GCE A-Level - Higher 1 (H1) · Mathematics (8865)

Exponential and logarithmic functions and Graphing techniques: Practice Questions

5 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Exponential and logarithmic functions and Graphing techniques.

9 questions18 marksFree, no account

Question 1

1 mark

Using the laws of logarithms, simplify the expression \(2 \ln a - \ln b\).

Question 2

1 mark

The graph of the function \(y = \ln(3 - x) + 2\) has a vertical asymptote. What is the equation of this asymptote?

Question 3

1 mark

Using a graphing calculator or software, determine the number of real roots for the equation \( e^x = 4 - x^2 \).

Question 4

1 mark

Solve the equation \(\ln x + \ln 2 = \ln 10\) for \(x\).

Question 5

1 mark

Consider the graph of the function \( y = \ln(x - 2) \). What is the equation of its vertical asymptote?

Question 6

2 marks

Solve the equation \( \ln(2x - 1) = 0 \).

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Question 7

3 marks

State the equations of the vertical and horizontal asymptotes for the graph of \( y = \ln(x + 3) - 4 \).

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Question 8

3 marks

Solve the logarithmic equation \(2\log_{10}(x) - \log_{10}(x + 4) = \log_{10}(2)\), giving your answer(s) to 3 decimal places where necessary.

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Question 9

5 marks

Consider the function \(y = 3 - e^{-2x}\).
(a) State the equation of the horizontal asymptote of the graph of the function.
(b) Find the coordinates of the point where the graph crosses the \(x\)-axis.
(c) Sketch the graph of the function, labeling the intercept found in part (b) and the horizontal asymptote.

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