Edexcel IAL P1 Integration Questions
Indefinite integration of xⁿ (n ≠ −1) and sums of such terms; finding the constant of integration from a point on the curve.
- P1 · Pure Mathematics 1
- Non-calculator
- 32 practice questions
What the questions test
The 32 P1 integration practice questions cover:
Worked example 1
Given that $f''(x) = 12x - 4$, $f'(1) = 2$ and $f(-1) = 5$, find $f(x)$.
Mark scheme
- M1 for integrating $f''(x)$ to find $f'(x) = 6x^2 - 4x + c_1$.
- M1 for substituting $f'(1) = 2$ to find $c_1$: $2 = 6(1)^2 - 4(1) + c_1 \implies c_1 = 0$.
- M1 for substituting $c_1 = 0$ and integrating again to find $f(x) = 2x^3 - 2x^2 + c_2$.
- M1 for substituting $f(-1) = 5$: $5 = 2(-1)^3 - 2(-1)^2 + c_2$.
- M1 for solving for $c_2$: $5 = -2 - 2 + c_2 \implies c_2 = 9$.
- A1 for the final correct function $f(x) = 2x^3 - 2x^2 + 9$.
Worked example 2
The gradient of a curve is given by $\frac{dy}{dx} = 4\sqrt{x} - 1$. The curve passes through the point $(9, 20)$. Find the equation of the curve.
Mark scheme
- M1 for rewriting as $4x^{\frac{1}{2}} - 1$ and integrating: $y = \frac{4x^{\frac{3}{2}}}{\frac{3}{2}} - x + c$.
- A1 for simplifying the integral to $y = \frac{8}{3}x^{\frac{3}{2}} - x + c$.
- M1 for substituting the point $(9, 20)$: $20 = \frac{8}{3}(9)^{\frac{3}{2}} - 9 + c$.
- M1 for evaluating $9^{\frac{3}{2}} = 27$ to solve for $c$: $20 = 72 - 9 + c \implies c = -43$.
- A1 for the final equation $y = \frac{8}{3}x^{\frac{3}{2}} - x - 43$.
FAQ
What integration is in Edexcel IAL P1?
Indefinite integration of xⁿ (n ≠ −1) and sums of such terms; finding the constant of integration from a point on the curve.
Is P1 a calculator paper?
No. P1 is non-calculator, so every integration question has to be done by hand, with exact values where the question asks for them.
How are P1 integration questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.