A-LevelMathematicsLogarithmic and exponential functions9709/31 · Oct/Nov 2021 · Q14 Marks

Solve the equation 4|5ˣ – 1| = 5ˣ, giving your answers correct to 3 decimal places.

Solve the equation 4|5ˣ – 1| = 5ˣ, giving your answers correct to 3 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[M1] State or imply non-modular equation 4(5ˣ −1)² = (5ˣ)² or pair of equations 4(5ˣ - 1) = ±5ˣ
[A1] Obtain 5ˣ = ⁴⁄₃ and 5ˣ = ⁴⁄₅ (or 5ˣ⁺¹ = 4)
[M1] Use correct method for solving an equation of the form 5ˣ = a, or 5ˣ⁺¹ = b where a > 0, or b > 0
[A1] Obtain answers x = 0.179 and x −0.139
Alternative method for question 1
[B1] Obtain 5ˣ = ⁴⁄₃ by solving an equation
[B1] Obtain 5ˣ = ⁴⁄₅ (or 5ˣ⁺¹ = 4) by solving an equation
[M1] Use correct method for solving an equation of the form 5ˣ = a, or 5ˣ⁺¹ = b where a > 0, or b > 0
[A1] Obtain answers x = 0.179 and x −0.139

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.

Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2021 Paper 3 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