plumiExponentials and logarithms: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.5 Exponentials and logarithms, 2019–2025, with its mark scheme and examiner’s report.
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All 23 questions on Exponentials and logarithms, as a list
- June 2025, AS Pure 2 (P2), Q6 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. (i) Solve 2log2 (4 – x) = 3 + log2 11
- June 2025 (A), AS Pure 2 (P2), Q4 (9 marks): O y x 1 5 Figure 1 Figure 1 shows a sketch of part of the curve with equation y = log3 (x + 1) – log3 x The point P(a, 4) lies on the curve. (a) Find the exact
- January 2025, AS Pure 2 (P2), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) The table below shows val
- October 2024, AS Pure 2 (P2), Q6 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Using the laws of logarithms,
- June 2024, AS Pure 2 (P2), Q3 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Using the laws of logarit
- June 2024, AS Pure 2 (P2), Q6 (9 marks): (a) Sketch the curve with equation y = a x + 4 where a is a positive constant greater than 1 On your sketch, show • the coordinates of the point of intersection
- June 2024 (R), AS Pure 2 (P2), Q9 (9 marks): Given that 3 log2 (t + 4) – 2 log2 (t – 2) = 7 (a) verify that t = 4 is a solution of the above equation, (b) show that t 3 – 116t 2 + 560t – 448 = 0 (c) Hence,
- January 2024, AS Pure 2 (P2), Q4 (9 marks): (a) Sketch the curve with equation y = a – x + 4 where a is a constant and a > 1 On your sketch show • the coordinates of the point of intersection of the curve
- January 2024, AS Pure 2 (P2), Q6 (8 marks): (a) Given that 2 3 4 2 1 2 4 4 4 log log log x x x show that x 3 + 6x 2 + x – 4 = 0 (b) Given also that –1 is a root of the equation x 3 + 6x 2 + x – 4 = 0 (i)
- October 2023, AS Pure 2 (P2), Q5 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve 3 a = 70 giving the
- June 2023, AS Pure 2 (P2), Q5 (5 marks): Use the laws of logarithms to solve log2 (16x) + log2 (x + 1) = 3 + log2 (x + 6)
- January 2023, AS Pure 2 (P2), Q4 (6 marks): (i) Using the laws of logarithms, solve log3(4x) + 2 = log3(5x + 7) (ii) Given that log log a r r a r r y y = = ∑ ∑ ( ) = ( ) 1 2 1 2 y > 1, a > 1, y ≠ a find y
- October 2022, AS Pure 2 (P2), Q4 (8 marks): The weight of a baby mammal is monitored over a 16‑month period. The weight of the mammal, w kg, is given by w = loga(t + 5) – loga4 2 t 18 where t is the a
- October 2022, AS Pure 2 (P2), Q10 (7 marks): Given a = log2 3 (i) write, in simplest form, in terms of a, (a) log2 9 (b) log2 3 16 (ii) Solve 3x × 2x + 4 = 6 giving your answer, in simplest form,
- June 2022, AS Pure 2 (P2), Q4 (6 marks): In this question you must show all stages of your working. Give your answers in fully simplified surd form. Given that a and b are positive constants, solve the
- June 2022, AS Pure 2 (P2), Q9 (9 marks): A scientist is using carbon‑14 dating to determine the age of some wooden items. The equation for carbon‑14 dating an item is given by N = kλt where • N grams i
- January 2022, AS Pure 2 (P2), Q4 (5 marks): Using the laws of logarithms, solve log3 (32 – 12x) = 2 log3 (1 – x) + 3
- June 2021, AS Pure 2 (P2), Q2 (8 marks): O x y y = 4 x Figure 1 Figure 1 shows a sketch of the curve with equation y = 4 x A copy of Figure 1, labelled Diagram 1, is shown on the next page. (a) On Diag
- June 2021, AS Pure 2 (P2), Q7 (10 marks): (a) Given that 3 log3(2x – 1) = 2 + log3(14x – 25) show that 2x3 – 3x2 – 30x + 56 = 0 (b) Show that –4 is a root of this cubic equation. (c) Hence, using algebr
- January 2021, AS Pure 2 (P2), Q3 (8 marks): (i) Solve 7 x + 2 = 3 giving your answer in the form x = log7 a where a is a rational number in its simplest form. (ii) Using the laws of logarithms, solve 1 +
- October 2020, AS Pure 2 (P2), Q9 (10 marks): (i) Find the exact value of x for which log3(x + 5) – 4 = log3(2x – 1) (ii) Given that 3 y + 3 × 2 1 – 2y = 108 (a) show that 0.75 y = 2 (b) Hence find the valu
- January 2020, AS Pure 2 (P2), Q9 (7 marks): (a) Sketch the curve with equation y = 3 × 4 x showing the coordinates of any points of intersection with the coordinate axes. The curve with equation y = 6 1–x
- June 2019, AS Pure 2 (P2), Q8 (9 marks): (i) Find the exact solution of the equation 8 2x + 1 = 6 giving your answer in the form a + b log2 3, where a and b are constants to be found. (ii) Using the la
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