Algebra
Factorise:
6x2-11x-10
(2x-5)(3x+2)
solve the equation:
logx(64)=3
x=4
A function is given by f(x) = 2x2 - 10x +5
Find the gradient of the graph of f at the point where x=2
14
Find the x-coordinate of the point on the graph of h(x)=x2-12x where the gradient is equal to 4.
x=8
Nanaia Mahuta is New Zealands first what?
Female foreign minister
simplify:
(16x2)1/4
2x0.5
Lara says that she is thinking of a number. She:
squares the number
multiplies the answer by 6
adds 12 times the number she was first thinking of
subtracts 48
her answer is 0
What number could she be thinking of?
-4 or 2
The distance, s, of a tractior from a gate-post, in meters, is modelled by:
s=0.1t2+5t
Where t is the time in seconds since the tractor passed the gate-post and 0<=t<=20
Give the equation for the velocity of the tractor, and use this to find when the velocity of the tractor is 8ms-1
t=15 seconds
The curve y=f(x) passes through the origin (0,0) and has a gradient function
dy/dx=x2-2x
Find the co-ordinates of the point on the curve where x=6
(6,36)
What type of car featured in the back to the future movies
Delorean
Find the value of m so that only one value of x satisfies the equation:
4x^2-8x+m=0
m=4
x=1
Solve the equation:
3 X 2x+1/8x=96
x=-2
Find the equation of the tangent to the curve of h(x)=x2-12x at the point (1,-11)
y=-10x-1
The curve of f(x)=2x2+Ax+B has a tangent with a gradient 10 at the point (-2,33).
Find the coordinates of the point on the curve where x=4
(4,93)
Which creature was responsible for the most deaths of Australia's from 2000-2013?
Spider
Bee
Snake
Horse
Jellyfish
Croc
Tiger
Horse
The equation (x+2)-3sqr root (x+2)-4=0
x=14 and -1
-1 cannot be a solution.
Explain why the equation (3x+1)2=-7 does not have any real solutions and explain what this means graphically
discriminant=-252
therefore no real roots.
Graph of the parabola does not cut the x-axis
A train starts from rest.
Its acceleration t seconds after it starts is given by
a=1/4(20-t)ms-2
What distance does the train cover in the first 30 seconds?
s=1125 metres
A chemical is dropped into the water in a rectangular swimming pool at a point hal-way along its length.
After 0.1 minutes, the chemical spreads in a semi-circular shape with a radius r metres, where
r=1+2r
and t is the time in minutes since the chemical was added to the water.
When the chemical first reaches the far side of the pool area of the semi-circle is increasing at the rate of 60m2min-1
Find the width of the pool.
width=9.55 m
Which colour pill does Neo Swallow in the Matrix
Red
Rearrange the formula ax=5(x-1)
x=-log(5)/(log(a)-log(5))
Solve the equation
logx=2log(mx)
for x in terms of m
x=1/m2
g(x)=x3-9x2+24x-8
For what values of x is g a decreasing function?
You must justify your answer using calculus
2<x<4
And a justification
The consumption, f, of a car, in litres per 100km, is related to the velocity, v, in kmh-1, by the formula
f=16-0.2v+v2/250
Show that the fuel consumption is a minimum when v=25kmh-1
Shows that gradient function is = to 0 when v is 25
Justification of minimum
How many Cal does a Big mac have. (Within 20 Cal will be accepted
508 (488-528)