| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Topic | Completing the square and sketching |
| Type | Complete square then find vertex/turning point |
| Difficulty | Easy -1.2 This is a straightforward completing the square exercise with simple coefficients, followed by direct reading of the minimum from the completed square form. Both parts require only routine algebraic manipulation and basic understanding of quadratic properties, making it easier than a typical A-level question which would involve more steps or application. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
**(i)** Method to compare coefficients or complete the square — M1
Obtain $a = 4$ — A1
Obtain $b = -6$ — A1 **[3]**
**(ii)** State minimum $= -6$ or $y = -6$ — B1
State $x = 4$ — B1 **[2]**
SR Accept $(4, -6)$
SR If differentiation is used to find $x = 4$ award B11 (i) Express $x ^ { 2 } - 8 x + 10$ in the form $( x - a ) ^ { 2 } + b$ where $a$ and $b$ are integers to be found.\\
(ii) Hence write down the minimum value of $x ^ { 2 } - 8 x + 10$ and the corresponding value of $x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2014 Q1 [5]}}