Exam Revision
Simplify
(81x^(-4)y^5)/(36x^2y^(-2))
(9y^7)/(4x^6)
A particle moves in a straight line such that its displacement from a fixed point O at time t seconds is x metres. Find the initial velocity of the particle.
where
x=t^3/3-2t^2-5t+7
-5m/s
I have holes on the top and bottom. I have holes on my left and on my right. And i have holes in the middle, yet I still hold water. What am I?
A sponge
Where would you be if you were standing on the Spanish Steps?
Rome
State the natural domain and range for the function
y = (x+1)^2 - 5
(xER)
(y>=-5,yER)
Find the equation of the tangent to the curve
y = 3x^2 - 10x +1, x=2
y = 2x-11
What can you catch but not throw?
A cold
What is the largest Spanish speaking city in the world?
Mexico City
Conside the digits 0 to 9 inclusive and all the letters of the alphabet. Ten characters consisting of digits and letters are chosen. Determine the number of way of choosing exactly four vowels.
= 5C4 x 31C6
= 3 681 405
AT 1 pm on a hot day the rate, in cm^3 per minute, at which water in a swimming pool evaporates is given as below where t is the number of minutes after 1 pm. At what time will the evaporation stop on this particular day?
(dV)/dt = 60 -t/10
11pm
What can go up and down without moving?
The temperature
What is the highest-rated film on IMDb as of January 1st, 2022?
The Shawshank Redemption
Solve:
sin(x+10) = sqrt(3)/2
where 0<x<360
x+10 = 60, 120
x = 50, 110
A rectangular block has a square base of side x cm, a height a y cm and a volume of 80 cm^3. The base and top are to be covered with lacquer costing 5 cents/cm^2 and the sides with lacquer costing 4 cents/cm^2. Find the values of x and y for the minimum cost.
x=4, y=5
480c
What kind of room has no windows or doors?
A mushroom
What company was originally called "Cadabra"?
Amazon
Fully factorise the below expression, given that (2x+3) is a factor
6x^3-x^2-71x-84
(2x+3)(3x+7)(x-4)
A particle moves in a straight line so that at time t seconds, its displacement is x metres and its velocity is v m/s. Find the time taken to travel a total of 210 metres if the initial displacement is 3 metres away from the origin and
v = 2t^2 +3t+2
6 seconds
What goes around the world and stays in a corner?
A stamp
In what country would you find Mount Kilimanjaro?
Tanzania