Edexcel IAL P3 Algebraic Methods Questions
Simplifying rational expressions (factorising, cancelling, algebraic division).
- P3 · Pure Mathematics 3
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P3 algebraic methods practice questions cover:
Worked example 1
Express $\frac{x+2}{x^2 - 5x + 6} - \frac{x-1}{x^2 - 4x + 3}$ as a single fraction in its simplest form.
Mark scheme
- M1 for factorising $x^2-5x+6$ to $(x-2)(x-3)$.
- M1 for factorising $x^2-4x+3$ to $(x-1)(x-3)$.
- M1 for simplifying the second fraction: $\frac{x-1}{(x-1)(x-3)}$ cancels to $\frac{1}{x-3}$.
- M1 for creating a common denominator $(x-2)(x-3)$ and subtracting: $\frac{x+2}{(x-2)(x-3)} - \frac{x-2}{(x-2)(x-3)}$.
- A1 for reaching the final simplified answer $\frac{4}{(x-2)(x-3)}$.
Worked example 2
Show that $\frac{4x}{x^2 - 9} - \frac{2}{x-3}$ can be simplified to the form $\frac{a}{x+b}$, where $a$ and $b$ are integers.
Mark scheme
- M1 for factorising the denominator $x^2 - 9 = (x-3)(x+3)$.
- M1 for finding the common denominator and forming the numerator: $4x - 2(x+3)$.
- M1 for expanding the numerator to $4x - 2x - 6 = 2x - 6$ and factorising it to $2(x-3)$.
- A1 for cancelling $(x-3)$ to achieve $\frac{2}{x+3}$, meaning $a=2$ and $b=3$.
FAQ
What algebraic methods is in Edexcel IAL P3?
Simplifying rational expressions (factorising, cancelling, algebraic division).
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 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.