O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2019 · Q25 Marks

When lgy² is plotted against x, a straight line is obtained passing through the points (5, 12) and (3, 20). Find y in terms of x, giving your answer in the form y = 10ax+b, where a and b are integers.

When lgy² is plotted against x, a straight line is obtained passing through the points (5, 12) and (3, 20). Find y in terms of x, giving your answer in the form y = 10ax+b, where a and b are integers.[5]

Mark scheme

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

[1] B1 lg y² = mx + c
[1] B1 Gradient = -4 (=m) May be implied by subsequent work
[1] B1 c = 32
[1] M1 Dep on first B1 Use of lg y² = 2lg y and 10^(their (c/2 + mx/2)) Or use of y² = 10^(their c + their mx) and 10^(their (c/2 + mx/2))
[1] A1 y = 10^(16-2x)

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 2.

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