Quiz 5: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. A circle has the equation $$x^2+y^2-6x+8y-11=0$$. Determine the coordinates of its center.

   • $$(3,-4)$$
   • $$(-3,4)$$
   • $$(6,-8)$$
   • $$(-6,8)$$

2. Given $$f(x)=\frac{x^2-1}{x-1}$$, determine the value of $$f(x)$$ at $$x=2$$.

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

3. Vectors $$A=\langle4,-6,2\rangle$$ and $$B=\langle2,k,1\rangle$$ are parallel. Determine the value of $$k$$.

   • $$-3$$
   • $$-6$$
   • $$3$$
   • $$6$$

4. A dataset has a mean of $$40$$ and a standard deviation of $$10$$. Calculate the coefficient of variation $$CV$$.

   • $$10%$$
   • $$20%$$
   • $$25%$$
   • $$40%$$

5. Calculate the area of the region bounded by the curves $$y=x^2$$ and $$y=9$$.

   • $$12$$ square units
   • $$18$$ square units
   • $$24$$ square units
   • $$36$$ square units

6. Vectors $$A=\langle2,-1,k\rangle$$ and $$B=\langle3,4,-2\rangle$$ are perpendicular. Determine the value of $$k$$.

   • $$-1$$
   • $$1$$
   • $$2$$
   • $$5$$

7. A parabola has the equation $$y=\frac{x^2}{12}$$. Determine the coordinates of its focus.

   • $$(0,2)$$
   • $$(0,3)$$
   • $$(2,0)$$
   • $$(12,0)$$

8. A sample of $$25$$ observations has a mean of $$60$$ and a sample standard deviation of $$10$$. Using a t-value of $$0.264$$ for a $$95\%$$ confidence level with $$24$$ degrees of freedom, determine the upper limit of the confidence interval.

   • $$62.00$$
   • $$61.13$$
   • $$60.53$$
   • $$60$$

9. Determine the coordinates of the inflection point for the function $$f(x)=x^3-6x^2+4$$.

   • $$(1,-1)$$
   • $$(2,-4)$$
   • $$(3,-5)$$
   • $$(2,-12)$$

10. A vector $$v=\langle1,2,2\rangle$$ makes an angle $$\alpha$$ with the positive $$x$$-axis. Determine the value of $$\cos\alpha$$.

    • $$\frac{1}{3}$$
    • $$\frac{2}{3}$$
    • $$\frac{1}{\sqrt{9}}$$
    • $$\frac{2}{\sqrt{9}}$$