Quiz 1: FE Civil Mathematics and Statistics Practice

Questions in this quiz (10)

1. Determine the distance between the points $$A(2,5)$$ and $$B(-3,-1)$$ in the Cartesian plane.

   • $$5.83$$
   • $$6.40$$
   • $$7.81$$
   • $$8.49$$

2. Given vectors $$A=\langle2,-3,4\rangle$$ and $$B=\langle-1,5,2\rangle$$, calculate the dot product $$A\cdot B$$.

   • $$-9$$
   • $$3$$
   • $$7$$
   • $$11$$

3. Evaluate the definite integral $$\int_0^3(3x+2)dx$$

   • $$12$$
   • $$19.5$$
   • $$21$$
   • $$27.5$$

4. A dataset contains the values $$10,14,18,22,26$$. Calculate the population standard deviation.

   • $$5.66$$
   • $$6.32$$
   • $$7.21$$
   • $$8.00$$

5. Given the function $$f(x)=4x^3-3x^2+6x-2$$, determine the value of the derivative $$f'(x)$$ at $$x=1$$.

   • $$9$$
   • $$12$$
   • $$15$$
   • $$18$$

6. Determine the slope of the line passing through the points $$(1,-2)$$ and $$(5,6)$$.

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

7. Calculate the area under the curve $$y=2x$$ from $$x=0$$ to $$x=4$$.

   • $$8$$
   • $$12$$
   • $$16$$
   • $$20$$

8. Determine the magnitude of the vector $$v=\langle3,4,12\rangle$$.

   • $$5$$
   • $$13$$
   • $$15$$
   • $$169$$

9. A sample of $$100$$ measurements has a mean of $$60$$ and a standard deviation of $$10$$. Using a z-value of $$1.96$$ for a $$95$$ confidence level, what is the margin of error?

   • $$1.96$$
   • $$2.00$$
   • $$3.92$$
   • $$19.6$$

10. A circle has the equation $$x^2+y^2+4x-6y-12=0$$. Determine the radius of the circle.

    • $$3$$
    • $$4$$
    • $$5$$
    • $$7$$