A-LevelMathematicsIntegration9709/12 · Oct/Nov 2019 · Q34 Marks
A curve is such that dy/dx = k/√x, where k is a constant. The points P (1, -1) and Q (4, 4) lie on the curve. Find the equation of the curve.
- A curve is such that dy/dx = k/√x, where k is a constant. The points P (1, -1) and Q (4, 4) lie on the curve. Find the equation of the curve.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] (y =) kx^(1/2) / (1/2) (+c) = 2k√x (+c) OE
- [M1] Substitutes both points into an integrated expression with a '+c' and solve as far as a value for one variable. Expect to see -1 = 2k + c and 4 = 4k + c
- [A1] k = 2½ and c = -6 WWW
- [A1] y = 5√x - 6 OE From correct values of both k & c and correct integral.
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