Calculus

Derivatives

100

f(x)=x³

f'(x)=3x²

200

y=2x+4x²

dy/dx = 2+8x

300

f(x)=10x⁷+5x⁶

f'(x)=70x⁶+30x⁵

400

f(x)=x⁵+x⁴+x³+x²+x+1

f'(x)=5x⁴+4x³+3x²+2x+1

500

Find the anti-derivative:

f'(x) = 4x³-1

f(x) = x⁴-x+c

Finding Max/Min

100

Does y=x²-3x+4 have a minimum or a maximum?

minimum

200

Find the x-value of the maximum:

f(x)=-2x²+12x+4

max at x=3

300

Find the coordinate of the minimum:

y=x²+4

min at (0,4)

400

How many maximums and minimums (total) will the function y=x⁴+x3-x²-x-1 have?

3

500

Find the x-value of the maximum and minimum and classify:

f(x) = x³-3x²-9x+2

x=3 minimum

x=-1 maximum

Challenge

100

What is the anti-derivative of 0?

c

200

What is the derivative of velocity with respect to time?

Accelleration

300

Find the derivative:

f(x) = 60094 + 1243/256 - 8

f'(x)=0

400

What is the derivative of y=x^-1

dy/dx = -1x^-2

500

What is the derivative of f(x)=x^1/2

f'(x)=1/2 x^-1/2

Te Reo

100

What colour is kōwhai?

Yellow

200

If someone asks you “Kei te pēhea koe?” How could you reply?

Answers may vary

300

If someone is whā tekau mā ono years old, how old are they?

46

400

Who wrote the haka “Ka Mate”?

Te Rauparaha

500

What is the Māori name for Wellington?

Te Whanganui-a-Tara

Something Random Trivia

100

Tying what to a cat will result in a paradox if dropped?

Buttered bread/toast

200

What natural language has the fewest syllables with only 55?

Te Reo Māori

300

What country has more lakes than all other countries combined?

Canada

400

What three islands in the Pacific make up more than 90% of all land in the Pacific?

Papua New Guinea, North Island, South Island

500

What planet in the solar system has the largest mountain? Bonus points if you can name the mountain.

Mars, Olympus Mons