Moderate -0.8 This is a straightforward application of the binomial expansion formula requiring factoring out 9, applying the standard binomial coefficients for n=1/2, and simplifying. It's routine practice with no problem-solving element, though slightly more involved than basic index law recall due to the algebraic manipulation required.
Obtain a correct unsimplified version of the x or x2 term of the expansion of
1
(9−3x) 1 2 or 1− 1 x 2
Answer
Marks
Guidance
3
M1
1 1 11 1
E.g. − x or − 2 2 x2or
2 3 2 9
1 −1 1−1 −3
92 (−3x)1 or 2 2 92 (−3x)2 .
2 2
Not for symbolic coefficients in the form n C .
r
Answer
Marks
State correct first term 3
B1
1 1
Obtain the next two terms − x− x2
Answer
Marks
Guidance
2 24
A1 A1
A1 for each term correct.
Do not ISW.
1 1
1− x− x2
SC M1A1 for seen on its own or
6 72
as a factor.
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | Obtain a correct unsimplified version of the x or x2 term of the expansion of
1
(9−3x) 1 2 or 1− 1 x 2
3 | M1 | 1 1 11 1
E.g. − x or − 2 2 x2or
2 3 2 9
1 −1 1−1 −3
92 (−3x)1 or 2 2 92 (−3x)2 .
2 2
Not for symbolic coefficients in the form n C .
r
State correct first term 3 | B1
1 1
Obtain the next two terms − x− x2
2 24 | A1 A1 | A1 for each term correct.
Do not ISW.
1 1
1− x− x2
SC M1A1 for seen on its own or
6 72
as a factor.
4
Question | Answer | Marks | Guidance
Expand $(9 - 3x)^{\frac{1}{2}}$ in ascending powers of $x$, up to and including the term in $x^2$, simplifying the coefficients. [4]
\hfill \mbox{\textit{CAIE P3 2024 Q1 [4]}}