Combinatorics
How many ways can 7 people be arranged in a line?
7! (5040)
What is the expansion of (x+1)3
x3+3x2+3x+1
Differentiate cos(5x-2)
-5sin(5x-2)
What is the x-intercept of y=ln(x)
1
What is the range of y=sin-1x
y [-pi/2,pi/2]
How many ways can 6 green marbles and 6 white marbles be arranged in a line?
2
What is the coefficient of x5 in the expansion of (3-x)9
-10206
Differentiate (4x2 - 9)0.5
4x/(4x2-9)0.5
Solve 4=log3(x/2)
162
Simplify cos-1(sin(4pi/3))
5pi/6
Six pairs of shoes of different colours and styles have been thrown into my wardrobe randomly. If it's dark and I can't see properly, how many shoes do I need to take from the wardrobe to guarantee I have a matching pair?
7 shoes
Simplify (30.5+1)5-(30.5-1)5
152
Differentiate 1/(1+x2)
-2x/(1+x2)2
What would the equation of bacertical growth be represented by if the amount of bacteria starts at 350 and doubles every 6 hours. Where B is bacteria amount and t is time in days?
B=350*16t
Find the inverse of y=1-2sin(x/3) for x [-3pi/2,3pi/2]
y=3sin-1((1-x)/2)
A father, a mother and 6 children sit in a circle. How many ways can they be arranged if the mother and fathers don't sit next to each other?
3600
Find the greatest coefficient of (2x+3)7
22680
Differentiate ln(sin(x)/esin(x))
cotx-cosx
Find k in the following:
(7/4)ln16 - (2/3)ln8 = kln2
5
NO CALCULATORS
cos(sin-1(0)-cos-1(1/2))
1/2
From a standard pack of 52 playing cards how many hands of 5 cards can be formed if there are exactly 2 pairs and another random card?
13C24C24C244C1 (123552)
What is the coefficient of x7 in (1+x)2(1+x)10
792
Differentiate 3e4x-1/cotx
3e4x-1(4tanx+sec2(x))
log2(1/x)+log2(1/x2)+log2(1/x3)+log2(1/x4)=-40
16
Simplify cos(tan-1(x/(1-x2)0.5)+cos-1(x))
0