Quiz 4: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. A triangle has vertices $$A(0,0)$$, $$B(6,0)$$, and $$C(3,4)$$. Using the cross product method, determine the area of the triangle.

   • $$6$$ square units
   • $$9$$ square units
   • $$12$$ square units
   • $$18$$ square units

2. Given $$f(x)=\ln(2x^2+3)$$, determine the value of $$f'(x)$$ at $$x=1$$.

   • $$0.4$$
   • $$0.8$$
   • $$1.2$$
   • $$1.600$$

3. Determine the midpoint of the line segment connecting points $$A(4,-2,6)$$ and $$B(6,2,2)$$ in three-dimensional space.

   • $$(5,0,4)$$
   • $$(4,0,2)$$
   • $$(6,0,4)$$
   • $$(5,2,3)$$

4. A binomial experiment consists of $$4$$ trials with a probability of success of $$0.5$$ on each trial. Calculate the probability of exactly $$2$$ successes.

   • $$0.1250$$
   • $$0.25$$
   • $$0.375$$
   • $$0.5$$

5. Find the critical points of the function $$f(x)=x^3-6x^2+9x$$.

   • $$x=1$$ and $$x=4$$
   • $$x=1$$ and $$x=3$$
   • $$x=-1$$ and $$x=-4$$
   • $$x=2$$ and $$x=5$$

6. A triangle has vertices at $$A(2,4)$$, $$B(6,10)$$, and $$C(10,4)$$. Determine the coordinates of the centroid.

   • $$(6,6)$$
   • $$(6,5)$$
   • $$(8,6)$$
   • $$(6,8)$$

7. Evaluate the definite integral $$\int_0^1e^{3x}dx$$.

   • $$1.72$$
   • $$2.46$$
   • $$6.36$$
   • $$8.39$$

8. Given vectors $$A=\langle4,3\rangle$$ and $$B=\langle1,2\rangle$$, calculate the magnitude of the projection of $$A$$ onto $$B$$.

   • $$2$$
   • $$2\sqrt{2}$$
   • $$5$$
   • $$2\sqrt{5}$$

9. A population has a standard deviation of $$15$$. If a random sample of $$25$$ observations is taken, what is the standard error of the mean?

   • $$1.50$$
   • $$3$$
   • $$5$$
   • $$15$$

10. Determine the slope of the tangent line to the curve $$f(x)=\sqrt{x}$$ at the point where $$x=4$$.

    • $$\frac{1}{8}$$
    • $$\frac{1}{4}$$
    • $$\frac{1}{2}$$
    • $$2$$