The equation of a curve is such that dy/dx = 3x^(1/2) – 3x^(-1/2). The curve passes through the point (3, 5).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. B1 B1 Marks can be awarded for correct unsimplified expressions, 1 mark each for contents of { } ISW. [y =] [3x^(3/2) / (3/2)] - [3x^(1/2) / (1/2)] [+c] = 2x^(3/2) - 6x^(1/2)
2. M1 Correct use of (3,5) in an integrated expression (defined by at least one correct power) including + c. 5 = 2(3)^(3/2) - 6(3)^(1/2) + c
3. A1 Condone c = 5 as their final line if either y = or f(x) = seen elsewhere in the solution, but coefficients must not contain unresolved double fractions. y = 2x^(3/2) - 6x^(1/2) + 5
4. M1 Setting given differential to 0. 3x^(1/2) - 3x^(-1/2) = 0
5. A1 CAO WWW Condone extra solution of -1 only if it is rejected. [x=] 1
6. B1FT Allow >. x > 1 or x > "their 8(b)"