$$\begin{gathered} The centre and radius of the circle with equation {\mathcal{x}}^2+ {\mathcal{y}}^2– 6\mathcal{y} = 4\mathcal{x} are \\ \left(A\right) Centre (0,3 ) radius 2 \\ \left(B\right) Centre (0,9 ) radius 2 \\ \left(C\right) Centre ( 2,3 ) radius \sqrt{13} \\ \left(D\right) Centre (2,3 ) radius 13 \end{gathered}$$

$$\begin{gathered} The number of fish in an inlet is estimated u\sin g the equation N=500-250\cos \left(\frac{\mathrm{\pi t}}{6}\right) \\ where t is the number of hours \sin ce low tide. Which statement is FALSE? \end{gathered}$$

$$\begin{gathered} The formula V=\mathcal{x}x(9 -4{\mathcal{x}}^2 ) expresses the volume of an irregular solid as a function \\ of one of its dimensions, \mathcal{x}. \\ The volume of the solid is a maximum when the value of x is \end{gathered}$$

$$\begin{gathered} \int \frac{\mathcal{x}-4}{{\mathcal{x}}^2}can be expressed as: \\ \left(A\right)\frac{1}{2}\ln {\mathcal{x}}^2+4\mathcal{x}+C \\ \left(B\right) \ln {\mathcal{x}}^2+\frac{4}{\mathcal{x}}+C \\ \left(C\right) \ln \mathcal{x}+4\mathcal{x}+C \\ \left(D\right) \ln \mathcal{x}+\frac{4}{\mathcal{x}}+C \end{gathered}$$

$$\begin{gathered} Which of the following statements is true if\left(2,-5\right) is a minimum turning point of \\ f\left(\mathcal{x}\right)andf\left(\mathcal{x}\right)=-f\left(-\mathcal{x}\right)? \\ \left(A\right)(-2,-5)is a maximum turning point of f\left(\mathcal{x}\right) \\ \left(B\right)(-2,5)is a maximum turning point of f\left(\mathcal{x}\right) \\ \left(C\right)(-2,-5)is a maximum turning point of f\left(\mathcal{x}\right) \\ \left(D\right)(-2,5)is a maximum turning point of f\left(\mathcal{x}\right) \end{gathered}$$

$$\begin{gathered} The acceleration of a particle moving in a straight line is given by the formula \\ a = 12t + 6 . Initially the particle has a velocity of -36 m/s. When is the \\ particle at rest? \\ A. t=0 \\ B. t=1 \\ C. t=2 \\ D. t=3 \end{gathered}$$

$A particle is moving on a straight line according to the function \mathcal{x}=2\mathrm{sin\pi }t. What is the period of oscillation?$

$$\begin{gathered} Which statement correctly describes the roots of 2{\mathcal{x}}^2+4\mathcal{x}-5=0 \\ The roots are equal, real and irrational. \\ The roots are equal, real and rational. \\ The roots are unequal, real and irrational. \\ The roots are unequal and unreal. \end{gathered}$$

$$\begin{gathered} Boxes are stacked in layers, where each layer contains one box less than the layer below. \\ There are six boxes in the top layer, seven boxes in the next layer and so on. \\ There are n layers altogether. \\ Which of the following is the correct expression for the number of boxes in the bottom layer? \end{gathered}$$

$$\begin{gathered} Which of the following statements is true for the equation 1-4\mathcal{x}-5{\mathcal{x}}^2=0 \\ No real roots. \\ One real root. \\ Two real and rational roots. \\ Two real and irrational roots \end{gathered}$$