Timed Mini Exam 7 — Timed Mini Exams

Questions in this quiz (10)

1. Which of the following must always be true for two consecutive integers $$a$$ and $$b$$ with $$a$$ < $$b$$?

   • a is a prime number
   • $$b$$ is even
   • $$b^2-a^2$$ is even
   • $$a^2+b^2$$ is odd

2. A function Q is defined as follows. For $$x$$ > $$0$$, $$Q(x)=x^5+2x^4-10x-20$$. For $$x$$ < $$0$$, $$Q(x)=-x^5+2x^4+10x-20$$. What is the value of $$Q(-1)$$?

   • $$-27$$
   • $$-9$$
   • $$-29$$
   • $$-11$$

3. Maria is sewing a circular cover for a round table of diameter 36 inches. The finished cover must drape 6 inches over the edge on all sides. She will fold and hem 1 inch of fabric along the circular edge. Using one rectangular piece of fabric that is 54 inches wide, what is the minimum length, in inches, she must use to cut the cover in one continuous piece?

   • $$48$$
   • $$50$$
   • $$24$$
   • $$18$$

4. Two curves are given by $$f_1(t)=a_1\sin(b_1t)$$ and $$f_2(t)=a_2\cos(b_2t)$$ where $$b_1$$ > $$0$$ and $$b_2$$ > $$0.$$ From the graph, decide which statement about $$a_1$$ and $$a_2$$ must be true:

   • $$0$$ < $$a_1$$< $$a_2$$
   • $$0$$ < $$a_2$$ < $$a_1$$
   • $$a_1$$ < $$0$$ < $$a_2$$
   • $$a_1$$ < $$a_2$$ < $$0$$

5. For $$x$$ with $$0$$ < $$x$$ < $$\frac{\pi}{2}$$, simplify the expression $$\frac{\sqrt{1-\sin^2x}}{\cos x}+\frac{\sqrt{1-\cos^2x}}{\sin x}.$$

   • $$\sin 2x$$
   • $$-\cos 2x$$
   • $$\frac{1}{\tan 2x}$$
   • $$2$$

6. Let $$f(x)=\sqrt{x}$$ and $$g(x)=5x+c$$. The composition $$y=f(g(x))$$ passes through the point $$(3,4)$$. Find the value of c.

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

7. What is the real solution for x in the equation $$\log_3 81-\log_3 3=\log_9 x$$?

   • $$27$$
   • $$81$$
   • $$729$$
   • $$243$$

8. Triangle ABC has side lengths $$m$$, $$n$$,$$p$$ (in inches) and is not a right triangle.Reflect $$A$$ across side $$BC$$ to $$A'$$.What is the perimeter of quadrilateral $$A'BAC$$in terms of $$m$$, $$n$$, $$p$$?Note: $$AB=m$$, $$AC = p$$, $$BC=n$$

   • $$2(m+p)$$
   • $$2(n+p)$$
   • $$2(m+n)$$
   • $$4p$$

9. The point $$(4,6)$$ is shown in the coordinate plane. Which of the following lies on the line through $$(4,6)$$ with slope $$-\frac{3}{4}$$?

   • $$A(7,4)$$
   • $$B(8,3)$$
   • $$C(4,2)$$
   • $$D(8,8)$$

10. A function f is odd if and only if $$f(-x)=-f(x)$$ for every x in its domain. Which of the following is the graph of an odd function?