(a) Meera is using a graphical method to solve \(\quad 2x^2 - 3x = 0\)
She draws the graph of \(\quad y = 2x^2 \quad\) and a straight line graph on the same grid.
Here is the graph of \(\quad y = 2x^2\)
Complete her method to solve \(\quad 2x^2 - 3x = 0\) [2 marks]
(b) Levi is solving \(\quad 2x^2 + 5x = 0\)
He uses this method.
\[\begin{aligned} 2x^2 + 5x &= 0 && \text{subtract } 5x \text{ from both sides} \\ 2x^2 &= -5x && \text{divide both sides by } x \\ 2x &= -5 && \text{divide both sides by } 2 \\ x &= -2.5 && \end{aligned}\]
Evaluate his method and his answer. [2 marks]
Mark scheme (a)
Answer
Mark
Comments
Draws \(y = 3x\) and (\(x =\)) [−0.1, 0.1] and (\(x =\)) [1.4, 1.6]
B2
B1 Draws \(y = 3x\) or states \(y = 3x\) \(\pm\dfrac{1}{2}\) square tolerance for drawing graph Graph must be seen for \(x\) values from 0 to 1.5
Additional guidance
Ignore any \(y\) values seen
Solutions from a non-graphical method
B0
Ignore other lines drawn on grid
Mark scheme (b)
Answer
Mark
Comments
Full evaluation of method and answer
B2
eg1 Cannot divide by \(x\) as it could be zero eg2 Should have factorised and then he would have also found that \(x = 0\) eg3 Should have used the formula and then he would have also found that \(x = 0\) eg4 Should have used a graphical method then he would have also found that \(x = 0\) eg5 Should have completed the square then he would have also found that \(x = 0\)
B1 Partial evaluation eg1 \(x = 0\) has been omitted eg2 Should have factorised eg3 Should have used the formula eg4 Should have drawn a graph eg5 Only found one solution eg6 Cannot divide by zero
Additional guidance
For B2 there needs to be an evaluation of the method and an indication that \(x = 0\) has been omitted from the answer
