A-LevelMathematicsFunctions9709/22 · Feb/Mar 2023 · Q47 Marks

Sketch, on the same diagram, the graphs of y = |2x – 11| and y = 3x – 3.

(a)Sketch, on the same diagram, the graphs of y = |2x – 11| and y = 3x – 3.[2]
(b)Solve the inequality |2x – 11| < 3x − 3.[3]
(c)Find the smallest integer N satisfying the inequality |2 ln N – 11| < 3 ln N - 3.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[B1] (a) Draw V-shaped graph with vertex on positive x-axis
[B1] (a) Draw approximately correct graph of y=3x-3 with greater gradient Crossing x-axis between origin and vertex of first graph.
[M1] (b) Attempt solution of linear equation where signs of 2x and 3x are different
[A1] (b) Solve -2x+11=3x-3 to obtain x = 14/5 OE
[A1] (b) Conclude x > 14/5 OE
[M1] (b) Alternative method for Question 4(b): Attempt solution of 3-term equation (2x−11)² = (3x-3)² to obtain at least one value of x Or equivalent inequality.
[A1] (b) Alternative method for Question 4(b): Obtain at least x = 14/5 OE
[A1] (b) Alternative method for Question 4(b): Conclude x > 14/5 OE
[M1] (c) Attempt value of N (maybe non-integer at this stage) using logarithms and their answer to part (b).
[A1] (c) Conclude with single integer 17

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