} \right) = 0\)
\(x = \frac{2}{3}\) A1
\(x = 6\) A1
[4 marks]