| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2019 |
| 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 to check), which is routine A-level work. Part (ii) adds a straightforward substitution (let x = 2^y) and then solving for y using logarithms. While multi-step, both techniques are standard P2 content with no novel insight required, making this slightly easier than average overall. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| State or imply non-modular equation \((4x+5)^2=(x-7)^2\) or pair of different linear equations | B1 | |
| Attempt solution of 3-term quadratic equation or pair of linear equations | M1 | |
| Obtain \(\frac{2}{5}\) and \(-4\) | A1 | SC For \(x=-4\) only, from correct work, allow B1 |
| Total | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Apply logarithms and use power law for \(2^y=k\) where \(k>0\) from (i) | M1 | |
| Obtain \(-1.32\) only | A1 | AWRT |
| Total | 2 |
**Question 2(i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply non-modular equation $(4x+5)^2=(x-7)^2$ or pair of different linear equations | B1 | |
| Attempt solution of 3-term quadratic equation or pair of linear equations | M1 | |
| Obtain $\frac{2}{5}$ and $-4$ | A1 | SC For $x=-4$ only, from correct work, allow B1 |
| **Total** | **3** | |
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**Question 2(ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Apply logarithms and use power law for $2^y=k$ where $k>0$ from (i) | M1 | |
| Obtain $-1.32$ only | A1 | AWRT |
| **Total** | **2** | |
---2 (i) Solve the equation $| 4 x + 5 | = | x - 7 |$.\\
(ii) Hence, using logarithms, solve the equation $\left| 2 ^ { y + 2 } + 5 \right| = \left| 2 ^ { y } - 7 \right|$, giving the answer correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2019 Q2 [5]}}