◈ Oracle PrepSign Up Free
A-LevelMathematicsLogarithmic and exponential functions9709/21 · Oct/Nov 2024 · Q15 Marks

The variables x and y satisfy the equation a^(2y) = e^(3x+k), where a and k are constants. The graph of y against x is a straight line.

  1. (a)Use logarithms to show that the gradient of the straight line is (3 / (2 ln a)).[1]
  2. (b)Given that the straight line passes through the points (0.4, 0.95) and (3.3, 3.80), find the values of a and k.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [B1] AG – necessary detail needed.
  2. [M1] Equate 3/(2 ln a) to gradient of line
  3. [A1] Obtain a = 4.6 or a = e^(29/19) or equivalent and hence obtain a = 4.6 or a = e^(2.85/2.9)
  4. [M1] Substitute appropriate values to find value of k
  5. [A1] Obtain k=1.7

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 1, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

Logarithmic and exponential functionsFeb/Mar 20213m

Solve the equation ln(x³ – 3) = 3 ln x – ln 3. Give your answer correct to 3 significant figures.

Logarithmic and exponential functionsFeb/Mar 20225m

The variables x and y satisfy the equation y = 3^(2a)a^x, where a is a constant. The graph of ln y against x is a str…

Logarithmic and exponential functionsFeb/Mar 20238m

It is given that ∫₁ᵃ (4/(1 + 2x) + 3/x) dx = ln 10, where a is a constant greater than 1.

Differential equationsFeb/Mar 20257m

The variables x and θ satisfy the differential equation dx/dθ = (½x+1)sin²2θ, and x = 5 when θ = 0. Solve the differe…

VectorsFeb/Mar 20258m

Two lines have equations r = (-1 3 -4) + λ(2 3 -1) and r = (2 -3 -1) + μ(-1 -2 1).

AlgebraFeb/Mar 202510m

The polynomial 6x³ + ax² + bx + 9 is denoted by p(x), where a and b are constants. It is given that (x-3) is a factor…

← Browse all past-paper questions

© 2026 Oracle Prep