Edexcel IAL P2 The Binomial Expansion Questions
Binomial expansion of (a + bx)ⁿ for positive integer n; ⁿCr notation; using expansions for approximations.
- P2 · Pure Mathematics 2
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P2 the binomial expansion practice questions cover:
Worked example 1
The binomial expansion of $(1+ax)^b$, where $b$ is a positive integer, starts with $1 - 15x + 90x^2$. Find the values of $a$ and $b$.
Mark scheme
- M1 for equating the $x$ coefficient: $ab = -15$.
- M1 for equating the $x^2$ coefficient: $\frac{b(b-1)}{2} a^2 = 90 \implies b(b-1)a^2 = 180$.
- M1 for substituting $(ab) = -15$ or expanding to $a^2b^2 - a^2b = 180$ and substituting $a^2b^2 = 225$.
- M1 for solving for $a$: $225 - a(-15) = 180 \implies 15a = -45 \implies a = -3$.
- A1 for finding the corresponding value $b = 5$.
Worked example 2
The first three terms of the expansion $(a+bx)^6$ are $64 - 192x + cx^2$. Find the values of the constants $a$, $b$, and $c$.
Mark scheme
- M1 for equating the first term: $a^6 = 64 \implies a=2$.
- M1 for equating the $x$ coefficient to find $b$: $\binom{6}{1}a^5 b = -192 \implies 6(32)b = -192 \implies 192b = -192$.
- A1 for obtaining $b = -1$.
- A1 for finding the $x^2$ coefficient: $c = \binom{6}{2}a^4 b^2 = 15(16)(-1)^2 = 240$.
FAQ
What the binomial expansion is in Edexcel IAL P2?
Binomial expansion of (a + bx)ⁿ for positive integer n; ⁿCr notation; using expansions for approximations.
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 the binomial expansion 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.