Full Practice Exam 10 — Module 2
Questions in this quiz (22)
The total value of a rare comic book collection is $120 less than 7 times the number of comics, $$c$$. If the collection is worth 1,980 dollars, which equation represents this situation?
- $$7c+120=1980$$
- $$7c-120=1980$$
- $$120-7c=1980$$
- $$7(c-120)=1980$$
In the $$xy$$-plane, the line defined by $$y=\frac{3}{4}x-6$$ is line $$m$$. Line $$n$$ is perpendicular to line $$m$$. What is the slope of line $$n$$?
- $$\frac{3}{4}$$
- $$-\frac{4}{3}$$
- $$\frac{4}{3}$$
- $$-\frac{3}{4}$$
A basket contains $$5$$ green apples, $$4$$ red apples, and $$3$$ yellow apples. If one apple is chosen at random, what is the probability that the apple chosen is yellow?
- $$\frac{1}{4}$$
- $$\frac{1}{3}$$
- $$\frac{1}{5}$$
- $$\frac{1}{6}$$
A scientist begins with $$1200$$ bacteria in a petri dish. The bacteria population doubles every $$3$$ hours. Which equation models the population, $$P$$, after $$t$$ three-hour periods?
- $$P=1200+t^2$$
- $$P=1200(2)^t$$
- $$P=2400t$$
- $$P=1200\left(\frac{1}{2}\right)^t$$
A shipping company determines that the total weight, $$w$$, in pounds, of packages loaded onto a truck must be at least $$250$$ pounds less than $$180$$ times the number of crates, $$c$$. Which inequality represents this relationship?
- $$w\le180c-250$$
- $$w\ge180c-250$$
- $$w\le250-180c$$
- $$w\ge250-180c$$
A random sample of $$800$$ residents in a city found an average monthly electric bill of 92 dollars with a margin of error of 4 dollars. Which conclusion is most reasonable?
- Every resident pays between 88 dollars and 96 dollars each month.
- The average monthly electric bill for all residents is exactly 92 dollars.
- The plausible average monthly electric bill for all residents is between 88 dollars and 96 dollars.
- No conclusions can be made because only a sample was surveyed.
The perimeter of a rectangle is $$54$$ feet. The length is $$3$$ feet longer than twice the width. What is the width of the rectangle?
- $$6$$
- $$8$$
- $$12$$
- $$15$$
Circle $$A$$ has a radius that is $$14$$ times the radius of Circle $$B$$. The area of Circle $$A$$ is $$k$$ times the area of Circle $$B$$. What is the value of $$k$$?
- $$14$$
- $$28$$
- $$196$$
- $$392$$
In the equation $$7x+3sx=42$$, $$s$$ is a constant. If the equation has no solution, what is the value of $$s$$?
- $$-\frac{7}{3}$$
- $$\frac{7}{3}$$
- $$-3$$
- $$3$$
The frequency table below summarizes the scores of $$60$$ students on a mathematics competition.A new student joins the competition and earns a score of $$20$$. The new score is added to the data set. Which statement best compares the mean and median of the new data set to those of the original data set?
- The mean decreases and the median decreases.
- The mean decreases and the medians are equal.
- The mean increases and the median decreases.
- The mean increases and the medians are equal.
A square park has a perimeter of $$480$$ meters. A walking path is built along one diagonal of the square. The length of the diagonal is expressed as $$k\sqrt{2}$$ meters, where $$k$$ is a constant. What is the value of $$k$$?
- 120
In triangle $$ABC$$, the measure of angle $$B$$ is $$90^\circ$$, and $$BP$$ is an altitude to hypotenuse $$AC$$. The length of $$AB$$ is $$12$$, and the length of the hypotenuse $$AC$$ is $$4$$ greater than the length of $$AB$$. What is the value of the ratio $$\frac{BC}{BP}$$?
- $$\frac{4}{3}$$
- $$\frac{3}{2}$$
- $$\frac{8}{3}$$
- $$\frac{16}{3}$$
If $$a$$ and $$b$$ are numbers such that $$(a-4)(b+6)=0$$, then what is the smallest possible value of $$a^2+b^2$$?
- 16
The function $$f$$ is graphed in its entirety above. If the function $$g$$ is defined so that $$g(x)=f(-x)$$, then for what value of $$x$$ does $$g$$ attain its maximum value?
- $$-3$$
- $$-2$$
- $$0$$
- $$2$$
- $$3$$
The value of $$y$$ increased by $$12$$ is directly proportional to the value of $$x$$ decreased by $$6$$. If $$y=16$$, what is the value of $$x$$ when $$y=8$$.
- $$8$$
- $$\frac{52}{7}$$
- $$16$$
- $$\frac{10}{7}$$
The curve $$y=\frac{x^2}{2}$$ and the line $$y=\frac{x}{2}$$ intersect at the origin and at the point $$(a,b)$$, as shown in the figure above. What is the value of $$b$$?
- $$\\frac{1}{8}$$
- $$\\frac{1}{4}$$
- $$\\frac{1}{2}$$
- $$1$$
In the $$xy$$-plane, a parabola has vertex $$(9,-14)$$ and intersects the $$x$$-axis at two points. If the equation of the parabola is written in the form $$y=ax^2+bx+c$$, where $$a$$, $$b$$, and $$c$$ are constants, which of the following could be the value of $$a+b+c$$?
- $$-23$$
- $$-19$$
- $$-14$$
- $$-12$$
The table below shows student grades in four subjects.If one student grade is selected at random from all $$120$$ grades, which of the following is the probability that the selected grade is at least a $$B$$?
- $$\frac{19}{30}$$
- $$\frac{23}{40}$$
- $$\frac{31}{60}$$
- $$\frac{7}{20}$$
The table below shows the results of a student council election in three schools.Suppose a survey of $$350$$ randomly selected voters from all three schools accurately reflected the election results. Approximately how many of the surveyed voters would most likely have been supporters of Candidate X from North High?
- $$72$$
- $$84$$
- $$96$$
- $$108$$
If $$(x+1)^2=4$$ and $$(x-1)^2=16$$, what is the value of $$x$$?
- $$-3$$
- $$-1$$
- $$1$$
- $$3$$
The function $$q$$ is defined by $$q(x)=a|x-9|-53|x-9|+b$$, where $$a$$ and $$b$$ are constants, and $$a$$ > $$b$$ > $$53$$. If $$q(539)=h$$ and $$q(-521)=k$$, where $$h$$ and $$k$$ are constants, what is the value of $$32(-539)^{h-k}+347(9)^{k-h}$$?
- 379
The point $$(a,b)$$ is an intersection of the system of equations below when graphed in the $$xy$$-plane.$$3x^2-y-26=0$$$$y=-3x+10$$What is a possible value of $$a$$?
- $$-4$$
- $$6$$
- $$20$$
- $$26$$