Differentiate/Integrate

General

100

What exact time does school start in the morning?

8.24 am

200

What does ATAR stand for?

Australian Tertiary Admission Rank

300

How many children does your teacher have?

3

400

Name 4 suburbs of Newcastle that start with W.

Warners Bay, Wallsend, West Wallsend, Waratah

500

What can you find twice in a week, once in a year but never in a day?

Letter E

Derivates

100

Differentiate:  3x⁴−5x²+2x

12x³−10x+2

200

Differentiate:  ln⁡(x²+1)

2x/x²+1

300

Differentiate:    sin⁡(3x²)

6xcos(3x²)

400

Differentiate:   (x²+3)⁵

10x(x²+3)⁴

500

Differentiate:   x³cos(x²+1)

3x²cos(x²+1) - 2x⁴sin(x²+1)

Anti Derivatives

100

∫(8x³−2x)dx

2x⁴−x²+C

200

∫5e^5xdx

e^5x+C

300

∫3/x dx

3ln∣x∣+C

400

∫8x(x²+1)³dx

(x²+1)⁴+C

500

∫(2x+1)⁴dx

(2x+1)⁵/10+C

Equation of a Function

100

Find the equation of the function if:

f′(x)=4x and f(0)=3

f(x)=2x²+3  OR  y=2x²+3

 

200

Find the equation of the function if:

f′(x)=6x² and f(1)=5

f(x)=2x³+3  OR  y=2x³+3

300

Find the equation of the function if:

f′(x)=2x+3 and f(2)=7

f(x)=x²+3x−3  OR y=x²+3x-3

400

Find the equation of the function if:

f′(x)=3x²−4x and f(1)=2

f(x)=x³−2x²+3  OR y=x³−2x²+3

500

Find the equation of the function if:

f′(x)=x² + e^4x-1 and f(0)=1

f(x) = x³/3 + e^4x-1/4 + 1 − 1/4e

Challenging questions

100

Differentiate:  x²+1/x

1−1/x²

200

∫ x^-3 dx

−1/2x² + C

300

Differentiate ln⁡(x^1/2)

1/(2x)

400

If f′(x)=2/x and f(1)=4, find the equation of the function.

 f(x)=2 ln⁡∣x∣+4

500

Integrate:

∫ (3x²+2x)e^{x^3+x^2} dx

e^{x^3+x^2} + C