# 0.1 Cumulative review

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Note: Answers to the Cumulative Review can be found in the Supplemental Resources. Please visit http://openstaxcollege.org to view an updated list of the Learning Resources for this title and how to access them.

No exercises.

## Chapter 2 the language of algebra

Simplify:

$1.\phantom{\rule{0.4em}{0ex}}5\left(3+2·6\right)-{8}^{2}$

Solve:

$2.\phantom{\rule{0.4em}{0ex}}17=y-13$

$3.\phantom{\rule{0.4em}{0ex}}p+14=23$

Translate into an algebraic expression.

$4.\phantom{\rule{0.4em}{0ex}}11$ less than the product of $7$ and $x.$

Translate into an algebraic equation and solve.

$5.\phantom{\rule{0.2em}{0ex}}$ Twice the difference of $y$ and $7$ gives $84.$

$6.\phantom{\rule{0.2em}{0ex}}$ Find all the factors of $72.$

$7.\phantom{\rule{0.2em}{0ex}}$ Find the prime factorization of $132.$

$8.\phantom{\rule{0.2em}{0ex}}$ Find the least common multiple of $12$ and $20.$

## Chapter 3 integers

Simplify:

$9.\phantom{\rule{0.4em}{0ex}}|8-9|-|3-8|$

$10.\phantom{\rule{0.4em}{0ex}}-2+4\left(-3+7\right)$

$11.\phantom{\rule{0.4em}{0ex}}27-\left(-4-7\right)$

$12.\phantom{\rule{0.4em}{0ex}}28÷\left(-4\right)-7$

Translate into an algebraic expression or equation.

$13.\phantom{\rule{0.2em}{0ex}}$ The sum of $-5$ and $13,$ increased by $11.$

$14.\phantom{\rule{0.2em}{0ex}}$ The product of $-11\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8.$

$15.\phantom{\rule{0.2em}{0ex}}$ The quotient of $7$ and the sum of $-4\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}m\text{.}$

$16.\phantom{\rule{0.2em}{0ex}}$ The product of $-3$ and is $-51.$

Solve:

$17.\phantom{\rule{0.4em}{0ex}}-6r=24$

## Chapter 4 fractions

$18.\phantom{\rule{0.2em}{0ex}}$ Locate the numbers on a number line. $\frac{7}{8},\frac{5}{3},3\frac{1}{4},5.$

Simplify:

$19.\phantom{\rule{0.4em}{0ex}}\frac{21p}{57q}$

$20.\phantom{\rule{0.4em}{0ex}}\frac{3}{7}·\left(-\frac{28}{45}\right)$

$21.\phantom{\rule{0.4em}{0ex}}-6\frac{3}{4}÷\frac{9}{2}$

$22.\phantom{\rule{0.4em}{0ex}}-3\frac{3}{5}÷6$

$23.\phantom{\rule{0.4em}{0ex}}-4\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\left(-\frac{6}{7}\right)$

$24.\phantom{\rule{0.4em}{0ex}}\frac{-2\frac{1}{4}}{-\frac{3}{8}}$

$25.\phantom{\rule{0.4em}{0ex}}\frac{7·8+4\left(7-12\right)}{9·6-2·9}$

$26.\phantom{\rule{0.4em}{0ex}}-\frac{23}{36}+\frac{17}{20}$

$27.\phantom{\rule{0.4em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{1}{2}+\frac{1}{3}\phantom{\rule{0.2em}{0ex}}}{\frac{3}{4}-\frac{1}{3}}$

$28.\phantom{\rule{0.4em}{0ex}}3\frac{5}{8}-2\frac{1}{2}$

$29.\phantom{\rule{0.4em}{0ex}}-\frac{2}{3}r=24$

## Chapter 5 decimals

Simplify:

$30.\phantom{\rule{0.4em}{0ex}}24.76-7.28$

$31.\phantom{\rule{0.4em}{0ex}}12.9+15.633$

$32.\phantom{\rule{0.4em}{0ex}}\left(-5.6\right)\left(0.25\right)$

$33.\phantom{\rule{0.4em}{0ex}}6.29÷12$

$34.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\left(13.44-9.6\right)$

$35.\phantom{\rule{0.4em}{0ex}}\sqrt{64}+\sqrt{225}$

$36.\phantom{\rule{0.4em}{0ex}}\sqrt{121{x}^{2}{y}^{2}}$

$37.\phantom{\rule{0.2em}{0ex}}$ Write in order from smallest to largest: $\frac{5}{8},0.75,\frac{8}{15}$

Solve :

$38.\phantom{\rule{0.4em}{0ex}}-8.6x=34.4$

$39.\phantom{\rule{0.2em}{0ex}}$ Using $3.14$ as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is $8$ inches.

$40.\phantom{\rule{0.2em}{0ex}}$ Find the mean of the numbers, $18,16,20,12$

$41.\phantom{\rule{0.2em}{0ex}}$ Find the median of the numbers, $24,29,27,28,30$

$42.\phantom{\rule{0.2em}{0ex}}$ Identify the mode of the numbers, $6,4,4,5,6,6,4,4,4,3,5$

$43.\phantom{\rule{0.2em}{0ex}}$ Find the unit price of one t-shirt if they are sold at $3$ for $\text{28.97}.$

## Chapter 6 percents

$44.\phantom{\rule{0.2em}{0ex}}$ Convert $\text{14.7%}$ to (a) a fraction and (b) a decimal.

Translate and solve.

$45.\phantom{\rule{0.4em}{0ex}}63$ is $35%$ of what number?

$46.\phantom{\rule{0.2em}{0ex}}$ The nutrition label on a package of granola bars says that each granola bar has $180$ calories, and $81$ calories are from fat. What percent of the total calories is from fat?

$47.\phantom{\rule{0.2em}{0ex}}$ Elliot received $\text{510}$ commission when he sold a $\text{3,400}$ painting at the art gallery where he works. What was the rate of commission?

$48.\phantom{\rule{0.2em}{0ex}}$ Nandita bought a set of towels on sale for $\text{67.50}.$ The original price of the towels was $\text{90}.$ What was the discount rate?

$49.\phantom{\rule{0.2em}{0ex}}$ Alan invested $\text{23,000}$ in a friend’s business. In $5$ years the friend paid him the $\text{23,000}$ plus $\text{9,200}$ interest. What was the rate of interest?

Solve:

$50.\phantom{\rule{0.4em}{0ex}}\frac{9}{p}=\frac{-6\phantom{\rule{0.2em}{0ex}}}{14}$

## Chapter 7 the properties of real numbers

$51.\phantom{\rule{0.2em}{0ex}}$ List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

(e) real numbers $-5,-2\frac{1}{4},-\sqrt{4},0.\overline{25},\frac{13}{5},4$

Simplify:

$52.\phantom{\rule{0.4em}{0ex}}\left(\frac{8}{15}+\frac{4}{7}\right)+\frac{3}{7}$

$53.\phantom{\rule{0.4em}{0ex}}3\left(y+3\right)-8\left(y-4\right)$

$54.\phantom{\rule{0.4em}{0ex}}\frac{8}{17}·49·\frac{17}{8}$

$55.\phantom{\rule{0.2em}{0ex}}$ A playground is $55$ feet wide. Convert the width to yards.

$56.\phantom{\rule{0.2em}{0ex}}$ Every day last week Amit recorded the number of minutes he spent reading. The recorded number of minutes he read each day was $48,26,81,54,43,62,106.$ How many hours did Amit spend reading last week?

$57.\phantom{\rule{0.2em}{0ex}}$ June walked $2.8$ kilometers. Convert this length to miles knowing $1$ mile is $1.61$ kilometer.

## Chapter 8 solve linear equations

Solve:

$58.\phantom{\rule{0.4em}{0ex}}y+13=-8$

$59.\phantom{\rule{0.4em}{0ex}}p+\frac{2}{5}=\frac{8}{5}$

$60.\phantom{\rule{0.4em}{0ex}}48=\frac{2}{3}x$

$61.\phantom{\rule{0.4em}{0ex}}4\left(a-3\right)-6a=-18$

$62.\phantom{\rule{0.4em}{0ex}}7q+14=-35$

$63.\phantom{\rule{0.4em}{0ex}}4v-27=7v$

$64.\phantom{\rule{0.4em}{0ex}}\frac{7}{8}y-6=\frac{3}{8}y-8$

$65.\phantom{\rule{0.4em}{0ex}}26-4\left(z-2\right)=6$

$66.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}x-\frac{2}{3}=\frac{1}{2}x-\frac{5}{6}$

$67.\phantom{\rule{0.4em}{0ex}}0.7y+4.8=0.84y-5.3$

Translate and solve.

$68.\phantom{\rule{0.2em}{0ex}}$ Four less than $n$ is $13.$

## Chapter 9 math models and geometry

$69.\phantom{\rule{0.2em}{0ex}}$ One number is $8$ less than another. Their sum is negative twenty-two. Find the numbers.

$70.\phantom{\rule{0.2em}{0ex}}$ The sum of two consecutive integers is $-95.$ Find the numbers.

$71.\phantom{\rule{0.2em}{0ex}}$ Wilma has $\text{3.65}$ in dimes and quarters. The number of dimes is $2$ less than the number of quarters. How many of each coin does she have?

$72.\phantom{\rule{0.2em}{0ex}}$ Two angles are supplementary. The larger angle is $24\text{°}$ more than the smaller angle. Find the measurements of both angles.

$73.\phantom{\rule{0.2em}{0ex}}$ One angle of a triangle is $20\text{°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measurements of all three angles.

$74.\phantom{\rule{0.2em}{0ex}}$ Erik needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $12$ feet tall and Erik has $15$ feet of wire. How far from the base of the antenna can he attach the wire?

$75.\phantom{\rule{0.2em}{0ex}}$ The width of a rectangle is $4$ less than the length. The perimeter is $96$ inches. Find the length and the width.

$76.\phantom{\rule{0.2em}{0ex}}$ Find the (a) volume and (b) surface area of a rectangular carton with length $24$ inches, width $18$ inches, and height $6$ inches.

## Chapter 10 polynomials

Simplify:

$77.\phantom{\rule{0.4em}{0ex}}\left(8{m}^{2}+12m-5\right)-\left(2{m}^{2}-7m-1\right)$

$78.\phantom{\rule{0.4em}{0ex}}{p}^{3}·{p}^{10}$

$79.\phantom{\rule{0.4em}{0ex}}{\left({y}^{4}\right)}^{3}$

$80.\phantom{\rule{0.4em}{0ex}}{\left(3{a}^{5}\right)}^{3}$

$81.\phantom{\rule{0.4em}{0ex}}{\left({x}^{3}\right)}^{5}{\left({x}^{2}\right)}^{3}$

$82.\phantom{\rule{0.4em}{0ex}}\left(\frac{2}{3}{m}^{3}{n}^{6}\right)\left(\frac{1}{6}{m}^{4}{n}^{4}\right)$

$83.\phantom{\rule{0.4em}{0ex}}\left(y-4\right)\left(y+12\right)$

$84.\phantom{\rule{0.4em}{0ex}}\left(3c+1\right)\left(9c-4\right)$

$85.\phantom{\rule{0.4em}{0ex}}\left(x-1\right)\left({x}^{2}-3x-2\right)$

$86.\phantom{\rule{0.4em}{0ex}}{\left(8x\right)}^{0}$

$87.\phantom{\rule{0.4em}{0ex}}\frac{{\left({x}^{3}\right)}^{5}}{{\left({x}^{2}\right)}^{4}}$

$88.\phantom{\rule{0.4em}{0ex}}\frac{32{a}^{7}{b}^{2}}{12{a}^{3}{b}^{6}}$

$89.\phantom{\rule{0.4em}{0ex}}\left(a{b}^{-3}\right)\left({a}^{-3}{b}^{6}\right)$

$90.\phantom{\rule{0.2em}{0ex}}$ Write in scientific notation: $\text{(a)}\phantom{\rule{0.2em}{0ex}}4,800,000\phantom{\rule{0.5em}{0ex}}\text{(b)}\phantom{\rule{0.2em}{0ex}}0.00637$

Factor the greatest common factor from the polynomial.

$91.\phantom{\rule{0.4em}{0ex}}3{x}^{4}-6{x}^{3}-18{x}^{2}$

## Chapter 11 graphs

Graph:

$92.\phantom{\rule{0.4em}{0ex}}y=4x-3$

$93.\phantom{\rule{0.4em}{0ex}}y=-3x$

$94.\phantom{\rule{0.4em}{0ex}}y=\frac{1}{2}x+3$

$95.\phantom{\rule{0.4em}{0ex}}x-y=6$

$96.\phantom{\rule{0.4em}{0ex}}y=-2$

$97.\phantom{\rule{0.2em}{0ex}}$ Find the intercepts. $2x+3y=12$

Graph using the intercepts.

$98.\phantom{\rule{0.4em}{0ex}}2x-4y=8$

$99.\phantom{\rule{0.2em}{0ex}}$ Find slope.

$100.\phantom{\rule{0.2em}{0ex}}$ Use the slope formula to find the slope of the line between the points $\left(-5,-2\right),\left(3,2\right).$

$101.\phantom{\rule{0.2em}{0ex}}$ Graph the line passing through the point $\left(-3,4\right)$ and with slope $m=-\frac{1}{3}.$

#### Questions & Answers

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
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A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?