Calculus flashcards

17 practice cards drawn from the Calculus lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

Read the Calculus lessons in full →

On y = x², is the curve steeper at x = 4 or at x = 6?

x = 6

from “The Gradient of a Curve”

On y = x², is the curve steeper at x = 1 or at x = 3?

x = 3

from “The Gradient of a Curve”

What does 1 + 1/n as n grows without limit close in on?

1

from “Limits”

What does (2n + 1)/n as n grows without limit close in on?

2

from “Limits”

For y = x², what is the gradient at x = 6?

12

from “From First Principles”

For y = x², what is the gradient at x = 7?

14

from “From First Principles”

Differentiate 3x^3

9x^2

from “Differentiating Powers”

Differentiate 1x^7

7x^6

from “Differentiating Powers”

For y = x² at x = 4, what is the equation of the tangent?

y = 8x − 16

from “Tangents and Normals”

A tangent has gradient 6. What is the gradient of the normal?

−1/6

from “Tangents and Normals”

y = x² − 2x. Where is the gradient zero?

x = 1

from “Stationary Points”

y = x² − 4x. Where is the gradient zero?

x = 2

from “Stationary Points”

Integrate x^6

x^7/7 + c

from “Integration”

Integrate x^2

x^3/3 + c

from “Integration”

The area under y = x² from 0 to 3 is what?

9

from “Area Under a Curve”

The area under y = x² from 0 to 1 is what?

1/3

from “Area Under a Curve”

What does 1/2 + 1/4 + 1/8 + … do?

settles on 1

from “Two Infinite Sums, Opposite Fates”

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