Advanced Quizzes — Quiz 11

Questions in this quiz (10)

1. The expression $$6x^4+17x^2+7$$ can be rewritten as $$(3x^2+a)(2x^2+b)$$, where $$a$$ and $$b$$ are positive integers, or as $$(3x^2+c)(2x^2+d)$$, where $$c$$ and $$d$$ are positive nonintegers. What is the value of $$a+c$$?

   • $$\frac{17}{2}$$
   • $$\frac{3}{2}$$
   • $$\frac{14}{3}$$
   • $$\frac{7}{3}$$

2. The function $$f(n)=7(20.44)^{\frac{n}{4}}$$ gives each term of a sequence as a function of the term's position, $$n$$, in the sequence, where $$n$$ is a whole number. The value of the term in position $$14$$ is $$p\%$$ more than the value of the term in position $$10$$. What is the value of $$p$$?

   • $$20.44$$
   • $$44$$
   • $$1944$$
   • $$2044$$

3. The expression $$bx^2-13x+22$$ can be rewritten as $$(hx-k)(x+j)$$, where $$b$$ is a constant and $$h$$, $$j$$, and $$k$$ are integer constants. Which of the following must be an integer?

   • $$\frac{k-13}{h}$$
   • $$\frac{13}{b}$$
   • $$-\frac{j}{22}$$
   • $$\frac{k}{22}$$

4. The table shows three values of $$x$$ and their corresponding values of $$y$$, where $$s$$ is a constant.There is a linear relationship between $$x$$ and $$y$$. Which of the following equations represents this relationship?

   • $$-9x+sy=-62$$
   • $$sx-9y=-62$$
   • $$-sx+9y=-62s$$
   • $$-9x+sy=-62s$$

5. For two acute angles, $$\angle A$$ and $$\angle B$$, $$\cos A=\sin B$$. The measures, in degrees, of $$\angle A$$ and $$\angle B$$ are $$9x+10$$ and $$48+5x$$, respectively. What is the value of $$x$$?

   • $$\frac{1}{18}$$
   • $$\frac{16}{7}$$
   • $$\frac{8}{7}$$
   • $$\frac{7}{5}$$

6. The table gives the volume of two similar cylinders. If the radius of cylinder $$A$$ is $$6$$ cm, what is the value of $$r-s$$?

   • 8640

7. The area of a triangle is equal to $$z^2$$ square inches. The base of the triangle is $$21-z$$ inches, and the height of the triangle is $$4-z$$ inches. Which of the following could be the value of $$z$$?

   • $$-28$$
   • $$-3$$
   • $$\frac{1}{3}$$
   • $$2$$

8. For the exponential function $$g$$, the value of $$g(3)$$ is $$q$$, where $$q$$ is a constant. Which of the following equivalent forms of the function $$g$$ shows the value of $$q$$ as the coefficient or the base?

   • $$g(x)=27(1.2)^{x+3}$$
   • $$g(x)=64(1.2)^{x-1}$$
   • $$g(x)=172(1.2)^x$$
   • $$g(x)=1036(1.2)^{x-3}$$

9. In $$\triangle ABC$$, $$\overline{AD}$$ is an altitude to $$\overline{BC}$$, with point $$D$$ on $$\overline{BC}$$. $$\overline{AE}$$ is an angle bisector of $$\angle BAC$$, with point $$E$$ on $$\overline{BC}$$. If $$\angle B=60^\circ$$, $$\angle C=30^\circ$$, and the length of $$\overline{AD}$$ is $$6\sqrt{3}$$, what is the length of $$\overline{DE}$$?

   • $$6\sqrt{3}-6$$
   • $$12\sqrt{3}-18$$
   • $$18-6\sqrt{3}$$
   • $$12\sqrt{3}-6$$

10. A data set consists of five distinct positive integers. The mean of the data set is $$10$$. If the smallest number in the data set is increased by $$2$$ and the largest number in the data set is decreased by $$2$$, which of the following statements must be true?

    • The mean increases.
    • The median decreases.
    • The median decreases.
    • The standard deviation increases.