Logarithmic & exponential functions: AS Level Mathematics questions with answers
Free Logarithmic & exponential functions questions for AS Level Mathematics (9709), part of Pure Mathematics 2. Each question has the answer and the marking points an examiner would look for.
Logarithmic & exponential functions practice questions
Question 1Structured · 5 marksA* challenge
The variables x and y satisfy the equation y = A xn, where A and n are constants. The graph of ln y against ln x is a straight line passing through the points (0.8, 2.17) and (3.5, 6.16).
Find the values of A and n, giving your answers correct to 3 significant figures.
[5]
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Part
Answer and marking points
Marks
A = 2.69, n = 1.48
ln y = ln A + n ln x stated B1 gradient from the two points M1 n = 1.48 A1 intercept found and exponentiated M1 A = 2.69, n = 1.48 A1
5
Question 2Structured · 3 marks
Solve 3x + 1 = 7x, giving your answer correct to 3 significant figures.
[3]
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Part
Answer and marking points
Marks
1.3
take logs M1 x(ln 7 − ln 3) = ln 3 A1 1.3 A1
3
Question 3Structured · 4 marks
Solve the equation 32x − 82(3x) + 81 = 0.
[4]
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Part
Answer and marking points
Marks
x = 0, x = 4
u = 3xM1 u2 − 82u + 81 = 0 A1 u = 1, u = 81 A1 x = 0, x = 4 A1
4
Question 4Structured · 5 marksA* challenge
The variables x and y satisfy the equation y = A xn, where A and n are constants. The graph of ln y against ln x is a straight line passing through the points (0.6, 1.94) and (4.2, 5.18).
Find the values of A and n, giving your answers correct to 3 significant figures.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
A = 4.06, n = 0.9
ln y = ln A + n ln x stated B1 gradient from the two points M1 n = 0.9 A1 intercept found and exponentiated M1 A = 4.06, n = 0.9 A1
5
Question 5Structured · 3 marks
Solve 2x + 1 = 5x, giving your answer correct to 3 significant figures.
[3]
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Part
Answer and marking points
Marks
0.756
take logs M1 x(ln 5 − ln 2) = ln 2 A1 0.756 A1
3
Question 6Structured · 3 marks
Solve the equation 3x+1 = 5x, giving your answer correct to 3 significant figures.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
x = 2.15
Take logs of both sides M1 (x + 1) ln 3 = x ln 5 M1 2.15 A1
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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in