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O-LevelAdditional MathematicsSimultaneous equations4037/22 · Oct/Nov 2017 · Q45 Marks

Solve the simultaneous equations log2(x + 4) = 2log2y, log2 (7y - x) = 4.

  1. Solve the simultaneous equations log2(x + 4) = 2log2y, log2 (7y - x) = 4.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] x + 4 = y²
  2. [B1] 7y-x=16; allow 2^4 for 16
  3. [M1] y² -7y+12 → (y-3)(y−4)(= 0) or x² -17x+60→(x-5)(x-12)(= 0); Attempt to eliminate x or y to obtain a three term quadratic.
  4. [M1] Solve a three term quadratic; M1dep
  5. [A1] → y = 3, x = 5 or y = 4 x=12; Allow for values seen even if correct pairs not clear.

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2017 Paper 2 Variant 2, question 4.

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