Advanced Quizzes — Quiz 3

Questions in this quiz (10)

1. $$x-4=\sqrt{9x-20}$$What is the sum of the solutions to the equation?

   • $$\frac{17+\sqrt{145}}{2}$$
   • $$18$$
   • $$9$$
   • $$4$$

2. What is the sum of the solutions of $$(3x-2)^2=(x+4)^2$$

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

3. The function $$f(x)=x^4-6x^2$$ is graphed in the $$xy$$-plane. If $$k$$ is a constant such that the equation $$f(x)=k$$ has exactly $$4$$ real solutions, which of the following could be the value of $$k$$?

   • $$-10$$
   • $$-5$$
   • $$0$$
   • $$8$$

4. Which of the following is equivalent to $$x^4-20x^2+101$$

   • $$(x^2-10)^2+1$$
   • $$(x^2+10)^2+1$$
   • $$(x^2-5)^2+76$$
   • $$(x^2+5)^2-76$$

5. The price of a bicycle is increased by $$30\%$$, then decreased by $$20\%$$, then increased by $$10\%$$. The final price is what percent of the original price?

   • $$105.6\%$$
   • $$110\%$$
   • $$114.4\%$$
   • $$120\%$$

6. Sophia has 2000 dollars in a checking account and 5000 dollars in a savings account. The checking account earns $$2\%$$ interest compounded annually, and the savings account earns $$5\%$$ interest compounded annually. Assuming she leaves both accounts untouched, which expression represents how much more interest Sophia will earn from the savings account than from the checking account after $$4$$ years?

   • $$5000(1.05)^4-2000(1.02)^4$$
   • $$(5000(1.05)^4-5000)-(2000(1.02)^4-2000)$$
   • $$5000(1.05)(4)-2000(1.02)(4)$$
   • $$(5000(1.05)(4)-5000)-(2000(1.02)(4)-2000)$$

7. The radius of a circle is increased by $$40\%$$. By what percent does the area of the circle increase?

   • $$40\%$$
   • $$80\%$$
   • $$96\%$$
   • $$116\%$$

8. The force of attraction between two particles can be determined by the formula:$$F=\frac{12q_1q_2}{r^2}$$where $$F$$ is the force between them, $$r$$ is the distance between them, and $$q_1$$ and $$q_2$$ are constants representing the charges. If the distance between the particles is tripled, the resulting force is what fraction of the original force?

   • $$\frac{1}{3}$$
   • $$\frac{1}{9}$$
   • $$\frac{1}{18}$$
   • $$\frac{1}{27}$$

9. The graph of $$y=P(x)$$ is shown. Which of the following functions could represent the graph?

   • $$P(x)=x^2-8x+12$$
   • $$P(x)=x^3-8x^2+12x$$
   • $$P(x)=x^2+8x+12$$
   • $$P(x)=x^3+8x^2+12x$$

10. Which of the following lists all solutions to the system of equations shown above?

    • $$(2,5)$$
    • $$(0,1)$$
    • $$(1,0),(3,7)$$
    • $$(2,3)$$