| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| 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 (a) is a standard modulus equation requiring case analysis (4 cases or critical point method), which is routine A-level work. Part (b) adds a straightforward exponential substitution (x = 2^(-y)) followed by taking logarithms—mechanical application of techniques with no novel insight required. Slightly above average due to the two-part structure and substitution step, but still well within standard textbook territory. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| State or imply non-modulus equation \((2x-5)^2 = (x+6)^2\) or pair of linear equations | B1 | |
| Attempt solution of 3-term quadratic equation or of pair of linear equations | M1 | |
| Obtain \(-\frac{1}{3}\) and \(11\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Apply logarithms and use power law for \(2^{-x} = k\) where \(k > 0\) from (a) | M1 | |
| Obtain \(-3.46\) | A1 | AWRT |
## Question 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| State or imply non-modulus equation $(2x-5)^2 = (x+6)^2$ or pair of linear equations | B1 | |
| Attempt solution of 3-term quadratic equation or of pair of linear equations | M1 | |
| Obtain $-\frac{1}{3}$ and $11$ | A1 | |
## Question 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms and use power law for $2^{-x} = k$ where $k > 0$ from (a) | M1 | |
| Obtain $-3.46$ | A1 | AWRT |4
\begin{enumerate}[label=(\alph*)]
\item Solve the equation $| 2 x - 5 | = | x + 6 |$.
\item Hence find the value of $y$ such that $\left| 2 ^ { 1 - y } - 5 \right| = \left| 2 ^ { - y } + 6 \right|$. Give your answer correct to 3 significant figures.
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2020 Q4 [5]}}