The Exponential and Logarithmic Functions (HSC SSCE Mathematics Advanced): Quizzes

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Applications of Differentiation
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Which point do both y=exy = e^x and y=e−xy = e^{-x} pass through?

(0,1)(0, 1)

What is the gradient of y=exy = e^x at the point (0,1)(0, 1)?

11

As x→∞x \to \infty, what is the horizontal asymptote for y=e−xy = e^{-x}?

The xx-axis

How are y=exy = e^x and y=e−xy = e^{-x} geometrically related?

Reflections in the yy-axis

Which situation is an application of exponential decay y=e−xy = e^{-x}?

Radioactive decay

What is the first step in the six-step curve sketching method?

Write down the domain

What is dydx\frac{dy}{dx} for y=xe−xy = xe^{-x}?

e−x(1−x)e^{-x}(1-x)

Where is the stationary point of y=xe−xy = xe^{-x}?

(1,1e)(1, \frac{1}{e})

What is lim⁡x→∞xe−x\lim_{x \to \infty} xe^{-x}?

00

What transformation relates y=xe−xy = xe^{-x} to y=−xexy = -xe^x?

Reflection in the yy-axis

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

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Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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