Easy -1.8 This is a straightforward algebraic manipulation requiring only two steps: multiply both sides by 5/3, then take the square root. It tests basic rearrangement skills with no problem-solving element, making it significantly easier than average A-level content.
M2 for \([b^2 =] \frac{3a}{2c}\) soi or M1 for other \([b^2 =] \frac{ka}{c}\) or \([b^2 =] \frac{a}{kc}\) oe; allow M1 for a triple-decker or quadruple-decker fraction or decimals eg \(\frac{1.5a}{c}\), if no recovery later; and M1 for correctly taking the square root of their \(b^2\), including the \(±\) sign
[3]
Question 3(i):
Answer
Marks
Guidance
25
2
M1 for \(\frac{1}{25}\) or \(\left(\frac{1}{25}\right)\) or \(5^2\) or \(\frac{25}{1}\)
[2]
Question 3(ii):
Answer
Marks
Guidance
\(\frac{4}{9}\)
2
M1 for 4 or 9 or \(\frac{1}{9}\) or \(\frac{2}{3}\) or \(\left(\frac{2}{3}\right)^2\) or \(\sqrt{\frac{64}{729}}\) seen
[2]
$[b =]± \sqrt{\frac{3a}{2c}}$ oe www | 3 | M2 for $[b^2 =] \frac{3a}{2c}$ soi or M1 for other $[b^2 =] \frac{ka}{c}$ or $[b^2 =] \frac{a}{kc}$ oe; allow M1 for a triple-decker or quadruple-decker fraction or decimals eg $\frac{1.5a}{c}$, if no recovery later; and M1 for correctly taking the square root of their $b^2$, including the $±$ sign | square root must extend below the fraction line
| [3] |
# Question 3(i):
25 | 2 | M1 for $\frac{1}{25}$ or $\left(\frac{1}{25}\right)$ or $5^2$ or $\frac{25}{1}$
| [2] |
# Question 3(ii):
$\frac{4}{9}$ | 2 | M1 for 4 or 9 or $\frac{1}{9}$ or $\frac{2}{3}$ or $\left(\frac{2}{3}\right)^2$ or $\sqrt{\frac{64}{729}}$ seen | 0 for just $\left(\frac{64}{729}\right)^{1}$
| [2] |