Logarithmic functions and indices: Edexcel International GCSE Further Maths questions

Edexcel International GCSE Further Maths past-paper questions on 1 Logarithmic functions and indices, 2019–2025, with mark schemes and examiner’s reports where available.

All 38 questions on Logarithmic functions and indices, as a list

June 2025 (R), Paper 1, Q1 (3 marks): w 8 6 50 Without using a calculator, find the value of w 6 where a and b are integers and c is prime. Give your answer in the form a + b c Show your working cle
June 2025 (R), Paper 2, Q9 (9 marks): (i) Solve the equation 3 log 9 log 27 1 a a Give your answer in the form a = bc where b is prime and c is an integer. (3) (ii) Solve the equation log p log 256
June 2025, Paper 1, Q10 (11 marks): Solve the equation (i) log4 6 y 5 3 (2) (ii) log ( x 2 x 2 4 3 ) log ( 5 ) 3 0 4 2 Show clear algebraic working. Give your answer to 3 significant figures. (9)
June 2025, Paper 2, Q3 (5 marks): Given that a b 5 9 4 5 where a, b and c are prime numbers, c 6 2 5 find the value of a, the value of b and the value of c (5)
June 2025, Paper 2, Q7 (10 marks): (a) Complete the table of values for y x giving your answers to log 3 4 ( ) 3 2 decimal places. x 0 0.5 1 1.5 2 2.5 3 3.5 y 4.26 4 3.63 3 2.37 (2) (b) On the gr
November 2024, Paper 2, Q4 (8 marks): (a) Complete the table of values for y x x giving your answers log10 6 1 to 2 decimal places. x 0.25 0.5 1 1.5 2 2.5 3 y –0.20 –0.30 –0.60 (2) (b) On the grid o
November 2024, Paper 2, Q6 (11 marks): (i) Solve the equation 5 log 9 log 3 3 b b (4) (ii) Solve the equation 3 log x 3 log 27 8 log 128 3 x 4 Give your answers in exact form. (7)
June 2024 (R), Paper 1, Q1 (4 marks): Without using a calculator, solve the inequality x x 50 18 6 5 Give your answer in an exact form with a rationalised denominator. Show your working clearly. (4)
June 2024 (R), Paper 1, Q7 (9 marks): The curve C has equation y x log4 4 (a) Using the axes below, sketch the graph of C. Label the coordinates of the points of intersection of C with the coordinat
June 2024, Paper 1, Q9 (9 marks): 3 9 (a) Find the value of a such that loga 8 = 4 (2) (b) Show that x 3 1 x x x x x 3 log 4 log 8 6 log 8 log log 8 2 16 4 2 2 (4) (c) Hence solve the equation 3
November 2023, Paper 1, Q1 (4 marks): A Diagram NOT accurately drawn (2 + 4√5) cm B C (a + b√5) cm Figure 1 Figure 1 shows the triangle ABC ABC 90° AB cm where a and b are integers. 2 4 5 cm BC a b
November 2023, Paper 1, Q11 (8 marks): Solve the simultaneous equations x y 2 2log4 log 3 3 log x 3 8 log y 13 2 9 Show your working clearly. (8)
June 2023 (R), Paper 1, Q1 (4 marks): Diagram NOT ( a + b 2 cm A B accurately drawn ( 4 − 2 cm D C Figure 1 Figure 1 shows the rectangle ABCD. AD BC 4 2 cm and AB DC a b 2 cm where a and b are integ
June 2023 (R), Paper 2, Q10 (7 marks): Solve the equation x 3 log 8 log 64 22 x 4 (7)
June 2023, Paper 1, Q6 (8 marks): Solve the equation 3 + log4x 2 – 3 logx 2 = 0 log2x giving your answers to 3 significant figures. (8)
June 2023, Paper 2, Q1 (5 marks): Given that a 2 5 11 b 5 where a is an integer and b is prime, 2 3 5 find the value of a and the value of b Show your working clearly. (5)
January 2023 (R), Paper 1, Q1 (4 marks): Given that a − 48 1 can be written in the form b 3 – 9 where a and b are integers, 3 + find the value of a and the value of b Show your working clearly. (4)
January 2023 (R), Paper 2, Q10 (13 marks): 3y 10 (a) Show that 9 (6y–5) = 3 243 (4) (b) Solve the simultaneous equations 3y 9 (x–2) = 27 243 log10 6xy = log4 2 (9)
January 2023, Paper 1, Q9 (8 marks): Giving each value in your solution to 2 decimal places, solve the simultaneous equations e2y – x + 2 = 0 ln(x + 3) – 2y – 1 = 0 (8)
June 2022 (R), Paper 1, Q6 (8 marks): Given that a + 5 = + 11 5 5 5 − 2 (a) without using a calculator, find the value of a Show your working clearly. (2) Triangle PQR is such that PR = (x + 3) cm Q
June 2022 (R), Paper 1, Q7 (11 marks): A curve C has equation y = log10 (x + 2) (a) Using the axes below, sketch the graph of C. Label the coordinates of the points of intersection of C with the coor
June 2022, Paper 1, Q1 (3 marks): Given that 2 3 − 4 can be written in the form a + b 3 where a and b are integers, + 3 3 5 find, without using a calculator, the value of a and the value of b Sh
June 2022, Paper 2, Q10 (5 marks): Solve the equation log4x + log16 x + log2 x = 10.5 Show your working clearly. (5)
January 2022, Paper 1, Q7 (8 marks): (a) Write down the value of log216 (1) Given that 4 + 2 log4 x = log2 y (b) show that y = 16x (4) (c) Hence solve the equation 4 + 2 log4 x = log2 (4x + 5) (3)
November 2021, Paper 1, Q5 (7 marks): Solve the equation log3 x − 5 + log9 (x + 3) – 1 = 0 Show clear algebraic working. (7)
June 2021, Paper 1, Q8 (8 marks): Given that n satisfies the equation loga n = loga 3 + loga(2n – 1) (a) find the value of n. (3) Given that logp x = 3 and logp y – 3 logp 2 = 4 (b) (i) express
June 2021, Paper 2, Q8 (8 marks): Use an algebraic method to solve the simultaneous equations log4 a + 3 log8b = 5 2 2a = 16 4 2 4 b (8)
November 2020 (R), Paper 1, Q9 (7 marks): Showing your working clearly, use algebra to solve the equations 16 1 x = 8 4 y 4 2 = 16 x y (7)
November 2020 (R), Paper 2, Q8 (7 marks): Solve the equation log3 x – 2 logx 3 = 1 (7)
November 2020, Paper 2, Q4 (7 marks): (i) Solve the equation 16logr 4 = log4 r (2) (ii) Solve the equation log5 9 + log5 12 + log5 15 + log5 18 = 1 + log5 x + log5 x2 (5)
January 2020 (R), Paper 1, Q1 (4 marks): a + 3 1 Given that 3 = 11 + b 3 where a and b are integers, 2 − find the value of a and the value of b. (4)
January 2020 (R), Paper 1, Q5 (9 marks): (a) Show that log4 32 = 5 2 (2) (b) Hence, or otherwise, find the exact solutions of the equation log2 x – log4 32 + 1 4 logx 16 = 0 (7)
January 2020, Paper 1, Q7 (5 marks): Solve the equation log7 (8x2 − 6x + 3) − log49 x2 = 3 log7 2 (5)
June 2019 (R), Paper 1, Q3 (7 marks): (a) Write down the value of log3 9 (1) 2 (b) Solve the equation log3 9t = log9 12 ⎛ ⎞ ⎠⎟ + 2 where t 0 ⎝⎜ t Give your answer in the form a b where a and b are p
June 2019 (R), Paper 1, Q8 (11 marks): (a) Complete the table of values for y = 2 + ln (2x + 1) giving your answers to 2 decimal places. (2) x 0 0.25 0.5 1 1.5 2 3 y 2 3.10 3.39 (b) On the grid oppos
June 2019, Paper 1, Q2 (3 marks): 4+2V3 a+bV3 2 Given that can be written in the form - where a and b are integers 5-2N3 and c is prime, find the value of a, the value of b and the value of c. S
June 2019, Paper 1, Q8 (10 marks): (a) Solve 5p' - 9p + 4 = 0 (2) (b) Hence solve 52x+1 - 9(5*) + 4 = 0 Give your answers to 3 significant figures where appropriate. (4) The curve with equation y
June 2019, Paper 1, Q9 (12 marks): (a) Solve the equation 2l0g,9 + 310g;P = 8 (6) Given that 10g,3 = l0g, 3k (b) find the value of k (2) (c) Show that Grlog, + - 3rlog,3 - slog, x + 1010g,3 = log

Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Edexcel International GCSE Further Maths past papers.

The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.

476 questions