A-LevelMathematicsDifferential equations9709/31 · May/June 2017 · Q99 Marks
Express 1 / (x(2x + 3)) in partial fractions.
- (i)Express 1 / (x(2x + 3)) in partial fractions.[2]
- (ii)The variables x and y satisfy the differential equation x(2x + 3) dy/dx = y, and it is given that y = 1 when x = 1. Solve the differential equation and calculate the value of y when x = 9, giving your answer correct to 3 significant figures.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- Carry out a relevant method to obtain A and B such that 1/(x(2x+3)) = A/x + B/(2x+3) or equivalent M1
- Obtain A = ⅓ and B = -⅔, or equivalent A1
- Separate variables and integrate one side B1
- Obtain term ln y B1
- Integrate and obtain terms ⅓ ln x - ⅔ ln(2x+3), or equivalent B2 FT
- Use x = 1 and y = 1 to evaluate a constant, or as limits, in a solution containing a ln y, b ln x, c ln(2x+3) M1
- Obtain correct solution in any form, e.g. ln y = ⅓ ln x - ⅔ ln(2x+3) + ⅓ ln 5 A1
- Obtain answer y = 1.29 (3s.f. only) A1
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