A curve is such that dy/dx = (2x + 1)². The curve passes through the point (4, 10).

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [B2] [=] (2x+1)³ / (2×3) (+ c) oe or B1 for (2x+1)³/(..) (+c)
2. [M1] 10 = (2(4)+1)³ / 6 + c oe for valid attempt to find c; condone slips e.g. omission of power or sign error
3. [A1] y = (2x+1)³ / 6 + 1 isw must have y = ....; condone f(x) = ..
4. [B1 + B1] ∫((2x+1)³/6 + 1)dx = (2x+1)⁴ / (15) + x (+ const) B1 for (2x+1)⁴ / 15, B1 for + x
5. [B1ft] B1 ft their c from (i) provided c≠0
6. [M1] for a genuine attempt to find F(1.5) – F(0) in an attempt to integrate their y; if their F(0) is 0 must see at least their F(1.5)– 0; condone + c as long as their c is not numerical.
7. [A1] 107/30 oe isw if decimal 3.57 or more accurate e.g. 3.566