Moderate -0.8 This is a straightforward integration question requiring only the power rule for √x and a constant term, followed by substituting a point to find C. It's slightly easier than average as it involves standard techniques with no complications, though the algebraic manipulation of √x = x^(1/2) and subsequent integration is a basic skill expected at this level.
The gradient of a curve is given by \(\frac{dy}{dx} = 6\sqrt{x} - 2\). Given also that the curve passes through the point \((9, 4)\), find the equation of the curve. [5]
“y =” need not be stated at this point, but must be seen
at some point for full marks
must see “+ c”
Question 5:
5 | dy 1
=6x2 −2
dx
3
y =kx2 −2x+c o.e.
3
y =4x2 −2x+c o.e.
correct substitution of x = 9 and y = 4
in their equation of curve
3
y =4x2 −2x−86 | M2
A1
M1
dep
A1 | 3
M1 for kx2 and M1 for -2x + c
dependent on at least M1 already
awarded
allow A1 for c = −86 i.s.w. if simplified
equation for y seen earlier | 1
x6 is a mistake, not a misread
“y =” need not be stated at this point, but must be seen
at some point for full marks
must see “+ c”
The gradient of a curve is given by $\frac{dy}{dx} = 6\sqrt{x} - 2$. Given also that the curve passes through the point $(9, 4)$, find the equation of the curve. [5]
\hfill \mbox{\textit{OCR MEI C2 Q5 [5]}}