5.15 Slope fieldsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.15 Slope fields

1. A slope field is drawn for the differential equation $\frac{dy}{dx}=x-y$.
   A solution curve passes through the point $(0,1)$. Find the equation of the tangent to the solution curve at this point.2 marks
2. A slope field is drawn for the differential equation $\frac{dy}{dx}=\frac{x}{y}$, for $y\neq0$.
   A solution curve passes through the point $(1,2)$. Use the gradient of the slope field at this point to estimate the value of $y$ on this curve when $x=1.2$.2 marks
3. The population $P$, in hundreds, of fish in a lake at time $t$ years is modelled by $\frac{dP}{dt}=0.2P(5-P)$ for $P\ge0$. A slope field is drawn for this differential equation.
   Find the values of $P$ at which the line segments are horizontal, and interpret your answer in context.3 marks