SAMPLE Nursing Entrance Exam Prep
THE ULTIMATE CREDIT-BY-EXAM STUDY GUIDE FOR:
Nursing Entrance Exam Prep
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Nursing Entrance Exam Preparation Study Guide
3rd Edition 9/30/2022
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Table of Contents Chapter 1: Reading
1.1 Key Ideas and Details 1.1.1 Summarizing Complex Text 1.1.2 Question-Answer Relationships 1.1.3 Inference 1.1.4 Topic, Main Idea, Supporting Details, Genres, and Themes 1.1.5 Topic and Summary Sentences 1.1.6 Predictions, Inferences, and Conclusions 1.1.7 Informational Source Comprehension 1.2.1 Facts, Opinions, Biases, and Stereotypes 1.2.2 Text Structure 1.2.3 Characteristics of Different Passage Types 1.2.4 The Meaning of Words and Phrases 1.2.5 Context Clues 1.2.6 Figurative Language 1.2.7 Technical and Connotative Meaning 1.2.8 Position and Purpose 1.2.9 Evaluating the Author’s Point of View (POV) 1.2.10 Historical Context 1.2.11 Text Feature Basics 1.3 Integrative Knowledge and Ideas 1.3.1 Primary Sources 1.3.2 Culture and Themes in Literature 1.3.3 Genre vs. Theme 1.3.4 Using Evidence to Make Predictions and Draw Conclusions 1.3.5 Evaluate an Argument Chapter 1: Review Questions 1.2 Craft and Structure
10 10 10 11 11 12 13 13 13 15 15 15 16 18 18 19 20 21 22 22 23 24 24 25 25 25 26 27 35 35 35 38 38 40 43 45 45 45
2.1 Language Usage 2.1.1 Spelling Capitalization
Chapter 2: English and Language Usage
2.1.2 Punctuation and Grammar 2.1.3 Subject Verb Agreement 2.1.4 Formal and Informal Language 2.2.1 Sentence Parts of Speech Colons, Semicolons, and Commas
2.2 Writing
2.2.2 Sentence Structures 2.2.3 Well-Organized Paragraphs 2.3 Elements of the Writing Process 2.3.1 Prewriting 2.3.2 Writing 2.3.3 Revising 2.3.4 Editing 2.3.5 Publishing Chapter 2: Review Questions 3.1 Order of Operations 3.2 Fractions 3.2.1 Addition and Subtraction of Fractions 3.2.2 Multiplication of Fractions 3.2.3 Division of Fractions 3.3 Percentages 3.3.1 Converting Fractions to Percentages 3.3.2 Calculations with Percentages 3.3.3 Percent Increase and Decrease 3.4 Measurement 3.4.1 Metric Conversions 3.4.2 Temperature 3.5 Algebra 3.5.1 Inequalities
45 46 46 47 48 49 49 49 50 53 53 54 54 54 55 55 56 57 58 58 58 59 60 60 62 63 64 65 66 66 67 69 72 72 72 73 75 75 77
Chapter 3: Math – Part 1
3.5.2 Mathematical Translations of Equalities from Words 3.5.3 Mathematical Translations of Inequalities from Words 3.5.4 Solving Equations 3.5.5 Solving Inequalities 3.5.6 Ratios and Proportions 3.5.7 Coordinate Plane 3.5.8 Linear Equations
Chapter 3: Review Questions 4.1 Data Interpretation 4.1.1 Data Tables 4.1.2 Histograms
Chapter 4: Math – Part 2
4.1.3 Vertical Bar Graphs 4.1.4 Horizontal Bar Graphs 4.1.5 Line Graphs
4.1.6 Pie Charts 4.1.7 Scatterplots 4.2 Numerical Summaries 4.2.1 Mean 4.2.2 Median 4.2.3 Mode 4.2.4 Range 4.3 Geometry 4.3.2 Perimeter 4.3.3 Area 4.3.4 Circles Chapter 4: Review Questions 5.1 Basic Conversions 5.1.1 Customary Units 5.1.2 Metric Units Chapter 5: Review Questions 6.1 Anatomical Positions 6.2 Homeostasis 6.3 Water Balance 6.4 Gas Exchange 6.5 Electrolytes 6.6 Bodily Systems 6.6.1.1 Functions 6.6.1.2 Components
78 78 79 79 80 81 82 82 82 83 84 85 85 86 86 87 92 92 92 93 95 97 98 99
4.3.1 Regular vs Irregular Shapes 4.3.5 Congruent Circles 4.3.6 Types of Angles 4.3.7 Area of a Sector of a Circle
Chapter 5: Conversions
Chapter 6: Human Anatomy & Physiology – Part 1
100 100 101 103 103 104 104 106 107 107 108 109 111 112 112
6.6.1 The Integumentary System – Tour of the System 6.6.1.3 Common Diseases and Disorders 6.6.1.4 Medical Terminology 6.6.2 The Skeletal System – Tour of the System 6.6.2.1 Functions 6.6.2.2 Components 6.6.2.3 Common Diseases and Disorders 6.6.2.4 Medical Terminology 6.6.3 The Nervous System – Tour of the System
6.6.3.1 Functions 6.6.3.2 Components 6.6.3.3 Common Diseases and Disorders 6.6.3.4 Medical Terminology 7.1.1 Brain Regions and Landmarks 7.1.2 Embryology of the Brain 7.1.3 Ventricles of the Brain 7.1.4 Protection and Support of the Brain 7.1.5 The Blood Supply to the Brain 7.1.6 The Blood-Brain Barrier 7.1.7 Brain Functions Pons The Cerebellum The Mesencephalon The Diencephalon The Hypothalamus 7.2.1 Sensory Receptors 7.2.2 The Detection of Stimuli 7.2.3 The Interpretation of Sensory Information 7.2.4 Adaptation 7.2.5 General Sensory Receptors 7.2.6 Special Senses 7.3 The Endocrine System – Tour of the System 7.3.1 Functions 7.3.2 Components 7.3.3 Common Diseases and Disorders 7.3.4 Medical Terminology 7.4 The Cardiovascular System – Tour of the System 7.4.1 The Pericardium 7.4.2 Superficial Anatomy of the Heart 7.4.3 The Heart Wall 7.4.4 Cardiac Muscle Tissue 7.4.5 Internal Anatomy and Organization 7.4.5 Phases of the Cardiac Cycle 7.4.6 Blood Flow to the Heart 7.5 The Immune System – Tour of the System Chapter 6 Review Questions 7.1 The Human Brain 7.2 The Sensory System
114 114 115 115 117 119 119 119 120 121 121 121 121 122 122 123 123 124 124 126 127 127 128 128 128 129 134 135 135 137 138 138 139 140 141 141 141 146 146 147
Chapter 7: Human Anatomy & Physiology – Part 2
7.5.1 The Lymphatic System and Body Defenses 7.5.2 Nonspecific Defenses 7.5.3 Specific Defenses 7.5.4 Functions 7.5.5 Components 7.5.6 Common Diseases and Disorders
147 148 148 149 149 151 152 154 154 155 155 156 156 156 157 158 159 159 160 161 161 162 163 163 164 164 165 165 166 167 168 170 170 170 170 171 171 172 172
Chapter 7 Review Questions Chapter 8: Anatomy & Physiology – Part 3
8.1 The Respiratory System – Tour of the System 8.1.1 Inhalation 8.1.2 Exhalation 8.1.3 Functions 8.1.4 Components 8.1.5 Common Diseases and Disorders 8.1.6 Medical Terminology 8.2 The Digestive System – Tour of the System 8.2.1 Functions 8.2.2 Components 8.2. Common Diseases and Disorders 8.2.4 Medical Terminology 8.3 The Genitourinary System – Tour of the System 8.3.1 Functions 8.3.2 Components 8.3.3 Common Diseases and Disorders 8.3.4 Medical Terminology 8.4 The Reproductive System – Tour of the System 8.4.1 Functions 8.4.2 Components 8.4.3 Common Diseases and Disorders 8.4.4 Medical Terminology Chapter 8 Review Questions
9.1 The Scientific Method 9.1.2 Hypothesis 9.1.3 Prediction 9.1.4 Experiment 9.2 Life and Physical Science 9.2.1 Macromolecules
Chapter 9: General Sciences
9.1.1 Observation and Analysis
9.2.2 Chromosomes, Genes, Proteins, DNA, and RNA 9.2.3 Mitosis and Meiosis 9.3 Mendel’s Laws of Heredity Phenotypes and Genotypes 9.3.1 Heredity: Genes and Mutation 9.3.2 Heredity: Mendelian Inheritance 9.3.3 Law of Segregation 9.3.4 Punnett Squares 9.3.5 Law of Independent Assortment 9.4 General Biology 9.4.1 Ecology 9.4.2 Natural Selection 9.5 Atomic Structure 9.5.1 Atoms 9.5.2 Elements 9.6 The Periodic Table 9.7 Chemical Reactions 9.7.1 Compound 9.7.2 Substance 9.7.3 Molecule 9.6.1 Structure of the Periodic Table 9.7.4 Ions and salts 9.7.5 Acids and Bases 9.7.6 Phase 9.7.7 Redox 9.7.8 Bonding 9.7.9 Reaction 9.7.10 Equilibrium 9.8.1 Solid 9.8.2 Liquid 9.8.3 Gas 9.8.4 Plasma 9.8.5 Evaporation 9.8.6 Vaporization 9.8.7 Condensation 9.8.8 Oxidation and Reduction 9.8 Properties of Substances States of Matter
173 175 176 177 179 179 180 180 181 181 183 184 184 185 185 186 187 187 187 188 189 190 190 191 191 191 192 192 192 193 193 193 194 194 195 195 196 198
Chapter 9 Review Questions Chapter Review Questions Answer Key
Chapter 1: Reading Overview
Thischapterwillfocusonkeyconceptsanddetails,structure,andhowtoassembleitsothatitis readable to others. Integrative knowledge and ideas combine whatyoualreadyknowandwhat youreadtocomeupwithconclusionsandotherideasthatmakewhatyoureadandwritemore meaningful. 1.1 Key Ideas and Details 1.1.1 Summarizing Complex Text Tosuccessfullyanswerthequestionsinyourexaminationandunderstandthereadingmaterial you will encounter in the future, it is necessary to summarize complex texts. ● Comprehension ● Onemustreadandunderstandthetext,whichmayrequirebreakingdownlongsentences andunderstandingdifficultwords.Next,theymustidentifythemainideasandkeypoints, which means they must have a good enough understanding of the text to know the difference between what is essential and what is not. ● Communication To condense information into a smaller space. To reduce the number of words in your writing. To select thebestwordsthatconveyyourmessageandeliminatewordsthatadd novaluetoyourwriting.Thismeansreducinginformationtoessentialideastoexpandthe breadth or depth of your writing.
Text Summary What is included in the Text Summary? - Main Idea - Important Ideas - Key words - Use your own words The purpose of text summaries is to determine
your ability to identify and comprehend the main idea, purpose, and key supporting ideas of apieceofreadingmaterial.Todoso,youwillfirstneedtoreadthematerialinitsentirety.Once you have done so, take a moment to consider the following questions: ● What is the main idea of the piece? ● What is the author's purpose for writing it? ● What are the key supporting ideas? Once you have considered these questions, you should be able tosummarizethepieceinyour own words.
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1.1.2 Question-Answer Relationships The Question-Answer Relationship (QAR) strategy can be used after students have read atext. QAR teaches students how toidentifythetypeofquestionandwheretofindtheanswerwithin the text. There are four main types of questions that are examined in the QAR strategy.
1.1.3 Inference What is an inference?
Inferenceistheprocessofderivingaconclusionbasedonevidenceandreasoning.Itallowsusto go beyond the information that is explicitly stated in a passage or text and to make logical deductions based on what we know or assumes to be true.
In simple terms, to make an inference is to draw a logical conclusion from the information. Inferences are often made from literature and are sometimes called literary inferences.There aretwotypesofinferences:literalandinterpretive.Literalinferencesarebasedontheliteral,or actual,wordsinthetext.Aninterpretiveinferenceisbasedontheimpliedmeaningofthewords and text.
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Inference - Drawing a Logical Conclusion Themainideaofatextcanbeimpliedthroughtheanalysisofindividualsentences.Todothis,we needtoconsiderwhateachsentencesaysaboutthecommontopic,identifywhatisthecommon threadtheindividualsentencesseemtoshare,andthinkoftheideathatemergesastheauthor’s implied main idea. Finally, we need to think about the purpose of the text. Types of Inference Questions ● Factual Questions (explicit, will be clearly statedin the passage) and helps us draw factual conclusions. ● Implicit Questions which require us to look at thebigger picture. ● Clarifying Questions by understanding the meaningof a word or a phrase. Answering Inference Questions - Strategies ● Lookfor keywords suchasimply,infer,predict,conclude,etc.Theyidentifythequestionas an inference question. ● Make notes while reading. Pay special attentiontowordssuchas:but,yet,although,since, except, moreover, unless, nonetheless,however,inthepassage.Thesewordssignalashift, and the ideas that follow these words are often the subject of inference questions. ● Elimination, look for wrong answers . Incorrect answers to inference questions often involve making an unsupported leap based on the details of the passageorcontainingan error that goes against the information provided. The elimination of obviously wrong choicesmakesiteasiertofindtherightanswer.Inthesecases,itisbestnottoanticipatean answer but simply evaluate the answer choices given. 1.1.4 Topic, Main Idea, Supporting Details, Genres, and Themes ● A topicisthegeneralsubjectmatterofthetext.Forexample,abooktitled EatingClean:A Simple, Healthy DietingSolution isaboutanewtypeofdietforhealthyeating.Whatisthe book’stopic?Thereareseveralanswerswhichincludedieting,healthyeating,andcooking healthy meals. All these answers are correct, but some are more general than others. ● Themainideaofatextisitsspecificmessage.Itisalsothereasonwhythetextwaswritten. Forthedietingbookintheexampleabovethemainideacanbeexpressedas,“Inorderto live a healthy lifestyle, eating a healthy, clean diet is imperative.” ● The supporting details of the text explain the main idea. These details give the reader reasons to believe the main idea. The supporting details for the dieting book in the examplecouldincludestudiesconductedonhealthyeating,specificfoodswhicharegood for your health, and examples of healthy recipes. ● Agenreisacategoryofliterature(orart/music)characterizedbysimilaritiesinform,style, andorsubjectmatter.Comedy,Sci-Fi,Romance,Fantasy,Action&Adventurearejustafew formsofagenre.Genresaretypicallydefinedbasedonthecontentorintentionofastory. For example, comedies are meant to be humorous and elicit laughter.Whileanythingin the horror genre should scare the audience.
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● A theme is an idea, subject, or concept that a text refers to repeatedly. Eating Clean: A Simple,HealthyDietingSolutionmighthavethefollowingthemes:achievinggoodhealth, self-improvement, and positive body image. 1.1.5 Topic and Summary Sentences Topic sentences reveal the main point of a paragraph, essay, or book. It makes a statement that will be explained, discussed, or elaborated. Supporting sentences follow the topic sentence and contain ideas that support the topic sentence. Summary sentences areatthe endofaparagraph,chapter,section,ordocument.Theyoftensummarizethemainpointand draw a conclusion based on the topic. 1.1.6 Predictions, Inferences, and Conclusions An inference is a logical conclusionthatisnotwritteninthetext.Instead,itisthoughtofby the reader based on information found in the text. Inferences are also known as reading between the lines and can be thought of as predictions. Predictions, conclusions, and inferences are based on personal judgment and prior experiences. 1.1.7 Informational Source Comprehension In informational source comprehension questions, a graphic or statement willbegiven,and you must answer questions related to the graphic or statement. You will be askedquestions related to: ● Sets of directions ● Graphic Representation of Information ● Recognizing events in a sequence Sets of Directions Directions can take the form of lists or can appear in paragraph form. If theyarefoundin paragraph form, it may be helpful to rearrange them into a list. Each step in a set of instructionsmayrequireyoutousetheresultsfromtheprevioussteps.Ifthisisthecase,it may be helpful to write down the steps as you complete them, as in the following example. Example Read the following set of directions, then answer the question. 1. Start with the word “CINEMA” 2. Add the word “TO” at the end of the word. 3. Add the word “GRAPH” at the end of the word. 4. Add the letter “Y” at the end of the word. What new word has been spelled? a. Cinema b. Graphics c. Cinematography
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d. Cinematograph The new word that has been spelled is cinematography. Graphic Representations of Information
Graphic representations of data can come in the form of charts, graphs,maps,drawings,or photos.Allchartsandgraphshavethesamegoal:tovisuallyrepresentnumericalinformation so the viewer can easily beinformedandmakejudgmentsbasedonthedatarepresented.A pie chart represents a concept in the form of a circle where the circle is divided up into representational portions according to the data (given in percentages). Example Use the pie chart to answer the question.
The pie chart breaks down the data collected on the most popular months for families to go camping. Which was the most popular month for families to go camping?
ThemostpopularmonthforcampingwasApril,giventhatittakesupthelargestportionof the pie chart. Recognizing Events in a Sequence The ability to identify the components of a story, including the beginning, middle, and end, as well as to retell the events within a text in the order in which they occurred, is known as sequencing.Oneofthemostimportantskillsforunderstandingatext,particularlynarratives,is the ability to put the events in order. Sequential - Does not use a time element. It refersto a fixed order in which there is a logical pattern. E.g. First, second, then, now, afterwards. Chronological - Uses a time element. It refers toevents in an order in which they happen and requires a time element. E.g. Today, later, often, seldom, all day, since, last year.
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1.2 Craft and Structure 1.2.1 Facts, Opinions, Biases, and Stereotypes
Factsarebasedonreal,provableevents,orsituations.Opinionsarebeliefsthatarebasedon personalideas,judgments,orthoughtsratherthanonindisputablefacts.Itcanbedifficultto tell when a writer’s work is fact or opinion when they personally believe that their strong opinions are facts. Biases and stereotypes can alter a writer’s ability to draw accurate conclusions. Biases are ideas or opinions that can cloud a person’s judgment and preventa person from making fair judgments. Stereotypes are oversimplified opinions about entire groupsofpeopleorthingsthatdonotconsiderindividualdifferences.Criticalreadingisused to carefully analyze a text, judge its credibility and determine the author’s intentions in writing.
1.2.2 Text Structure Text structure refers to the way in which a text is organized. A sequence of ideas can be presented in a bulleted or numbered list so that therelevantinformationistogetherandin sequential order. A problem-solution structure can be used to organize problemsandtheir solutions in a way that is easy to read. Problems can be addressed in one paragraph and solutionsinthenext.Acause-effectstructurecanbeusedtodescribeanactionfirstandthen the consequence. A descriptive passage does not follow a formatting style but uses many adjectives to flesh out an idea or concept and make it more visible to the reader. Example Read the following text, and then answer the question about text structure. Ingredients: ● 2 cups of sugar
● 1 cup of milk ● 1 cup of flour ● 1 cup of coconut
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● ½ cup of chocolate chips ● 1 tsp salt ● 1 tsp vanilla
Determine the text structure:
a. Problem-solution structure b. Cause-effect structure
c. Descriptive passage d. A sequence of ideas
Thetextisasequenceofideasandfollowstheconventionsofthattextstructurebecauseitisa list. 1.2.3 Characteristics of Different Passage Types Narrative, expository, technical, and persuasive are different types of passages. A narrative text tells a story. It can also relate to a chain of events. An expository text introduces or explains a certain subject. It can also give background information neededto under- stand later concepts. Expository texts analyze information objectively. Technical writing involves precise information on a specific topic and a formal style of writing. Persuasive writing tries to change the opinion of the reader.
Onetextcanfitunderseveraldifferentcategoriesofpassages.Forexample,ascientistmaybe writing an article about whales. The article may contain background information about whalesincludinghowtheyliveandwhattheyeat.Thearticlecouldalsocontainthescientist’s opinion on whale hunting,andtheauthormaytrytopersuadereaderstobelievethatwhale hunting is wrong. In this case, the article is both expository and persuasive because it contains background information on whales and it contains the author-’sopiniononwhale hunting.
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Chapter 2: English and Language Usage Overview
In this chapter we will discuss English language usage. We will pay special attention to spelling, punctuation, and grammar, formal and informal language. Additionally, we will focus on writing, how to form sentence structures, how to organize paragraphs, and the elements of the writing process. 2.1 Language Usage 2.1.1 Spelling It is important to note common spelling rules and be able to identify incorrectly spelled words. One should also be able to determine the correct selections of homophones based on context. Here is a brief review of common usage mistakes ofthe English language. ● May and might o ‘May’ can act as a principal verb, which can express permission or possibility. ▪ Examples: Let’s wait, the meeting may have started. -- May I begin now? o ‘May’ can act as an auxiliary verb, which expresses a purpose or wish ▪ Examples: May you find kindness in the sight of your employer. -- May your wishes come true. -- People go to school so that they may be educated. o ‘Might’ is the past tense of may. ▪ Example: I asked if I might begin o ‘Might’ signifies a weak or slim possibility or polite suggestion. ▪ Examples: You might find him in his office, but I doubt it. -- You might offer to help if you want to. ● Lie and lay o The verb lay should always take an object. The three forms of the verb lay are: laid, lay, and laid. ▪ Examples: Lay on the bed. -- The tables were laid by the students. -- Let the little kid lie. -- The patient lay on the table. o The verb lie (recline) should not take any object. The three forms of the verb lie are: lay, lie, and lain. ▪ Example: The dog has lain there for 30 minutes. o Note: The verb lie can also mean “to tell a falsehood”. This verb can appear in three forms: lied, lie, and lied. This is different from the verb lie (recline) mentioned above. ▪ Examples: The accused is fond of telling lies. -- Did she lie?
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● Would and should o The two verbs ‘would and should’ can be correctly used interchangeably to signify obligation. The two verbs also have some unique uses too. Should is used in three persons to signify obligation. o The past tense of will is “would,” and so “would” generally follows the same principles as “will.” o “Would” is specially used in any of the three persons to signify willingness, determination, and habitual action. ▪ Examples: They would go for a test run every Saturday. -- They would not ignore their duties. --She would try to be punctual. o The past tense of shall is ‘should’, and so “should” generally follows the same principles as “shall.” ▪ Examples: I should go after work. -- People should exercise every day. -- You should be generous. ● Principal and auxiliary verbs o Two principal verbs can be used along with one auxiliary verb as long as the auxiliary verb form suits the two principal verbs. ▪ Examples: Several people have been employed and some promoted. -- A new tree has been planted, and the old has been cut down. ● Again, note the difference in the verb form. ● Can and could o Can is used to express capacity or ability. ▪ Examples: I can complete the assignment today. -- He can meet up with his target o Can is also used to express permission. ▪ Examples: Yes, you can begin. o In the sentence below, “can” was used to mean the same thing as “may.” However, the difference is that the word “can” is used for negative or interrogativesentences,while“may”isusedinaffirmativesentencestoexpress possibility. ▪ Examples: They may be correct. ● Positive sentence - use may. Can this statement be correct? A question using “can.” It cannot be correct. Negative sentence using “can.” o The past tense of “can” is “could”. It can serve as a principal verb when it is used to express its own meaning. ▪ Examples: In spite of the difficulty of the test, he could still perform well. ● “Could” here is used to express ability.
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Chapter 3: Math – Part 1 3.1 Order of Operations
Mathematical operations must be performed in the correct order when you are performing calculations with numbers. First, you must perform the operations in parenthesis. From there you would then simplifytheexponentsandthencompleteany multiplication or division from left to right. Finally, addition or subtraction is completed. ● Parenthesis – (anything in here first) ● Exponents – Then %* or - a square root is also atype of exponent ● Multiplication and Division – next × or ÷ ● Addition and Subtraction – finally + or – or ± Use the mnemonic device PEMDAS (Please Excuse My Dear Aunt Sally) to help you to remember the order of operations. Example Simplify the following expression: 5 + 5 × 5 − 5 ÷ 5 = a. 9 b. 29 Example Simplify the following expression: (2 + 2) × 2 2 = a. 10
b. 4 c. 8 d. 16
c. 5 d. 0
The correct answer is B. To simplify this expression, go through the order of operations.
The correct answer is D. To simplify this expression, go through the order of operations.
5 + 25 − 5 ÷ 5 = 5 + 25 − 1 =
4 × 2 2 =
5 + 24 = 29
4 × 4 = 16
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3.2 Fractions 3.2.1 Addition and Subtraction of Fractions
Begin by converting any mixed numbers (if there areany)intoimproperfractions.This meansconvertinganynumberthatrepresentsthesumofawholenumberandaproper fractionintoafractionwhosenumeratorisgreaterthanthedenominator.Thenyouwill determine the least common denominator (LCD) for the fractions. The LCD is the smallest common multiple of the denominators. This is the least number that both denominators divide into evenly. Once you have the LCD, then you will rewrite each fractionasanequivalentfractionwiththeleastcommondenominator.Thenyouwilladd or subtract the numerators, while keeping the common denominator the same. Lastly, check to make sure that the fraction is the simplest fraction. This means that the only common factor between the numerator and the denominator is 1. Example
Question What is the sum of
Solution The LCD of 8 and 12 is 24
a. b. c. d.
Therefore, the answer is A.
3.2.2 Multiplication of Fractions Firstconvertanymixednumberstoimproperfractions.Then,simplifythefactorsinthe numerator(thetopnumberinthefraction)withfactorsinthedenominator(thebottom numberofthefraction).Lastly,multiplythenumeratorstogetherandthedenominators together. Be sure that the fraction is simplified (the only common factor between the numerator and the denominator is1).Whenworkingwithwordproblemskeepinmind that the word “of” usually signifies multiplication. Example: Simplify the expression: 1 2 3 × 2 1 7 Since they are mixed numbers, change them to improper fractions: 1 2 3 = 5 3 2 1 7 = 1 7 5 © 2022 Achieve Page 53 of 198
Chapter 4: Math – Part 2 4.1 Data Interpretation
Dataplaysaveryvitalroleinourdaytodaylife.Whenthedataathandissmall,itiseasyto understand, analyze and interpret in order to formsubstantialdecisions.However,incase thedataisverylarge,thenitisgenerallypresentedindifferentways,likedatatables,graphs, bar charts, pie charts, scatterplots, histograms etc. In such cases, it is imperative that the userisabletounderstandandanalyzethedataprecisely.Theprocessofunderstandingthe data from its represented form is known as data interpretation. Nowweshalltakeeachofthesepreciseformsandunderstandhowtheycanbeinterpreted using some examples. 4.1.1 Data Tables Usingdatatables,datacanberepresentedinaformoftabularrepresentation.Tablescanbe single or multiple with horizontal rows and vertical columns. The data corresponding to eachcellcorrespondstoitsuniquerowandcolumn.Aninstanceofthedatatableisgivenas under: Sale of different models of cars (in million) Year Hyundai General Motors Mercedes Honda 2012 50 76 43 67 2013 54 74 48 73 2014 57 69 55 69 Intheabovetable,wearegiventhesaleoffourcarmodelsforthreeconsecutiveyears.From this data table, we can find, analysis, and interpret the following information: Examples ● General Motors sold more models in 2012 than any other year ● The sale of Hyundai increased by 8% in 2013 as compared to 2012 ● Mercedes witnessed maximum growth of about 14.58% in 2014 as compared to previous year
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4.1.2 Histograms Is a commonmethodtographicallyrepresentthefrequenciesdataset.Ahistogramcanbe used for a larger data set. For example, if you have a large population and are gathering statisticalexamscoresfromnumerousareacolleges,youmayhave100studentsoutof500 who receive a 94 on an exam. That is a large data set and it is not practical to generate a stem-and-leafplot.Histogramsareusuallygeneratedusinggraphingorstatisticalsoftware. You can also generate them by hand! Let’s take a look at a histogram.
This is the typical structureofahistogram.Whattypeofinformationcanweobtainfroma histogram? Although I have not assigned any actual data or numerical values, we can see that there are several parts to the histogram. ● The solid box seems to be the highest.Thisrepresentsthehighestfrequencyforthe dataset.Therefore,ifweweretolookatadataset,themajorityofthevalueswouldfall within the region of the solid box. ● Now looking to the right and left of our highest frequency, we can see that the histogram is dividedintotwosides.Thepolka-dotandstripedboxesaretotheleftof our highest frequencies. These representhighervaluesthanourfrequency.Ifthatis confusing, think of it this way. We will say thedatarepresentstheamountoftimeit takesstudentstocompleteanexam.Mostofthestudentstake65minutestocomplete the exam (solid box), the polka-dot and striped boxes represent the number of studentswhotakelessthan65minutestocompletetheexam.Wewillsaythestriped boxrepresentsstudentswhocancompletetheexamin55minutesandthepolka-dot box represents students who can complete the exam in 45 minutes. o You can see that there are fewer students who completed the exam in 45 minutes.
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Chapter 5: Conversions
5.1 Basic Conversions From converting from one unit to another, you first need to recognize if your unit is a customaryormetricunit.CustomaryunitsarethoseunitsusedintheUnitedStates.Below is a list of some common customary units.
5.1.1 Customary Units
Common Customary Measurements
Length
Weight
Time
Capacity
1 foot = 12 inches 1 yard = 36 inches 1 yard = 3 feet 1 mile = 5280 feet 1 mile = 1760 yards
1 pound = 16 ounces 1 ton = 2000 pounds
1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 year = 12 months
1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 quart = 4 cups 1 gallon = 4 quarts 1 gallon = 16 cups
1 year = 365 days 1 leap year = 366 days
To convert from one unit to another you need to use dimensional analysis. Dimensional analysis requires that you know a conversion factor(s) that relates one unit of measure to another. See the example for more instructions. Example Convert 2 yards into inches. Step 1: Start with your given amount and divide it by one. 2 yards 1 Step 2: Identify a conversion factor that will relate your factor to the next. This might require more than one conversion factor. ● 1 yard = 3 feet ● 1 foot = 12 inches Step 3: Multiply your original amount by the conversion factors. Set these factors up as a fraction so that the original unit is on the bottom and the new unit is on the top. 2 yards × 3 feet × 12 inches 1 1 yard 1 foot
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Step 4: Notice which units have both a top and bottom component. You cancanceltheseunitsout.Ifyousetuptheconversionscorrectly,thenyou should only have one unit remaining.
Step5:Calculateyourfinalvaluebymultiplyingthefractionstogether.Tomultiply fractions, multiply all the top numbers together and then the entire bottom numbers together. Simplify if necessary.
Solution: 2 yards is equal to 72 inches.
5.1.2 Metric Units Themetricsystem,whichisusedbymostoftheworld,andfrequentlyinthesciencefields, usesunitsbasedonmultiplesoften.Thebasicunitsofmeasureinthemetricsystemarethe meter, the liter, and the gram. The prefix of the metric unit tells what multiple of ten the basic unit is multiplied by. Below is a chart of metric prefixes and their values. Metric System Acronym (K)ing (H)enry (D)ied (B)y (D)rinking (C)hocolate (M)ilk Prefix Kilo Hecto Deca Base Deci Centi Milli Meaning 1000 100 10 1 0.1 0.01 0.001 There are other prefixes than the ones mentioned in the table, but those are the primary ones we use. Common Metric Conversions Length Weight Volume 1 km = 1000 m 1 kg = 1000 g 1kL = 1000 L 1m = 0.001 km 1 g = 0.001 kg 1 L = 0.001 kL 1 m = 100 cm 1 g = 100 cg 1 L = 100 cL 1 cm = 0.01 m 1 cg = 0.01 g 1 cL = 0.01 L 1 m = 1000 mm 1 g = 1000 mg 1 L = 1000 mL 1 mm = 0.001 m 1 mg = 0.001 g 1 mL = 0.001 L Scientific Notation 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3
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