Moderate -0.5 This is a straightforward application of the binomial expansion formula for fractional powers with n=1/3, requiring routine differentiation of the general term and identification of the validity condition |2x|<1. While it involves the generalised binomial theorem (a C4 topic), it's a standard textbook exercise with no problem-solving or novel insight required, making it slightly easier than average.
2 Find the first four terms of the binomial expansion of \(\sqrt [ 3 ] { 1 - 2 x }\). State the set of values of \(x\) for which the expansion is valid.
Correct shape drawn — a connected path of line segments equidistant (in taxicab metric) from A and B
B1
For correct overall shape/region
Correct position on grid
B1+B1
[3] total
# Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| A = (2, 1), B = (4, 4) identified from grid | | |
| Locus is the taxicab perpendicular bisector of AB | | |
| Correct shape drawn — a connected path of line segments equidistant (in taxicab metric) from A and B | B1 | For correct overall shape/region |
| Correct position on grid | B1+B1 | [3] total |
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2 Find the first four terms of the binomial expansion of $\sqrt [ 3 ] { 1 - 2 x }$. State the set of values of $x$ for which the expansion is valid.
\hfill \mbox{\textit{OCR MEI C4 2013 Q2 [6]}}