Edexcel IAL P2 Algebraic Methods Questions
Algebraic long division; factor and remainder theorems; proof by deduction, exhaustion and counter-example.
- P2 · Pure Mathematics 2
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P2 algebraic methods practice questions cover:
Worked example 1
Let $f(x) = x^3 + cx^2 + dx - 4$. Given $f(x)$ has a factor $(x+2)$ and leaves a remainder of $-10$ when divided by $(x-3)$, find the values of $c$ and $d$.
Mark scheme
- M1 for applying the Factor Theorem for $(x+2)$: $f(-2) = 0 \implies -8 + 4c - 2d - 4 = 0 \implies 4c - 2d = 12$.
- M1 for applying the Remainder Theorem for $(x-3)$: $f(3) = -10 \implies 27 + 9c + 3d - 4 = -10 \implies 9c + 3d = -33$.
- M1 for simplifying both equations (e.g., $2c - d = 6$ and $3c + d = -11$).
- M1 for solving the simultaneous equations (e.g., adding them gives $5c = -5$).
- A1 for finding the correct values $c = -1$ and $d = -8$.
Worked example 2
When $f(x) = 2x^3 + px^2 + qx + 1$ is divided by $(2x-1)$ the remainder is 2. When $f(x)$ is divided by $(x+1)$ the remainder is -4. Find the values of $p$ and $q$.
Mark scheme
- M1 for applying the Remainder Theorem with $x = 0.5$: $f(0.5) = 2 \implies 2(\frac{1}{8}) + \frac{p}{4} + \frac{q}{2} + 1 = 2$.
- M1 for simplifying the first equation: $\frac{1}{4} + \frac{p}{4} + \frac{2q}{4} = 1 \implies p + 2q = 3$.
- M1 for applying the Remainder Theorem with $x = -1$: $f(-1) = -4 \implies -2 + p - q + 1 = -4 \implies p - q = -3$.
- M1 for solving the simultaneous equations (e.g., subtracting them gives $3q = 6$).
- A1 for stating $q = 2$ and $p = -1$.
FAQ
What algebraic methods is in Edexcel IAL P2?
Algebraic long division; factor and remainder theorems; proof by deduction, exhaustion and counter-example.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 algebraic methods 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.