CAIE P3 2024 November — Question 4 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeQuadratic in exponential form
DifficultyModerate -0.3 This is a straightforward exponential equation requiring recognition that 5^(x+2) = 25·5^x, leading to a simple linear equation in 5^x. The algebraic manipulation is routine and the question only requires applying logarithms at the end—slightly easier than average due to minimal steps and standard technique.
Spec1.06g Equations with exponentials: solve a^x = b
Solve the equation \(5^x = 5^{x+2} - 10\). Give your answer correct to 3 decimal places. [3]
Question 4:
AnswerMarks Guidance
4Use laws of indices correctly and solve for 5x *M1
E.g. obtain 5x = OE.
12
Allow for y = … if they have previously stated
y=5x.
Could be implied if they have a correct
simplified equation in 5x, e.g. 125x =5.
AnswerMarks Guidance
Use a correct method for solving an equation of the form5x =a,where a > 0DM1 10
Allow x ln5 = ln  .
24
AnswerMarks Guidance
Obtain answer –0.544A1 CWO. If no working shown, 0/3.
Note: 3 dp required.
3
Question 4:
4 | Use laws of indices correctly and solve for 5x | *M1 | 5
E.g. obtain 5x = OE.
12
Allow for y = … if they have previously stated
y=5x.
Could be implied if they have a correct
simplified equation in 5x, e.g. 125x =5.
Use a correct method for solving an equation of the form5x =a,where a > 0 | DM1 | 10
Allow x ln5 = ln  .
24
Obtain answer –0.544 | A1 | CWO. If no working shown, 0/3.
Note: 3 dp required.
3
Solve the equation $5^x = 5^{x+2} - 10$. Give your answer correct to 3 decimal places. [3]

\hfill \mbox{\textit{CAIE P3 2024 Q4 [3]}}
This paper (11 questions)
View full paper
Q1 4 Q2 3 Q3 5 Q4 3 Q5 4 Q6 4 Q7 6 Q8 8 Q9 11 Q10 13 Q11 14