Moderate -0.5 This is a straightforward algebraic manipulation requiring expansion of squared terms and simplification. While it involves multiple terms and careful bookkeeping, it's purely mechanical with no conceptual insight or problem-solving required—students simply expand, collect like terms, and verify the equivalence. Easier than average due to its routine nature.
16 Show that the expression \(a \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) ^ { 2 } + b \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) + c - a \left( \frac { x _ { P } - x _ { Q } } { 2 } \right) ^ { 2 }\) is equivalent to \(a x _ { P } x _ { Q } + b \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) + c\), as given in lines 15 and 16 .
Terms may be moved together or worked with in original positions
Correctly manipulate the factor \(a\) terms (e.g. squaring brackets or difference of two squares)
A1
Must be convincing; give A0 for any error seen in working
## Question 16:
| Working/Answer | Marks | Guidance |
|---|---|---|
| Work with the two terms with factor $a$ | M1 | Terms may be moved together or worked with in original positions |
| Correctly manipulate the factor $a$ terms (e.g. squaring brackets or difference of two squares) | A1 | Must be convincing; give A0 for any error seen in working |
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16 Show that the expression $a \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) ^ { 2 } + b \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) + c - a \left( \frac { x _ { P } - x _ { Q } } { 2 } \right) ^ { 2 }$ is equivalent to $a x _ { P } x _ { Q } + b \left( \frac { x _ { P } + x _ { Q } } { 2 } \right) + c$, as given in lines 15 and 16 .
\hfill \mbox{\textit{OCR MEI Paper 3 2024 Q16 [2]}}