| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Easy -1.2 This is a straightforward completing the square exercise followed by a routine sketch. Both parts require only standard techniques taught early in A-level: completing the square is mechanical algebra, and sketching requires finding roots (by factoring or formula) and the vertex (already given by part (i)). No problem-solving or insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
(i) $x^2 + 2x - 3 = (x+1)^2 - 4$, ($a = 1$, $b = -4$) — B1, B1 **[2]**
(ii) u-shaped parabola — B1; Vertex at $(-1, -4)$ — B1 ft; Let $x = 0$ and solve — M1; Intersecting: $x$-axis at $-3$ and $1$ — A1; $y$-axis at $-3$ — B1 **[5]**
**Total: [7]**3 (i) Express $x ^ { 2 } + 2 x - 3$ in the form $( x + a ) ^ { 2 } + b$, where $a$ and $b$ are integers to be found.\\
(ii) Sketch the graph of $y = x ^ { 2 } + 2 x - 3$ giving the coordinates of the vertex and of any intersections with the coordinate axes.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q3 [7]}}