A-LevelMathematicsAlgebra9709/21 · Oct/Nov 2023 · Q47 Marks

Sketch, on the same diagram, the graphs of y = |3x – 5| and y = 2x + 7.

(a)Sketch, on the same diagram, the graphs of y = |3x – 5| and y = 2x + 7.[2]
(b)Solve the equation |3x – 5| = 2x + 7.[3]
(c)Hence solve the equation |3ʸ⁺¹ − 5| = 2 × 3ʸ + 7, giving your answer correct to 3 significant figures.[2]

Mark scheme

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

[B1] Draw V-shaped graph with vertex on positive x-axis
[B1] Draw (more or less) correct graph of y=2x+7 with smaller gradient And crossing y-axis above y-intercept of modulus graph.
[B1] Solve 3x-5=2x+7 to obtain x=12
[M1] Attempt solution of linear equation where signs of 3x and 2x are different 3x-5=-2x-7 OE.
[A1] Obtain x = −2/5
[B1] State or imply non-modulus equation (3x-5)² = (2x + 7)² Must be working with (3x-5)² = (2x + 7)²
[M1] Attempt solution of 3-term quadratic equation
[A1] Obtain −2/5 and 12
[M1] Apply logarithms and use power law for 3ʸ = k where k>0 or correct equivalent Using their positive answer from part (b) or greater accuracy; and no other values.
[A1] Obtain 2.26

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