A-LevelMathematicsFunctions9709/33 · May/June 2025 · Q14 Marks
Sketch the graph of y = |3x-2a|, where a is a positive constant.
- (a)Sketch the graph of y = |3x-2a|, where a is a positive constant.[1]
- (b)Hence or otherwise solve the inequality |3x-2a|<x+5a.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] Symmetrical. In correct position. Lines intended to be straight. Must be in both first and second quadrants. Key coordinates must be correct. Ignore y = x + 5a if seen.
- [B1] Obtain critical value 7a/2 from x+5a=3x-2a. Allow if seen in an inequality.
- [B1] Obtain critical value 3a/4 from x+5a=2a-3x. Allow if seen in an inequality.
- [B1] State final answer 3a/4 < x < 7a/2. SC B1 only for 3a/4 < x < 7a/2 with their a from part (a). Allow any equivalent notation. Allow 3a/4 < x and x < 7a/2.
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