Timed Mini Exam 14 — Timed Mini Exams

Questions in this quiz (10)

1. What is the complex conjugate of $$(3-2i\sqrt{5})^2+(4+i\sqrt{3})(1-2i)?$$

   • $$2\sqrt{3}+i\sqrt{3}$$
   • $$-7+8i$$
   • $$\sqrt{3}-2i\sqrt{3}$$
   • $$-7+2\sqrt{3}-i(\sqrt{3}-8-12\sqrt{5})$$

2. In the figure, lines $$PQ$$ and $$RS$$ intersect at $$T$$, and $$UT$$ ⟂ $$PQ$$. If $$∠QTS=40°$$, find the value of $$2a+3b−c$$.

   • $$50$$
   • $$60$$
   • $$70$$
   • $$80$$

3. What is the solution set to $$|3x+5|\le10$$?

   • $$(-\infty,-5]$$
   • $$[-5,\frac{5}{3}]$$
   • $$(-\infty,-5)$$
   • $$(-5,3)$$

4. Describe the symmetry of the graph of the relation $$y=|x|^3-4|x|.$$

   • Symmetric only with respect to the x-axis
   • Symmetric with respect to the x-axis and y-axis, but not the origin
   • Symmetric with respect to the x-axis, y-axis, and the origin
   • Symmetric only with respect to the y-axis

5. Angles $$α$$ and $$β$$ lie in Quadrant I. If $$\cos(\alpha)=\frac{4}{5}$$ and $$\sin(\beta)=\frac{5}{13}$$, what is the value of $$\cos(\alpha+\beta)$$?

   • $$\frac{32}{65}$$
   • $$\frac{8}{13}$$
   • $$\frac{1}{5}$$
   • $$\frac{33}{65}$$

6. A hyperbola has its center at the origin and a horizontal transverse axis of length $$20$$ units. The distance between the center of the hyperbola and each focus is $$13$$ units. What is the equation of the hyperbola?

   • $$\frac{x^2}{13^2}+\frac{y^2}{10^2}=1$$
   • $$\frac{x^2}{10^2}-\frac{y^2}{13^2}=1$$
   • $$\frac{x^2}{10^2}-\frac{y^2}{69}=1$$
   • $$\frac{x^2}{10^2}+\frac{y^2}{13^2}=1$$

7. A teacher has 18 students and will assign 3 different students to 3 distinct topics (Algebra, Geometry, Statistics), one student per topic, with no student doing more than one topic. In how many ways can this be done if order matters?

   • $$\frac{18!}{3!}$$
   • $$4896$$
   • $$\frac{18!}{15!+3!}$$
   • $$4500$$

8. Find the minimum and maximum values of the function $$f(x,y)=x-4y$$ on the region defined by $$x\le3,$$ $$1\le y\le6,$$ $$y\le2x+4.$$

   • Min Value: $$-21$$ Max Value: $$3$$
   • Min Value: $$-23$$ Max Value: $$3$$
   • Min Value: $$-18$$ Max Value: $$3$$
   • Min Value: $$-23$$ Max Value: $$-1$$

9. Which graph represents the inverse of the given function?

10. Which graph shows a function with period $$\frac{\pi}{2}$$ and amplitude $$2$$?