X1 10MC (BB20)

Five Year 11 students and five Year 12 students are seated around a circular table.

 How many ways can the students be seated if the Year 11 Students and Year 12 students must alternate?

What is the derivative of $$\cos^{-1}3x\ ?$$  

A differential equation is given by $$y'=x^2+y^2+1$$ .

Which of the following slope fields best represents the differential equation?

What is the primitive function of $$y=\sin x\cos^3xdx\ ?$$

The diagram shows the graph of an inverse trigonometric function.

Which function produces the graph in the diagram?

The polynomial $$P\left(x\right)=x^3-12x^2+21x+k=0$$ has a double root.

What are the possible values of k ?

A fair coin is tossed 25 times.

 The cumulative probability of some z-scores on the normal distribution are provided:

$$P\left(Z<1\right)=0.84134$$  

$$P\left(Z<1.2\right)=0.88493$$  

$$P\left(Z<1.4\right)=0.91924$$  

$$P\left(Z<1.6\right)=0.94520$$  

What is the best estimate of the probability that the number of heads is greater than 15?

A solid of revolution is to be formed by rotating the shaded area shown between the graphs of $$y=x^2$$  and $$y=5-4x^2$$  about the y-axis.

Which integral would give the volume of the solid of revolution?

The variable y is a function of x as given by $$y=2x^2-x+1.$$  The variable x is a function of t, for $$t\ge0.$$  

$$x\left(t\right)$$  is initially 0 and decreases at a constant rate with respect to t.

Which of the following is true about the rate of change of y with respect to t?