3D Vectors
Vector Calculus
Complex Numbers
Integration
Random Facts about Mr Cafun
100

Consider the points A(0,2,3) and B(4,5,2), determine the vector AB 

AB=(4,3,-1)

100

Determine the derivative of r(t) = (t2+1)i + (t-3)j

r'(t)=2ti + j

100

Consider the complex number a= 2 + 2i. Convert this to polar form.

a=(2.83, pi/4)

100

Determine the indefinite integral of sin2(2x)

1/2x - 1/8sin(4x)+c

100

What subjects does Mr Cafun teach this year.

12 MAS, 12PHY, 10PPH, 10PSM, 9MAT

200
Determine the vector perpendicular to the plane 3x-5y+2z=15

n=(3,-5,2) or n=3i - 5j + 2k

200

If the velocity of an object is v(t) = (2t+4)i +(3t2+5)j determine the displacement function if the initial displacement is s(0)=4i - 2j

s(t)=(t2+4t+4)i + (t3+5t-2)j

200

Consider the complex number z=3i. Determine z4

z4=81cis(2pi)=81

200

Determine the indefinite integral of sin4(x)cos(x)dx

1/5 sin5(x) + c

200

How long has Mr Cafun been teaching for

Since 2016, 8 years.

300

Consider the points A(1,-5,-2) and B(3,5,-1). Determine the vector equation of the line from A to B.

r = (1,-5,2) + k(2,10,1) or r=i - 5j +2k + k(2i + 10j +k)
300

Consider the vector function r(t)=2+3cos(t)i + 3+3sin(t)j. Describe the motion of the particle that follows this function.

Circular Motion, Centre (2,3), Radius 3, Anticlockwise Motion

300

Consider the function f(z)=z2+4z+5, determine if the complex number z=1+2i is a factor of f(z).

No by factorising z=-2+i or z=-2-i. By factor theorem z(1+2i)=6+12i.

300
Calculate the definite integral of xcos(x) from 0 to pi.

-2

300

What subjects did Mr Cafun do in year 12. There were 7 of them, points for 5 or more.

Maths B(Methods), Maths C(Specialist), Physics, IPT(Digital Solutions), English, Study of Religion and Tech Studies (Engineering).

400

Consider the points A(0,2,3), B(4,2,1) and C(3,0,-4). Determine the equation of the plane that contains these points.

2x-11y+4z=10

400

Consider the displacement functions of 2 particles r1(t) = (t+3)i + (t2+3t+4)j and r2(t)=(2t+2)i + (t+7)j. Determine if these particles will collide and if so where will they collide.

Will collide at t=1 at point (4,8) or position vector 4i + 8j

400

Determine the roots of the equation z3=81i.

z=4.32cis(-pi/2), z=4.32cis(pi/6), z=4.32cis(5pi/6)

400

Solve the following differential equation dy/dx = 3xy, y(0)=8.

y=8e3/2x^2

400

What other teachers is in the same aisle as Mr Cafun in the staffroom? There are 8 teachers per aisle.

Miss Ngo, Mrs Zeidler, Mrs Baker (Ms Chou), Mr Chen, Ms Johnson and just recently left Ms Schultz.

500

Determine the point of intersection of the line r= (-2, 3, 4)+ k(2,-1,-2) with the plane 3x+2y-5z=11

Intersection (0,2,2)

500

An object is shot out of a canon with a velocity of 20m/s at an angle of 300 to the horizontal.  If the cannon is on a platform that is 2m above the ground.  Determine if it will hit a target that is 4m high and 30m away from the canon.

Answer is no, when the object is at 30 will be 4.6m above the ground. Alternatively when the object is 4m above the ground isn31.5m away from target.

500

Factorise the equation f(z)=z4-2z3+3z2-2z+2

f(z)=(z+i)(z-i)(z-1+i)(z-1-i)

500

The population is governed by the equation dP/dt = kP. With the following conditions P(1) = 10, P(2) = 1500.  Determine the population at time t=4.

P= 34,000,000

500

What are Mr Cafun's top 3 most played computer games by play time.

World of Warcraft, League of Legends, Valheim.

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