Edexcel IAL P2 Logarithms and Exponentials Questions
aˣ and logₐx, laws of logarithms, solving aˣ = b, change of base (natural logs and eˣ are P3).
- P2 · Pure Mathematics 2
- Calculator allowed
- 35 practice questions
What the questions test
The 35 P2 logarithms and exponentials practice questions cover:
Worked example 1
Solve the equation $\log_2 x + \log_x 2 = 2.5$ for $x > 0, x \ne 1$.
Mark scheme
- M1 for applying the reciprocal rule: $\log_x 2 = \frac{1}{\log_2 x}$.
- M1 for making the substitution $u = \log_2 x$ to form $u + \frac{1}{u} = 2.5$.
- M1 for multiplying by $2u$ to form the quadratic $2u^2 - 5u + 2 = 0$ and solving it.
- M1 for finding the roots $u = 2$ and $u = \frac{1}{2}$.
- A1 for converting back to $x$ and finding both solutions: $x = 4$ and $x = \sqrt{2}$.
Worked example 2
Given that $\log_2 x = p$ and $\log_2 y = q$, express $\log_2(8x^2 y^3)$ in terms of $p$ and $q$.
Mark scheme
- M1 for splitting the logarithm into a sum: $\log_2 8 + \log_2 x^2 + \log_2 y^3$.
- B1 for evaluating $\log_2 8 = 3$.
- M1 for applying the power law: $2\log_2 x + 3\log_2 y$.
- A1 for the final expression $3 + 2p + 3q$.
FAQ
What logarithms and exponentials is in Edexcel IAL P2?
aˣ and logₐx, laws of logarithms, solving aˣ = b, change of base (natural logs and eˣ are P3).
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 logarithms and exponentials 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.