Quiz 3: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. Determine the angle in degrees between vectors $$A=\langle2,1,2\rangle$$ and $$B=\langle1,2,2\rangle$$.

   • $$27.3^\circ$$
   • $$35.3^\circ$$
   • $$45.5^\circ$$
   • $$60.0^\circ$$

2. Evaluate the limit: $$\lim_{x\to3}\frac{x^2-9}{x-3}$$

   • $$0$$
   • $$3$$
   • $$6$$
   • undefined

3. A hyperbola has the equation $$\frac{x^2}{25}-\frac{y^2}{9}=1$$. Determine the slope of its asymptotes.

   • $$\pm\frac{1}{5}$$
   • $$\pm\frac{3}{5}$$
   • $$\pm\frac{4}{5}$$
   • $$\pm1$$

4. Given $$f(x)=x^2\cos(x)$$, find the value of $$f'(x)$$ at $$x=\pi$$.

   • $$0$$
   • $$-\pi^2$$
   • $$\pi$$
   • $$-2\pi$$

5. For the data pairs $$(1,3)$$, $$(2,5)$$, $$(3,6)$$, $$(4,8)$$, $$(5,9)$$, calculate the Pearson correlation coefficient $$r$$.

   • $$0.612$$
   • $$0.742$$
   • $$0.993$$
   • $$0.993$$

6. Evaluate the definite integral $$\int_0^{\pi/2}\sin^2(x)dx$$.

   • $$0.500$$
   • $$0.785$$
   • $$1.000$$
   • $$1.571$$

7. Determine the perpendicular distance from the point $$(2,-1)$$ to the line $$3x-4y+5=0$$.

   • $$0.6$$
   • $$1.0$$
   • $$1.4$$
   • $$3.0$$

8. A frequency distribution has values $$5$$, $$10$$, $$15$$, and $$20$$ with corresponding frequencies $$2$$, $$3$$, $$5$$, and $$4$$ respectively. Calculate the mean of this distribution.

   • $$11.50$$
   • $$12.86$$
   • $$13.93$$
   • $$15.00$$

9. For the implicit equation $$x^2+y^2=13$$, determine the value of $$\frac{dy}{dx}$$ at the point $$(2,3)$$.

   • $$-\frac{2}{3}$$
   • $$-\frac{3}{2}$$
   • $$\frac{2}{3}$$
   • $$\frac{3}{2}$$

10. A test score of $$65$$ is obtained from a distribution with a mean of $$70$$ and a standard deviation of $$5$$. Calculate the z-score for this value.

    • $$-1.0$$
    • $$-0.5$$
    • $$0.5$$
    • $$1.0$$