A-LevelMathematicsFunctions9709/22 · May/June 2025 · Q25 Marks
Sketch on the same diagram the graphs of y = |2x-9| and y=4x-5.
- (a)Sketch on the same diagram the graphs of y = |2x-9| and y=4x-5.[2]
- (b)Solve the inequality |2x-9|<4x-5.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] Draw V-shaped graph with vertex on positive x-axis
- [B1] Draw correct graph of y = 4x-5 Correctly placed with reference to modulus graph and with steeper gradient.
- [M1] Solve linear equation or inequality with signs of 2x and 4x different
- [A1] Obtain -2x+9=4x-5 and hence x = 7/3 OE
- [A1] Conclude x > 7/3 OE, e.g. (7/3, ∞).
- [B1*] State or imply non-modulus equation (or inequality) (2x−9)² = (4x-5)²
- [DM1] Attempt solution of three-term quadratic equation (or inequality) 12x²-4x-56=0 leading to 7/3 and –2.
- [A1] Obtain at least 7/3 and conclude x > 7/3 Must be from correct work. OE, e.g. (7/3, ∞).
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