Easy -1.8 This is a straightforward application of the distance formula requiring only substitution, simplification of √45 to 3√5, and basic arithmetic. It's significantly easier than average as it's purely procedural with no problem-solving element—students simply execute a memorized formula and simplify a single surd.
5 Show that the distance between the points \(( 5,2 )\) and \(( 11 , - 1 )\) is \(a \sqrt { b }\), where \(a\) and \(b\) are integers to be determined.
\(\sqrt{(11-5)^2+(-1-2)^2}\) o.e. OR \(\sqrt{(5-11)^2+(2-(-1))^2}\)
M1
allow one sign error
\(\sqrt{45}\)
A1
\(3\sqrt{5}\)
A1
Condone \(\sqrt{45}\) for A1A1 and \(\sqrt{45}\) or \(3\sqrt{5}\) only implies full marks
# Question 5:
$\sqrt{(11-5)^2+(-1-2)^2}$ o.e. OR $\sqrt{(5-11)^2+(2-(-1))^2}$ | M1 | allow one sign error
$\sqrt{45}$ | A1 |
$3\sqrt{5}$ | A1 | Condone $\sqrt{45}$ for A1A1 and $\sqrt{45}$ or $3\sqrt{5}$ only implies full marks
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5 Show that the distance between the points $( 5,2 )$ and $( 11 , - 1 )$ is $a \sqrt { b }$, where $a$ and $b$ are integers to be determined.
\hfill \mbox{\textit{OCR MEI AS Paper 2 2023 Q5 [3]}}