O-LevelAdditional MathematicsSimultaneous equations4037/22 · Oct/Nov 2020 · Q46 Marks

Solve the simultaneous equations. log3 (x+y) = 2 2log3 (x + 1) = log3 (y+2)

Mark scheme

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

[B1] x+y=9
[B1] (x + 1)² = y + 2
[M1] x + (x + 1)² - 2 = 9 Replace y or x. Allow unsimplified using their three term expressions both containing x and y terms. Condone one sign or arithmetic error. Result must be a quadratic function. or (10 - y)² = y + 2
[A1] x² + 3x – 10 (= 0) Correct 3 term quadratic or y² – 21y + 98 (= 0)
[M1] x = -5 and x = 2 Dep on correct method to solve their quadratic or y = 7 and y = 14 or (x + 5)(x - 2) or (y – 7)(y – 14)
[A1] x = 2 and y = 7 only Reject x = −5, y = 14 as log -4 is not appropriate

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Topic: Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2020 Paper 2 Variant 2, question 4.

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