Full Practice Exam 13 — Module 2
Questions in this quiz (22)
The graphs of the equations $$x=8$$ and $$y=x^2-20$$ intersect at the point $$(x,y)$$ in the $$xy$$-plane. What is the value of $$y$$?
- $$28$$
- $$36$$
- $$44$$
- $$64$$
In triangle $$\triangle DEF$$, the length of side $$\overline{DE}$$ is equal to the length of side $$\overline{DF}$$. The measure of angle $$\angle E$$ is $$(3x-20)^\circ$$ and the measure of angle $$\angle F$$ is $$(x+40)^\circ$$. What is the measure of angle $$\angle D$$, in degrees?
- $$20^\circ$$
- $$40^\circ$$
- $$60^\circ$$
- $$80^\circ$$
In a circle with center $$O$$, the radius is $$12$$ units. Points $$A$$ and $$B$$ are on the circle such that the measure of central angle $$\angle AOB$$ is $$150^\circ$$. What is the length of chord $$\overline{AB}$$?
- $$12$$
- $$12\sqrt{2}$$
- $$12\sqrt{3}$$
- $$6(\sqrt{6}+\sqrt{2})$$
Points $$A$$, $$B$$, $$C$$, and $$D$$ are distinct points on a circle. The measure of arc $$AB$$ is $$70^\circ$$, the measure of arc $$BC$$ is $$110^\circ$$, and the measure of arc $$CD$$ is $$80^\circ$$. What is the measure, in degrees, of inscribed angle $$\angle BAD$$?
- $$40$$
- $$70$$
- $$95$$
- $$110$$
$$y=x^2-8x+12$$$$y=3x-4$$How many distinct $$(x,y)$$ solutions does the given system of equations have?
- Exactly one
- Exactly two
- Zero
- Infinitely many
In right triangle $$\triangle XYZ$$ with the right angle at $$Y$$, the value of $$\cos(X)$$ is $$\frac{5}{13}$$. What is the value of $$\tan(Z)$$?
- $$\frac{5}{12}$$
- $$\frac{12}{5}$$
- $$\frac{5}{13}$$
- $$\frac{12}{13}$$
Which of the following expressions is equivalent to $$(4x-3y)^2-(2x+5y)(2x-5y)$$?
- $$12x^2-24xy+34y^2$$
- $$12x^2-24xy-16y^2$$
- $$20x^2-24xy+34y^2$$
- $$20x^2-24xy-34y^2$$
A polling organization surveyed $$1,200$$ randomly selected voters in a state to determine support for a new law. The survey found that $$54\%$$ of the voters support the law, with a margin of error of $$2.5\%$$. Based on the survey results, which of the following is the most appropriate conclusion about the proportion of all voters in the state who support the law?
- Exactly $$54\%$$ of all voters in the state support the law.
- It is plausible that between $$51.5\%$$ and $$56.5\%$$ of all voters in the state support the law.
- More than $$56.5\%$$ of all voters in the state support the law.
- Less than $$51.5\%$$ of all voters in the state support the law.
The table shows the results of a survey asking $$300$$ drivers about their age group and preferred vehicle type.If a randomly selected driver from the survey is $$40$$ years old or over, what is the probability that this person prefers an SUV?
- $$\frac{80}{300}$$
- $$\frac{80}{150}$$
- $$\frac{130}{300}$$
- $$\frac{150}{300}$$
A linear function $$h$$ models the total cost, in dollars, of renting a kayak, where $$x$$ is the number of hours rented. A $$3$$-hour rental costs $$27$$ dollars, and a $$7$$-hour rental costs $$51$$ dollars. Which equation defines $$h(x)$$?
- $$h(x)=6x+9$$
- $$h(x)=9x$$
- $$h(x)=5x+12$$
- $$h(x)=6x+6$$
A solid sphere with a radius of $$9$$ centimeters is melted down and recast into several identical solid cylinders. Each cylinder has a height equal to three times its base radius. If the volume of the metal is conserved during the process, and $$18$$ such cylinders are formed, what is the radius, in centimeters, of the base of each cylinder?
- $$2$$
- $$3$$
- $$4$$
- $$\sqrt[3]{18}$$
The value of an investment increased by $$P\%$$ in its first year. In its second year, the value decreased by $$2P\%$$. If the initial value of the investment was $$10,000$$ dollars and its value after two years was $$8,800$$ dollars, what is the value of $$P$$?
- $$8$$
- $$9$$
- $$10$$
- $$12$$
The graph shows the profit of Company X and Company Y in each quarter of last year. In which quarter was Company X's profit twice Company Y's?
- $$1$$
- $$2$$
- $$3$$
- $$4$$
In $$\triangle ABC$$, $$\overline{AB}\cong\overline{AC}$$. Point $$D$$ is on $$\overline{AC}$$ such that $$\overline{BD}\cong\overline{BC}$$. The measure of $$\angle ABD$$ is $$40^\circ$$. What is the measure of $$\angle BAC$$?
- $$30^\circ$$
- $$\frac{100}{3}^\circ$$
- $$48^\circ$$
- $$\frac{125}{2}^\circ$$
The population of trees in a forest has been decreasing by $$6\%$$ every $$4$$ years. The population at the beginning of $$2015$$ was estimated to be $$14,000$$. If $$P$$ represents the population of trees after $$t$$ years from $$2015$$, which equation gives the population of trees over time?
- $$P=14000(0.06)^{t/4}$$
- $$P=14000+0.94(4t)$$
- $$P=14000(0.94)^{4t}$$
- $$P=14000(0.94)^{t/4}$$
The graph of the function $$f$$ and line segment $$\overline{AB}$$ are shown in the $$xy$$-plane. For how many values of $$x$$ between $$-3$$ and $$3$$ does $$f(x)=c$$?
- 3
A community center wants to build a rectangular playground with an area of at least $$480$$ square meters and a perimeter of at least $$100$$ meters. If the length of the playground is $$x$$ meters and the width is $$y$$ meters, which of the following systems of inequalities represents the requirements?
- $$xy\ge100,\ x+y\ge480$$
- $$xy\ge240,\ x+y\ge100$$
- $$xy\ge480,\ x+y\ge50$$
- $$xy\ge480,\ x+y\ge100$$
In the $$xy$$-plane, the line $$y=3x+c$$ intersects the parabola $$y=x^2+cx+7$$ at the point $$(4,k)$$. If $$c$$ is a constant, what is the value of $$k$$?
- $$12$$
- $$16$$
- $$20$$
- $$\frac{25}{3}$$
In the figure, $$\overline{AB}$$ is parallel to $$\overline{GH}$$ and $$\overline{DF}$$ is parallel to $$\overline{BC}$$. If $$DE=1$$, $$EH=3$$, $$EG=2$$, and $$HC=10$$, what is the length of $$AD$$?
- $$\frac{5}{2}$$
- $$\frac{3}{2}$$
- $$\frac{10}{3}$$
- $$\frac{11}{2}$$
The function $$f$$ is defined by $$f(x)=3x+2$$, and the function $$g$$ is defined by $$g(x)=f(2x)-1$$. What is the value of $$g(10)$$?
- 61
A factory produces cables that must measure between $$95$$ meters and $$105$$ meters in length. If $$x$$ is the length, in meters, of a cable that meets this requirement, which inequality expresses the possible values of $$x$$?
- $$|x-100|$$ < $$5$$
- $$|x-105|$$ < $$5$$
- $$|x+100|$$ < $$5$$
- $$|x-100|\le5$$
The dot plot summarizes the number of flights taken in a year by $$19$$ college students. If the student who took $$6$$ flights in a year is removed from the data, which of the following correctly describes the changes to the statistical measures of the data?I. The mean decreases.II. The median decreases.III. The range decreases.
- III only
- I and II only
- I and III only
- I, II, and III