Easy -1.2 This is a straightforward algebraic manipulation requiring finding a common denominator and combining fractions. It's simpler than typical partial fractions work (which involves decomposition) and requires only routine algebraic skills with no problem-solving insight needed.
Condone one sign error; if M0B0, SC1 for any pair of terms correctly combined into a single fraction, may be unsimplified
\(1-x^2\) oe
B1
Any correct denominator common to all three fractions
\(\frac{3-x^3}{1-x^2}\) oe cao
A1
Must be fully simplified; mark the final answer; eg \(\frac{x(3-x^3)}{x(1-x^2)}\) oe may score a maximum of M1B1A0
[3]
# Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x(1-x^2)+(1+x)+2(1-x)$ oe | M1 | Condone one sign error; if M0B0, SC1 for any pair of terms correctly combined into a single fraction, may be unsimplified |
| $1-x^2$ oe | B1 | Any correct denominator common to all three fractions |
| $\frac{3-x^3}{1-x^2}$ oe cao | A1 | Must be fully simplified; mark the final answer; eg $\frac{x(3-x^3)}{x(1-x^2)}$ oe may score a maximum of M1B1A0 |
| **[3]** | | |