| Date | November 2015 | Marks available | 3 | Reference code | 15N.1.hl.TZ0.3 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find and Hence | Question number | 3 | Adapted from | N/A |
Question
Write down and simplify the expansion of \({(2 + x)^4}\) in ascending powers of \(x\).
[3]
a.
Hence find the exact value of \({(2.1)^4}\).
[3]
b.
Markscheme
\({(2 + x)^4} = {2^4} + 4 \bullet {2^3}x + 6 \bullet {2^2}{x^2} + 4 \bullet 2{x^3} + {x^4}\) M1(A1)
Note: Award M1 for an expansion, by whatever method, giving five terms in any order.
\( = 16 + 32x + 24{x^2} + 8{x^3} + {x^4}\) A1
Note: Award M1A1A0 for correct expansion not given in ascending powers of \(x\).
[3 marks]
a.
let \(x = 0.1\) (in the binomial expansion) (M1)
\({2.1^4} = 16 + 3.2 + 0.24 + 0.008 + 0.0001\) (A1)
\( = 19.4481\) A1
Note: At most one of the marks can be implied.
[3 marks]
Total [6 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 1 - Core: Algebra » 1.3 » The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in N\) .
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