Quiz 2: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. The equation of a parabola is $$y=x^2-6x+8$$. Determine the coordinates of the vertex.

   • $$(3,-1)$$
   • $$(2,0)$$
   • $$(3,1)$$
   • $$(-3,1)$$

2. Given $$f(x)=(2x^2+3)^4$$, find the value of $$f'(x)$$ at $$x=1$$.

   • $$320$$
   • $$640$$
   • $$1280$$
   • $$2000$$

3. Given vectors $$A=\langle1,2,3\rangle$$ and $$B=\langle2,-1,4\rangle$$, calculate the magnitude of the cross product $$|A\times B|$$.

   • $$7.00$$
   • $$9.00$$
   • $$10.25$$
   • $$12.25$$

4. A set of data points is given as: $$(1,1)$$, $$(2,3)$$, $$(3,4)$$, $$(4,6)$$, $$(5,7)$$. Using the least squares method, determine the slope of the best-fit line.

   • $$1.2$$
   • $$1.4$$
   • $$1.5$$
   • $$1.8$$

5. Evaluate the definite integral $$\int_0^1xe^x dx$$.

   • $$0.500$$
   • $$0.718$$
   • $$1.000$$
   • $$1.718$$

6. An ellipse has the equation $$\frac{x^2}{36}+\frac{y^2}{16}=1$$. Determine the eccentricity of the ellipse.

   • $$0.33$$
   • $$0.55$$
   • $$0.75$$
   • $$0.89$$

7. Given $$f(x)=x^3-4x^2+5x+2$$, find the value of the second derivative $$f''(x)$$ at $$x=2$$.

   • $$-2$$
   • $$0$$
   • $$4$$
   • $$8$$

8. A normally distributed variable has a mean of $$80$$ and a standard deviation of $$10$$. What is the approximate probability that a randomly selected value is less than $$90$$?

   • $$0.50$$
   • $$0.68$$
   • $$0.84$$
   • $$0.98$$

9. Determine the unit vector in the direction of $$v=\langle5,12\rangle$$.

   • $$\langle \frac{5}{13}$$ , $$ \frac{12}{13} \rangle$$
   • $$\langle \frac{12}{13}$$ , $$ \frac{1}{12} \rangle$$
   • $$\langle \frac{12}{13}$$ , $$ \frac{1}{13} \rangle$$
   • $$\langle \frac{1}{13}$$ , $$ \frac{12}{13} \rangle$$

10. A sample dataset contains the values: $$6,8,10,12,14$$. Calculate the sample variance.

    • $$8.0$$
    • $$10.0$$
    • $$12.5$$
    • $$20.0$$