# Question 11:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\wedge$ shape in any position | B1 | 1.1b |
| Correct $x$-intercepts: $(k,0)$ and $(2k,0)$ | B1 | 1.1b — Allow coordinates written as $(0,k)$ and $(0,2k)$ if in correct places |
| Correct $y$-intercept: $(0,-2k)$ or $(-2k,0)$ | B1 | 1.1b — Condone $k-3k$ for $-2k$ |
| Correct vertex coordinates: $(1.5k, k)$ | B1 | 1.1b |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = k$ | B1 | 2.2a — Deduces correct critical value; may be implied by $x>k$ or $x<k$ |
| $k-(2x-3k) = x-k \Rightarrow x = \ldots$ | M1 | 3.1a — Attempts to solve $k-(2x-3k)=x-k$ or equivalent; allow for reaching $k=\ldots$ or $x=\ldots$ |
| $x = \frac{5k}{3}$ | A1 | 1.1b — Correct value |
| $\left\{x: x < \frac{5k}{3}\right\} \cap \{x: x > k\}$ | A1 | 2.5 — Correct set notation required; allow $\|$ for $:$ |

**Note:** $\left\{x: x<\frac{5k}{3}\right\}\cup\{x:x>k\}$ scores A0; $\left\{x: k<x,\ x<\frac{5k}{3}\right\}$ scores A0

## Part (c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $x = 3k$ **or** $y = 3-5k$ | B1ft | 2.2a — Follow through from their maximum coordinates from (a); must be in terms of $k$ |
| $x = 3k$ **and** $y = 3-5k$ | B1ft | 2.2a — Both correct coordinates; allow as coordinates $x=\ldots, y=\ldots$ |

**Note:** If coordinates given wrong way round and not seen correctly as $x=\ldots, y=\ldots$, e.g. $(3-5k,\ 3k)$ scores B0B0