OCR MEI C1 — Question 1 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem with a small positive integer power (n=4), requiring only systematic expansion and simplification of terms. It's easier than average as it involves routine algebraic manipulation with no problem-solving or conceptual challenges beyond direct formula application.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

1 Find and simplify the binomial expansion of \(( 3 x - 2 ) ^ { 4 }\).

Question 1:
\(81x^4 - 216x^3 + 216x^2 - 96x + 16\) [4]
M3 for 4 terms correct
or for all coefficients correct except for sign errors
or for correct answer seen then further 'simplified'
or for all terms correct eg seen in table but not combined
M2 for 3 terms correct
or for correct expansion seen without correct evaluation of coefficients [if brackets missing in elements such as \((3x)^2\) there must be evidence from calculation that \(9x^2\) has been used]
M1 for 1 4 6 4 1 row of Pascal's triangle seen
Guidance:
Condone eg \(+(−96x)\) or \(+96x\) instead of \(−96x\)
Any who multiply out instead of using binomial coefficients: look at their final answer and mark as per main scheme if 3 or more terms are correct, otherwise M0
Binomial coefficients such as \(\binom{4}{2}\) are not sufficient – must show understanding of these symbols by at least partial evaluation
Question 1:

$81x^4 - 216x^3 + 216x^2 - 96x + 16$ [4]

M3 for 4 terms correct
or for all coefficients correct except for sign errors
or for correct answer seen then further 'simplified'
or for all terms correct eg seen in table but not combined

M2 for 3 terms correct
or for correct expansion seen without correct evaluation of coefficients [if brackets missing in elements such as $(3x)^2$ there must be evidence from calculation that $9x^2$ has been used]

M1 for 1 4 6 4 1 row of Pascal's triangle seen

Guidance:
Condone eg $+(−96x)$ or $+96x$ instead of $−96x$

Any who multiply out instead of using binomial coefficients: look at their final answer and mark as per main scheme if 3 or more terms are correct, otherwise M0

Binomial coefficients such as $\binom{4}{2}$ are not sufficient – must show understanding of these symbols by at least partial evaluation
1 Find and simplify the binomial expansion of $( 3 x - 2 ) ^ { 4 }$.

\hfill \mbox{\textit{OCR MEI C1  Q1 [4]}}