Calculus Quiz

Polynomials

100

Differentiate x² + 5x

2x + 5

200

Integrate x⁴ + 3x

x⁵/5 + 3/2 x² + c

300

Differentiate 4x^-2 + 3

-8x^-3

400

Give an example of something that differentiates to 6x² + 8x + 5

3x³ + 4x² + 5x + 4

500

What integrates to 4x³ - 6x² + C

8x² - 12x

Trigonometry

100

Differentiate sin(3x)

3cos(3x)

200

Integrate cos(4x)

sin(4x)/4 + C

300

Differentiate cos(5x) + x²

-5sin(5x) + 2x

400

Integrate 4x² - sin(2x)

4/3 x³ + cos(2x)/2

Exponentials

100

Differentiate 3e^x

3e^x

200

Differentiate 3e^2x

6e^2x

300

Integrate 3e^0.5x

6e^0.5x + C

400

Differentiate e^4x - cos(2x)

4e^4x + 2sin(2x)

Trapezium Rule

100

The formula for h

h = (b-a)/n

200

We are integrating from 1 to 4 using 6 strips. What are the x values?

1, 1.5, 2, 2.5, 3, 3.5, 4

400

Use the trapezium to integrate y=x³ from 2 to 4 using 5 strips

60.48

500

Use the trapezium rule to integrate x²e^0.1x from 2 to 5 using 6 strips

58.1

Kinematics

100

What operation is used to change displacement to velocity?

Differentiation

200

What operation is used to change acceleration to velocity?

Integration

300

If a = 4t m/s², find the velocity at t=5s if the initial velocity was 1 m/s

51 m/s

400

A particle leaves the origin at a velocity of v = 5t⁴ mph. Find the distance travelled in miles after 2 hours.

32 miles

500

If v = t³ - 6t² m/s, find the times when the acceleration = 0

t=0, t=4