Functions
If f(x)=4x+5 and g(x)=3x2-1, find f(g(x))
f(g(x))=12x2+1
x=24˚, 156˚
Calculate the expected value of the probability distribution table below:
x 1 2 3 4
p(x) 0.6 0.1 0.2 0.1
E(X)=1.8
Differentiate f(x)=(3x2+1)4 with respect to x
f'(x)=24x(3x2+1)3
Sketch the graph of y=(x-1)2
Parabola shifted right by 1
If f(x)=3x-1 and g(x)=x2+2, calculate f(-2)+3g(2)
f(-2)+3g(2)=11
State the equation and sketch the graph of a cosine graph with amplitude 2 and midline y=-1 in the domain 0≤x≤360˚
y=2cosx-1
From a group of 30 students, 15 play tennis, 17 play hockey and 8 play both. Draw a Venn Diagram to represent this information.
If a student is chosen at random, find the probability that they play hockey, given that they play tennis.
P(H|T)=8/15
Find the gradient of the tangent to the graph y=2x2+3x-1 at the point (1,4)
m=7
Sketch the graph of y=(x+1)2(x-4)(x+2)3
Polynomial degree 6, x-intercepts at x=-2, -1, 4
State the domain and range of f(x)=sqrt(x+7)
D: [-7,inf)
R: [0,inf)
Find x if cos2x=¼ and 0≤x≤2pi
x=pi/3, 2pi/3, 4pi/3, 5pi/3
A bag contains 6 red balls and 4 black balls. A ball is taken, the colour is noted and the ball is not replaced. A second ball is taken and the colour is noted.
Find the probability of obtaining 2 balls of a different colour.
P(different colours)=8/15
For what value of x is the gradient of the tangent to the curve f(x)=1-x2 equal to -6?
x=3
Sketch the graph of (x-4)2+(y+1)2=25
Centre (4, -1)
Radius 5
If f(x)=x+1 and g(x)=16-x2, find g(f(x))
g(f(x))=-x2-2x+15
Solve sinx=cosx in the domain 0˚≤x≤360˚
x=45˚, 225˚
Selma buys 5 raffle tickets. Find the probability that she wins 3 prizes in a row if 100 tickets are sold altogether. Once a winning ticket is drawn, it is not replaced.
P(WWW)=1/16170
A particle moves in a straight line with a displacement from O given by d=t2-6t+2 metres at time t seconds, t≥0. Find the velocity when t=2 seconds.
v(2)=-2
Sketch the graph of y=3^x+2
Exponential shifted up by 2
If f(x)=3x+4 and g(x)=⅓(x-4), find f(g(2))
f(g(2))=2
Simplify: 1/(1+cosx)+1/(1-cosx)
2cosec2x
In a group of 25 students, 13 like Maths, 11 like English and 3 like both. Draw a two-way table to represent this information.
If a student is chosen at random, find P(M'|E)
State the equation of the normal to the graph y=1/(x-1) at x=2. Give your answer in general form.
x-y-1=0
Sketch the graph of y=-3/(x+2)+1
Negative hyperbola shifted left by 2 and up by 1