A-LevelMathematicsAlgebra9709/21 · May/June 2019 · Q26 Marks

Solve the inequality |3x – 5| < |x + 3|.

(i)Solve the inequality |3x – 5| < |x + 3|.[4]
(ii)Hence find the greatest integer n satisfying the inequality |3⁰.¹ⁿ⁺¹ – 5| < |3⁰.¹ⁿ + 3|.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] State or imply non-modular inequality (3x-5)² < (x + 3)² or corresponding equation or pair of different linear equations/inequalities
[M1] Attempt solution of 3-term quadratic equation/inequality or of two different linear equations/inequalities
[A1] Obtain critical values ½ and 4
[A1] State answer ½ < x < 4 or equivalent
[M1] Attempt to find n (not necessarily an integer so far) from 3⁰.¹ⁿ = or < their positive upper value from part (i) or 3⁰.¹ⁿ⁺¹ = or <3 × their positive upper value from part (i)
[A1] Conclude 12

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Algebra, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, May/June 2019 Paper 2 Variant 1, question 2.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content