A-LevelMathematicsFunctions9709/21 · May/June 2024 · Q38 Marks
Sketch on the same diagram the graphs of y = |3x-8|and y = 5-x.
- (a)Sketch on the same diagram the graphs of y = |3x-8|and y = 5-x.[2]
- (b)Solve the inequality | 3x-8|<5-x.[4]
- (c)Hence determine the largest integer N satisfying the inequality |3e0.1N -8|<5-e0.1N.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] Draw V-shaped graph with vertex on positive x-axis in the first quadrant.
- [B1] Draw correct graph of y = 5-x correctly positioned with respect to modulus graph.
- [B1] Solve 3x-8=5-x to obtain 13/4
- [M1] Solve linear equation or inequality with signs of 3x and x the same
- [A1] Obtain 3/2
- [A1] Conclude 3/2 < x < 13/4 or x>3/2 and x<13/4
- [M1] Attempt value of N (maybe non-integer at this stage) for e0.1N <their 13/4
- [A1] Conclude with single integer 11
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