A-LevelMathematicsFunctions9709/22 · Feb/Mar 2020 · Q59 Marks

Sketch, on the same diagram, the graphs of y = |x + 2k| and y = |2x – 3k|, where k is a positive constant. Give, in terms of k, the coordinates of the points where each graph meets the axes.

(a)Sketch, on the same diagram, the graphs of y = |x + 2k| and y = |2x – 3k|, where k is a positive constant. Give, in terms of k, the coordinates of the points where each graph meets the axes.[3]
(b)Find, in terms of k, the coordinates of each of the two points where the graphs intersect.[4]
(c)Find, in terms of k, the largest value of t satisfying the inequality |2ᵗ + 2k| > |2ᵗ⁺¹ – 3k|.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

(a) Draw two V-shaped graphs with one vertex on negative x-axis and one vertex on positive x-axis
(a) Draw correct graphs related correctly to each other
(a) State correct coordinates −2k, 2k, ¾k, 3k Either given on axes or stated separately
(b) State or imply non-modulus equation (x + 2k)² = (2x-3k)² or pair of linear equations
(b) Attempt solution of 3-term quadratic equation or pair of linear equations
(b) Obtain x = k, x=5k
(b) Obtain y=3k, y=7k If A0A0, award A1 for one pair of correct coordinates
(c) Relate 2ᵗ to larger value of x from part (b)
(c) Apply logarithms to obtain t = ln(5k)/ln(2) OE such as log₁₀(5k)/log₁₀(2) or log₂(5k)

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