Mini Exam 21 — Timed Mini Exams

Questions in this quiz (10)

1. Which of the following expressions is equivalent to $$x^3-5x^2+9x-45$$?

   • $$(x-5)(x^2+9)$$
   • $$(x-5)(x^2+9x+9)$$
   • $$(x^2+3)(x+5)$$
   • $$(x-3)(x^2-5)$$

2. A circle has a radius of $$8$$ centimeters. A central angle in the circle subtends an arc with a length of $$4\pi$$ centimeters. What is the measure of the central angle, in radians?

   • $$\frac{\pi}{4}$$
   • $$\frac{\pi}{2}$$
   • $$\frac{\pi}{3}$$
   • $$\frac{\pi}{6}$$

3. A school administrator wants to estimate the percentage of students who support adding more elective courses. She surveys $$120$$ students who are all members of the school's arts programs. Of these students, $$82\%$$ say they would like more elective options. Which of the following is true about the administrator's survey?

   • The survey accurately represents all students at the school.
   • The survey sample is biased because it includes a group that may have stronger opinions about electives.
   • The survey would be more accurate if only $$50$$ students were surveyed.
   • The survey results can be generalized to all schools in the state.

4. A circle has a radius of $$15$$ centimeters. A sector of this circle has a central angle measuring $$48^\circ$$. What is the area, in square centimeters, of the sector?

   • $$15\pi$$
   • $$30\pi$$
   • $$60\pi$$
   • $$90\pi$$

5. A person stands $$30$$ feet away from the base of a building. The angle of elevation from the person's eyes to the top of the building is $$40^\circ$$. The person's eyes are $$6$$ feet above the ground. What is the approximate height of the building, in feet?

   • $$25.2$$
   • $$31.2$$
   • $$36.2$$
   • $$41.2$$

6. The price of a certain tablet was originally $$P$$. The store first increased the price by $$25\%$$. A month later, the new price was decreased by $$20\%$$. By what percentage did the final price differ from its original price?

   • $$5\%$$ decrease
   • No change
   • $$5\%$$ increase
   • $$10\%$$ increase

7. A survey was conducted among $$150$$ students at Westview High School to determine whether they participate in a school sport. The results are summarized in the table.If a student surveyed is selected at random from those who participate in a sport, what is the probability that the student is female?

   • $$\frac{2}{5}$$
   • $$\frac{3}{7}$$
   • $$\frac{1}{2}$$
   • $$\frac{7}{15}$$

8. $$y=x^2+kx+5$$$$y=2x+1$$Consider the system of equations above, where $$k$$ is a constant. If the system has exactly one solution $$(x,y)$$, what is the sum of all possible values of $$k$$?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

9. Two linear functions, $$f(x)$$ and $$g(x)$$, are defined such that $$f(x)=ax+b$$ and $$g(x)=cx+d$$. The $$y$$-intercept of $$f(x)$$ is three times the $$y$$-intercept of $$g(x)$$, and the slope of $$f(x)$$ is $$4$$ greater than the slope of $$g(x)$$. If the graphs of $$f(x)$$ and $$g(x)$$ intersect at the point $$(2,8)$$, what is the value of $$b$$?

   • $$24$$
   • $$16$$
   • $$-12$$
   • $$-24$$

10. The mass, in grams, of a certain radioactive isotope $$t$$ days after an initial measurement can be modeled by the function $$M(t)=M_0(k)^t$$, where $$M_0$$ is the initial mass and $$k$$ is a constant. If the initial mass of the isotope is $$1024$$ grams and its mass is $$128$$ grams after $$3$$ days, what is the value of $$k$$?

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