| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2018 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve modulus equation then apply exponential/log substitution |
| Difficulty | Standard +0.3 Part (i) is a standard modulus equation requiring case analysis (4 cases) but straightforward algebra. Part (ii) adds an exponential substitution (let x = 3^y) and logarithm application, making it slightly above average difficulty, but the 'hence' structure guides students through the method with no novel insight required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| State or imply non-modular equation \((9x-2)^2 = (3x+2)^2\) or pair of linear equations | B1 | |
| Attempt solution of quadratic equation or of 2 linear equations | M1 | |
| Obtain \(0\) and \(\frac{2}{3}\) | A1 | SC: B1 for one correct solution |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Apply logarithms and use power law for \(3^y = k\) where \(k > 0\) | M1 | Must be using their answers to part (i) |
| Obtain \(-0.369\) | A1 | |
| Total: 2 |
## Question 1(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply non-modular equation $(9x-2)^2 = (3x+2)^2$ or pair of linear equations | B1 | |
| Attempt solution of quadratic equation or of 2 linear equations | M1 | |
| Obtain $0$ and $\frac{2}{3}$ | A1 | SC: B1 for one correct solution |
| **Total: 3** | | |
## Question 1(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Apply logarithms and use power law for $3^y = k$ where $k > 0$ | M1 | Must be using their answers to part (i) |
| Obtain $-0.369$ | A1 | |
| **Total: 2** | | |
---1 (i) Solve the equation $| 9 x - 2 | = | 3 x + 2 |$.\\
(ii) Hence, using logarithms, solve the equation $\left| 3 ^ { y + 2 } - 2 \right| = \left| 3 ^ { y + 1 } + 2 \right|$, giving your answer correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2018 Q1 [5]}}