User interface language: English | Español

Date November 2016 Marks available 2 Reference code 16N.1.sl.TZ0.3
Level SL only Paper 1 Time zone TZ0
Command term Write down Question number 3 Adapted from N/A

Question

The values in the fourth row of Pascal’s triangle are shown in the following table.

N16/5/MATME/SP1/ENG/TZ0/03

Write down the values in the fifth row of Pascal’s triangle.

[2]
a.

Hence or otherwise, find the term in \({x^3}\) in the expansion of \({(2x + 3)^5}\).

[5]
b.

Markscheme

1, 5, 10, 10, 5, 1     A2     N2

[2 marks]

a.

evidence of binomial expansion with binomial coefficient     (M1)

eg\(\,\,\,\,\,\)\(\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){a^{n - r}}{b^r}\), selecting correct term, \({(2x)^5}{(3)^0} + 5{(2x)^4}{(3)^1} + 10{(2x)^3}{(3)^2} +  \ldots \)

correct substitution into correct term     (A1)(A1)(A1)

eg\(\,\,\,\,\,\)\(10{(2)^3}{(3)^2},{\text{ }}\left( {\begin{array}{*{20}{c}} 5 \\ 3 \end{array}} \right){(2x)^3}{(3)^2}\)

 

Note: Award A1 for each factor.

 

\(720{x^3}\)     A1     N2

 

Notes: Do not award any marks if there is clear evidence of adding instead of multiplying.

Do not award final A1 for a final answer of 720, even if \(720{x^3}\) is seen previously.

 

[5 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 1 - Algebra » 1.3 » The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in \mathbb{N}\) .
Show 31 related questions

View options