CAIE P3 2012 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |f(x)| = |g(x)| with non-linear or exponential expressions
DifficultyModerate -0.3 This is a straightforward modulus equation requiring students to split into two cases (4 - 2^x = 10 or 4 - 2^x = -10), then solve simple exponential equations using logarithms. It's slightly easier than average as it's a direct application of standard technique with no conceptual complications, though the exponential component adds minor complexity beyond purely linear modulus equations.
Spec1.02l Modulus function: notation, relations, equations and inequalities1.06g Equations with exponentials: solve a^x = b

1 Solve the equation \(\left| 4 - 2 ^ { x } \right| = 10\), giving your answer correct to 3 significant figures.

Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
State or imply \(4 - 2^x = -10\) and \(10\)B1
Use correct method for solving equation of form \(2^x = a\)M1
Obtain \(3.81\)A1 [3]
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| State or imply $4 - 2^x = -10$ and $10$ | B1 | |
| Use correct method for solving equation of form $2^x = a$ | M1 | |
| Obtain $3.81$ | A1 | [3] |

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1 Solve the equation $\left| 4 - 2 ^ { x } \right| = 10$, giving your answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P3 2012 Q1 [3]}}