Full Practice Exam 20 — Module 2
Practice Full Practice Exam 20 — Module 2 on The School of Mathematics (Full Practice Exam 20) with 22 scored questions in about 35 min. This set covers problems such as: “Which of the following equations is equivalent to \frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-…”; “Which of the following equations is equivalent to \frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-…”; “Which of the following equations is equivalent to \frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-…”. Work carefully, check explanations for misses, then retake to track improvement before test day.
Questions in this quiz (39)
Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?
- $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
- $$3(x-1)-(3x-2)=18$$
- $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
- $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$
Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?
- $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
- $$3(x-1)-(3x-2)=18$$
- $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
- $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$
Which of the following equations is equivalent to $$\frac{1}{3}\left(\frac{x}{2}-\frac{1}{6}\right)-\frac{3x-2}{9}=2$$?
- $$6\left(\frac{x}{2}-\frac{1}{6}\right)-2(3x-2)=36$$
- $$3(x-1)-(3x-2)=18$$
- $$\frac{x}{6}-\frac{1}{18}-\frac{x}{3}+\frac{2}{9}=2$$
- $$\frac{3x-1}{18}+\frac{3x-2}{9}=2$$
Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?
- $$14$$
- $$15$$
- $$16$$
- $$17$$
Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?
- $$16$$
- $$15$$
- $$14$$
- $$13$$
Emily needs to buy $$28$$ muffins for a school event. A single muffin costs $$0.75$$ dollars, a box of $$8$$ muffins costs $$5$$ dollars, and a box of $$15$$ muffins costs $$8$$ dollars. What is the least amount of money needed to purchase at least $$28$$ muffins?
- $$16$$
- $$15$$
- $$14$$
- $$13$$
$$4x+y=8$$$$ax+2y=c$$If the system has no solution, which of the following must be true?
- $$a=8\text{ and }c=16$$
- $$a=8\text{ and }c=10$$
- $$a=-8\text{ and }c=16$$
- $$a=4\text{ and }c=8$$
Given the system $$4x+y=8$$ $$ax+2y=c$$ If the system has no solution, which of the following must be true?
- $$a=8\text{ and }c=16$$
- $$a=8\text{ and }c=10$$
- $$a=-8\text{ and }c=16$$
- $$a=4\text{ and }c=8$$
There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?
- $$\frac{x-3}{x+y-1}$$
- $$\frac{x+2}{x+y-1}$$
- $$\frac{x-3}{y+x+2}$$
- $$\frac{x+3}{x+y-1}$$
Given the system $$4x+y=8$$ $$ax+2y=c$$ If the system has no solution, which of the following must be true?
- $$a=8\text{ and }c=16$$
- $$a=8\text{ and }c=10$$
- $$a=-8\text{ and }c=16$$
- $$a=4\text{ and }c=8$$
There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?
- $$\frac{x-3}{x+y-1}$$
- $$\frac{x+2}{x+y-1}$$
- $$\frac{x-3}{y+x+2}$$
- $$\frac{x+3}{x+y-1}$$
There are $$x$$ boys and $$y$$ girls in a classroom. If three boys leave the classroom and two girls enter, what fraction of the students remaining are boys?
- $$\frac{x-3}{x+y-1}$$
- $$\frac{x+2}{x+y-1}$$
- $$\frac{x-3}{y+x+2}$$
- $$\frac{x+3}{x+y-1}$$
Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?
- $$10\%\le x\le20\%$$
- $$15\%\le x\le25\%$$
- $$10\%\le x$$ < $$25\%$$
- $$15\%\le x$$ < $$20\%$$
Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?
- $$10\%\le x\le20\%$$
- $$15\%\le x\le25\%$$
- $$10\%<x\le20\%$$
- $$10\%\le x<20\%$$
There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?
- $$400$$
- $$500$$
- $$600$$
- $$700$$
Forty liters of a $$30\%$$ salt solution is mixed with another $$40$$ liters of a solution with concentration $$x\%$$. If the resulting $$80$$-liter mixture has a concentration between $$20\%$$ and $$25\%$$, which of the following could represent the possible values of $$x$$?
- $$10\%\le x\le20\%$$
- $$15\%\le x\le25\%$$
- $$10\%<x\le20\%$$
- $$10\%\le x<20\%$$
There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?
- $$500$$
- $$400$$
- $$600$$
- $$700$$
The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?
- $$4$$
- $$3$$
- $$2$$
- $$1$$
There are $$2000$$ residents in a town. Among them, $$1100$$ like soccer, $$700$$ like basketball, and $$300$$ like both sports. How many residents like neither sport?
- $$500$$
- $$400$$
- $$600$$
- $$700$$
A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?
- $$4$$
- $$5$$
- $$6$$
- $$7$$
The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?
- $$4$$
- $$3$$
- $$2$$
- $$1$$
The remainder when $$x$$ is divided by $$5$$ is $$3$$. What is the remainder when $$x^2+2x+4$$ is divided by $$5$$?
- $$4$$
- $$3$$
- $$2$$
- $$1$$
A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?
- $$4$$
- $$5$$
- $$6$$
- $$7$$
A chemist needs $$12$$ liters of a solution containing $$35\%$$ salt. She mixes a $$20\%$$ salt solution with a $$50\%$$ salt solution. How many liters of the $$20\%$$ solution are needed?
- $$4$$
- $$5$$
- $$6$$
- $$7$$
The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?
- $$(4,2)$$
- $$(-5,2)$$
- $$(-5,-2)$$
- $$(5,2)$$
The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?
- $$f(x)=-x^2+2x+8$$ $$f(x)=x^2-2x+8$$
- $$f(x)=-x^2+2x+8$$
- $$f(x)=-x^2+4x+8$$
- $$f(x)=x^2+2x-8$$
The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?
- $$(5,2)$$
- $$(-5,2)$$
- $$(-5,-2)$$
- $$(2,5)$$
The center of a circle is $$(0,0)$$, and the point $$(5,-2)$$ lies on the circle. What are the coordinates of the point symmetric to $$(5,-2)$$ with respect to the $$x$$-axis?
- $$(5,2)$$
- $$(-5,2)$$
- $$(-5,-2)$$
- $$(2,5)$$
A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?
- $$704\sqrt{2}$$
- $$74(\sqrt[3]{11})$$
- $$780$$
- $$80(\sqrt[3]{32})^2$$
The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?
- $$f(x)=-x^2+2x+8$$
- $$f(x)=x^2-2x+8$$
- $$f(x)=-x^2+4x+8$$
- $$f(x)=x^2+2x-8$$
The graph of a parabola passes through $$(-2,0)$$, $$(4,0)$$, and $$(0,8)$$. Which of the following could be its equation?
- $$f(x)=-x^2+2x+8$$
- $$f(x)=x^2-2x+8$$
- $$f(x)=-x^2+4x+8$$
- $$f(x)=x^2+2x-8$$
A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?
- $$704$$
- $$736$$
- $$768$$
- $$800$$
- $$80(\sqrt[3]{32})^2$$
What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?
- 4
A rectangular prism has volume $$1536$$ cm$$^3$$. The ratio of its length, width, and height is $$3:4:4$$. What is the surface area of the prism?
- $$704$$
- $$736$$
- $$768$$
- $$800$$
- $$80(\sqrt[3]{32})^2$$
What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?
- $$4$$
- $$6$$
- $$3$$
- $$9$$
What is the value of $$t$$ in the equation $$t=\sqrt{t+12}$$?
- $$4$$
- $$6$$
- $$3$$
- $$9$$
If $$\angle ABC=30^\circ$$ in $$\triangle ABC$$, what is the value of $$p$$?
- $$80^\circ$$
A linear function $$f$$ is defined by $$f(x)=ax+c,$$ where $$a$$ and $$c$$ are constants. The graph of $$f$$ passes through the point $$(k,2k)$$. If $$f(x+1)-f(x)=5$$ for all real numbers $$x$$, what is the value of $$c$$ when $$k=3$$?
- -9
The graph above shows Bob's weekly salary in dollars for the first four weeks working at a public library. Bob's salary at week $$4$$ is what percent greater than his salary at week $$1$$?
- $$33\frac{1}{3}\%$$
- $$40\%$$
- $$50\%$$
- $$66\frac{2}{3}\%$$