| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | September |
| Marks | 6 |
| Topic | Modulus function |
| Type | Interpret or complete given sketch of two |linear| functions |
| Difficulty | Moderate -0.3 This is a straightforward modulus equation requiring students to consider cases where expressions inside are positive/negative. Part (i) involves simple substitution to find intercepts (routine). Part (ii) requires squaring both sides or case analysis, both standard techniques for AS-level. Slightly easier than average due to being a direct application of a well-practiced method with linear expressions only. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | \((\frac{2}{3}, 0), (0, 2), (-\frac{1}{2}, 0)\) and \((0, 1)\) all indicated | M1 |
| (i) | M1 | |
| (i) | A1 |
Total: [3]
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | \(2x + 1 = 3x - 2\), so \(x = 3\) | B1 |
| (ii) | \(2x + 1 = -3x + 2\) | M1 |
| (ii) | \(x = \frac{1}{5}\) | A1 |
Total: [3]
(i) | $(\frac{2}{3}, 0), (0, 2), (-\frac{1}{2}, 0)$ and $(0, 1)$ all indicated | M1 | one of $(\frac{2}{3}, 0)$ or $(-\frac{1}{2}, 0)$
(i) | | M1 | one of $(0, 2)$ or $(0, 1)$
(i) | | A1 | All four
Total: [3]
(ii) | $2x + 1 = 3x - 2$, so $x = 3$ | B1 | Obtain $x = 3$ www
(ii) | $2x + 1 = -3x + 2$ | M1 | Attempt to solve equation, with $2x$ and $3x$ of opposite signs
(ii) | $x = \frac{1}{5}$ | A1 | Obtain $x = \frac{1}{5}$ www
Total: [3]3 (i) The diagram below shows the graphs of $y = | 3 x - 2 |$ and $y = | 2 x + 1 |$.\\
\includegraphics[max width=\textwidth, alt={}, center]{e3942549-bfc0-432a-bf49-7d01d44af01a-4_423_682_1110_694}
On the diagram in your Printed Answer Booklet, give the coordinates of the points of intersection of the graphs with the coordinate axes.\\
(ii) Solve the equation $| 2 x + 1 | = | 3 x - 2 |$.
\hfill \mbox{\textit{OCR H240/01 2018 Q3 [6]}}