Edexcel IAL P3 Exponentials and Logarithms Questions
eˣ and ln x as inverse functions; exponential growth/decay; log-linear graphs for y = axⁿ and y = kbˣ.
- P3 · Pure Mathematics 3
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P3 exponentials and logarithms practice questions cover:
Worked example 1
The variables $x$ and $y$ satisfy the equation $y = a b^x$. A graph of $\ln y$ against $x$ is plotted and forms a straight line passing through $(0, 2)$ and $(4, 10)$. Find the exact values of the constants $a$ and $b$.
Mark scheme
- M1 for taking natural logarithms of both sides to get $\ln y = \ln a + x \ln b$.
- M1 for calculating the gradient of the line: $\ln b = \frac{10 - 2}{4 - 0} = 2$.
- A1 for solving to find exactly $b = e^2$.
- M1 for identifying the y-intercept from the coordinate $(0, 2)$, so $\ln a = 2$.
- A1 for solving to find exactly $a = e^2$.
Worked example 2
Solve the equation $2\ln x = \ln(3x + 4)$.
Mark scheme
- M1 for applying the power law to the LHS: $\ln(x^2) = \ln(3x + 4)$.
- M1 for equating the arguments: $x^2 = 3x + 4$.
- M1 for rearranging to $x^2 - 3x - 4 = 0$ and finding roots $x = 4$ and $x = -1$.
- A1 for rejecting $x = -1$ (since $\ln x$ must have $x > 0$) and giving $x = 4$.
FAQ
What exponentials and logarithms is in Edexcel IAL P3?
eˣ and ln x as inverse functions; exponential growth/decay; log-linear graphs for y = axⁿ and y = kbˣ.
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 exponentials and logarithms questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.