plumiLogarithmic and exponential functions: CAIE IGCSE Additional Maths questions
Every CAIE IGCSE Additional Maths exam question on 6 Logarithmic and exponential functions, June 2024 and the specimen papers, with its mark scheme and examiner’s report.
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![June 2024 Paper 1, question 3: (a) Write 1 lg ( x 2 1 ) 2 lg ( x 1 ), where x 2 1 , as a single logarithm to base 10. Give your + - - - answer in its simplest form. [4] (b) Solve the equation](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-03-qp.webp)
![June 2024 Paper 1, question 9: (a) Solve the following simultaneous equations. e x + y e 3 x - 2 y 1 # = 2 = x y 256 [5] 11 (b) Solve the equation 10 e ( 2 x - 1 ) 11 6 e ( 1 - 2 x ) , giving](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060611-jun24-09-qp.webp)
![Specimen Paper 1, question 5: (a) Given that logap + loga 5 – loga 4 = loga 20 , find the value of p. [2] (b) Solve the equation 32x+1 + 8(3x) – 3 = 0 . [3] (c) Solve the equation 4 logy 2 +](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060601-spec-05-qp.webp)
![Specimen Paper 1, question 6: (a) f(x) = 3e2x + 1 for x∈ℝ 6 g(x) = x + 1 for x∈ℝ (i) Write down the range of f and the range of g. [2] (ii) Find g2(0) . [1] (iii) Hence find fg2(0) . [2] 9 (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/060601-spec-06-qp.webp)
All 5 questions on Logarithmic and exponential functions, as a list
- June 2024, Paper 1, Q3 (9 marks): (a) Write 1 lg ( x 2 1 ) 2 lg ( x 1 ), where x 2 1 , as a single logarithm to base 10. Give your + - - - answer in its simplest form. [4] (b) Solve the equation
- June 2024, Paper 1, Q9 (9 marks): (a) Solve the following simultaneous equations. e x + y e 3 x - 2 y 1 # = 2 = x y 256 [5] 11 (b) Solve the equation 10 e ( 2 x - 1 ) 11 6 e ( 1 - 2 x ) , giving
- Specimen, Paper 1, Q5 (8 marks): (a) Given that logap + loga 5 – loga 4 = loga 20 , find the value of p. [2] (b) Solve the equation 32x+1 + 8(3x) – 3 = 0 . [3] (c) Solve the equation 4 logy 2 +
- Specimen, Paper 1, Q6 (12 marks): (a) f(x) = 3e2x + 1 for x∈ℝ 6 g(x) = x + 1 for x∈ℝ (i) Write down the range of f and the range of g. [2] (ii) Find g2(0) . [1] (iii) Hence find fg2(0) . [2] 9 (
- Specimen, Paper 2, Q2 (4 marks): For variables x and y, plotting ln y against ln x gives a straight-line graph passing through the points (6, 5) and (8, 9). Show that y = e pxq where p and q ar
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