Complex Numbers
Functions and Algebra
Calculus
Vectors
Other
100
The solutions are complex conjugate pairs and/or real values.
What are the solutions of a complex polynomial equation with real coefficients?
100
The straight line asymptotes of
y=(4x^3-1)/x^2.
What are y=4x, x=0 and y=0?
100
The slope of the curve y^2=x^2+sin(xy) for any given point.
CAS can be used.
What is
dy/dx=(2x+ycos(xy))/(2y-xcos(xy))?
100
The exact distance of the plane
3x-2y+z=5
from the origin.
What is 5/sqrt(14)?
100
The conclusion in a one-sided statistical test at the 5% level of significance if the p-value is 0.048.
What is: H0 should be rejected?
200
The specific type of graph that is the solution of abs(z+i)=abs(z-3+i) .
What is the perpendicular bisector line of the segment joining -i and 3 - i?
200
The Cartesian form and domain of the curve given parametrically by x=e^t and y=e^(-2t), t>=0.
What is
y=1/x^2, x>=1?
200
The integration technique or function used to integrate x/(4-x^2).
What is the substitution technique?
200
The cosine of the angle between the vectors
vec(AB)=3uli+4ulj and vec(CA)=2uli-ulj.
What is -2/(5sqrt(5))? ?
200
The contrapositive of: If a number is divisible by 15, then it is divisible by 5.
What is: "if a number is not divisible by 5 then it is not divisible by 15."
300
Arg(z^5 ) if z=2cis((2pi)/3) .
What is
-(2pi)/3?
300
The range of the function with rule f(x)=2arccos(3x-1)-pi/2 defined on its maximal domain.
What is [-pi/2,(3pi)/2]?
300
When x = 0.2, the value of y in exact form if Euler's method with a step size of 0.1 is used to solve the differential equation dy/dx=cos^2x with initial condition y = 1 when x = 0.
What is
1.1+0.1cos^2(0.1)?
300
The scalar projection of B onto A where
A=6ul(i)-2ulj+6ulk and B=-6uli-2ulj+ulk, correct to two decimal places.
What is -2.98?
300
The mean and standard deviation for consuming five chupa chups if the mean time to consume a single chupa chup is normally distributed with mean 2 minutes and standard deviation 0.5 minutes.
What is 10 minutes and sqrt(5)/2 mins?
400
The complex number w=i^3z is found by rotating z clockwise about the origin through this angle.
What is pi/2?
400
The solution of abs(x-2)>abs(x+1).
What is
x<1/2?
400
The differential equation for the amount of salt, Q g, present in the tank at time t minutes if a salt solution containing 5 g of salt per litre flows into a tank, initially filled with 40 L of water containing 4 g of salt, at 2 L/min, and the mixture is kept uniform by stirring and it flows out at the same rate it flows in.
What is
(dQ)/(dt)=10-Q/20?
400
The area of the parallelogram, to one decimal place, formed by the two vectors
ula=2uli+3ulj-ulk and ulb=-uli+4ulj+2ulk.
What is 15.2?
400
A possible solution for the differential equation with this slope field from a calculator, with
0<=x<=2 and -3<=y<=3.
What is y=1/x?
500
The simplified form of abs(iz)^2/(bar(z)) where z=a+bi, a, b in RR .
What is z?
500
An expression for sin(2t) in terms of t given that
tanx=t and pi<x<(3pi)/2.
What is (2t)/(1+t^2)?
500
The acceleration at x = 2 if
v=sqrt(4+2x^3).
What is 12?
500
The value of x if the three points with position vectors
ula=-uli-3ulj, ulb=xuli+3uljand ulc=2xuli+5ulj
are collinear.
What is 1/2?
500
The distance, to the nearest cm, travelled by a particle in the first 5 seconds if the velocity, v m/s, of the particle at time t seconds is given by
v=(3t)/(1+t^2), t>=0.
What is 4.89 m?