AP Calculus AB Implicit Differentiation Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Implicit Differentiation – Maths PDF

Cover of the book AP Calculus AB Math Tests with Answer Keys (PDF)

Download as a PDFThe AP Calculus AB tests book with answer keysPrintable PDFSee the book ›

Sommaire

This implicit quiz for AP Calculus AB covers implicit differentiation (Common Core AP CALC AB 3.2), with a free PDF to print.

Test yourself on implicit differentiation, slopes of curves, tangent lines, horizontal and vertical tangents and second derivatives with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 3.2

Implicit quiz: 10 questions

Question 1

For \(x^{2}+y^{2}=16\), what is \(\frac{dy}{dx}\)?

Question 2

What is \(\frac{d}{dx}[y^{3}]\)?

Question 3

What is \(\frac{d}{dx}[xy]\)?

Question 4

The ellipse 9x² + 16y² = 144.

What is the slope of \(9x^{2}+16y^{2}=144\) at \((0,3)\)?

Question 5

The curve xy = 12.

If \(xy=12\), what is \(\frac{dy}{dx}\) at \((3,4)\)?

Question 6

For \(\sin y=x\), what is \(\frac{dy}{dx}\)?

Question 7

The circle x² + y² = 9.

At which point does \(x^{2}+y^{2}=9\) have a vertical tangent?

Question 8

What is the tangent line to \(x^{2}+y^{2}=25\) at \((4,3)\)?

Question 9

For \(e^{y}=x\), what is \(\frac{dy}{dx}\)?

Question 10

For \(x^{2}+y^{2}=25\), which expression is \(\frac{d^{2}y}{dx^{2}}\)?

Remember

Differentiate every term with respect to x; a y term gets a factor dy/dx.
Use the product rule for terms such as xy, and the chain rule for sin y or e^y.
The derivative may contain both x and y; substitute a point on the curve to get a slope.
Horizontal tangents: numerator zero. Vertical tangents: denominator zero.

How to use this implicit quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the implicit quiz as a PDF with the button below and keep it with your notes.

All AP Calculus AB chapters: AP Calculus AB math.

Voter.. post

Free printable PDF