Edexcel IAL P4 The Binomial Expansion Questions
Expanding (a + bx)ⁿ for any rational n; validity |bx/a| < 1; using partial fractions with expansions.
- P4 · Pure Mathematics 4
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P4 the binomial expansion practice questions cover:
Worked example 1
The binomial expansion of $(a+bx)^{-2}$, where $a > 0$, begins $\frac{1}{9} - \frac{2}{27}x + \dots$. Find the values of the constants $a$ and $b$.
Mark scheme
- M1 for writing $(a+bx)^{-2} = a^{-2}(1 + \frac{b}{a}x)^{-2}$.
- M1 for equating the constant term: $a^{-2} = \frac{1}{9}$.
- A1 for finding $a = 3$ (since $a > 0$).
- M1 for equating the $x$ coefficient: $a^{-2}(-2)(\frac{b}{a}) = -\frac{2}{27}$.
- A1 for substituting $a=3$ to get $\frac{1}{9}(\frac{-2b}{3}) = -\frac{2}{27} \implies -\frac{2b}{27} = -\frac{2}{27} \implies b = 1$.
Worked example 2
Expand $(2-x)^{-2}$ up to the term in $x^2$. Use your expansion to find an approximate value for $\frac{1}{1.98^2}$.
Mark scheme
- M1 for rewriting as $2^{-2}(1 - \frac{x}{2})^{-2} = \frac{1}{4}(1 - \frac{x}{2})^{-2}$.
- M1 for expanding correctly: $\frac{1}{4}(1 + 2(\frac{x}{2}) + 3(\frac{x}{2})^2) = \frac{1}{4} + \frac{1}{4}x + \frac{3}{16}x^2$.
- M1 for deducing the appropriate value of $x$ to substitute is $x = 0.02$.
- M1 for substituting $x = 0.02$ into the expansion: $\frac{1}{4} + \frac{1}{4}(0.02) + \frac{3}{16}(0.0004)$.
- A1 for arriving at the correct approximation: $0.25 + 0.005 + 0.000075 = 0.255075$.
FAQ
What the binomial expansion is in Edexcel IAL P4?
Expanding (a + bx)ⁿ for any rational n; validity |bx/a| < 1; using partial fractions with expansions.
Is P4 a calculator paper?
Yes, a calculator is allowed in P4, but method marks are only given for working you write down.
How are P4 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.