| 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 |f(x)| = |g(x)| with non-linear or exponential expressions |
| Difficulty | Moderate -0.3 Part (i) is a standard modulus equation requiring consideration of cases (positive/negative expressions), yielding straightforward linear equations. Part (ii) applies substitution (letting y = 3^x) to convert to part (i), then uses basic logarithms to find x. This is a routine two-part question testing standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks |
|---|---|
| 1(i) | 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 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | A1 | SC: B1 for one correct solution |
| Answer | Marks | Guidance |
|---|---|---|
| 1(ii) | Apply logarithms and use power law for 3y =k where k >0 | M1 |
| Obtain −0.369 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(i) ---
1(i) | 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 2
3 | A1 | SC: B1 for one correct solution
3
--- 1(ii) ---
1(ii) | Apply logarithms and use power law for 3y =k where k >0 | M1 | Must be using their answers to part (i)
Obtain −0.369 | A1
2
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\roman*)]
\item Solve the equation $|9x - 2| = |3x + 2|$. [3]
\item Hence, using logarithms, solve the equation $|3^{x+2} - 2| = |3^{x+1} + 2|$, giving your answer correct to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2018 Q1 [5]}}