The SSAT Course Book MIDDLE & UPPER LEVEL

Focusing on the Individual Student

Instructor’s Edition

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Copyright Statement

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Copyright ©2013 Summit Educational Group, Inc.

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CONTENTS TEST-TAKING FUNDAMENTALS

About the SSAT 2 SSAT Structure 3 Scoring 4 Knowing Your Limits 5 Beating the SSAT 6 Making Your Best Guess 8 Using the Answer Choices 10 General Tactics 12

QUANTITATIVE General Information 16 Plugging In 18 Solving Backwards 20 Choosing Numbers 22 Math Tips 24 Chapter Review 25

ARITHMETIC

Vocabulary 29 Addition, Subtraction, Multiplication, and Division 30 Odd and Even Integers 34 Positive and Negative Numbers 36 Divisibility and Remainders 38 Multiples and Factors 40 Fractions 42 Reducing Fractions 46 Adding and Subtracting Fractions 50 Multiplying and Dividing Fractions 54 Decimals and Place Value 58 Rounding and Estimation 60 Decimal Operations 64 Percent – Decimal Conversion 66 Percent – Fraction Conversion 68 Solving Percent Problems 70

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Ratios 74 Proportions 78 Exponents 82 Multiplying and Dividing Numbers with Exponents 84 Roots 86 Order of Operations 88 Averages 90 Probability 94 Ordering and Sequences 98 Charts and Graphs 102 Chapter Review 106 Arithmetic Practice 108 Arithmetic Middle Level Practice 120 Arithmetic Upper Level Practice 134

ALGEBRA

Vocabulary 149 Algebraic Expressions 150 Algebraic Equations 154 Translating 158 Word Problems 160 SSAT Functions 164 Inequalities 168 Chapter Review 172 Algebra Practice 174 Algebra Middle Level Practice 180 Algebra Upper Level Practice 186

GEOMETRY

Vocabulary 195 Angles 196 Pairs of Angles 200 Parallel Lines 202 Triangles 204 Isosceles and Equilateral Triangles 206 Right Triangles 208 Area and Perimeter – Rectangle and Square 210 Area and Perimeter – Triangle 214

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Circles 218 Estimating Figures 220 Volume 222 Coordinate Plane 224 Slope 226 Graphing Lines 228 Chapter Review 230 Geometry Practice 232 Geometry Middle Level Practice 238 Geometry Upper Level Practice 244

VERBAL SYNONYMS

General Information 252 Anticipate the Answer 254 Secondary Definitions 256 Positive or Negative 258 Attractors 260 Roots 262 Common Roots 265 Word Groups 266 Chapter Review 280 Synonyms Middle Level Practice 282 Synonyms Upper Level Practice 286

ANALOGIES General Information 292 Defining the Relationship 294 Applying the Relationship 296 Refining the Relationship 298 Common Analogy Relationships 300 First and Third Analogies 302 Attractors 304 Being an Analogy Detective 306 Solving Backwards 308 Chapter Review 310 Analogies Middle Level Practice 312 Analogies Upper Level Practice 317

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READING COMPREHENSION General Information 324 Active Reading 326 Mapping the Passage 330 Anticipate the Answer 332 Process of Elimination 335 Passage Types 338 Answering the Questions 339 Main Idea Questions 340 Detail / Supporting Idea Questions 342 Vocabulary Questions 344 Tone / Attitude Questions 346 Inference Questions 348 Application Questions 352 Except / Least / Not Questions 354 Roman Numeral Questions 354 Chapter Review 356 Reading Middle Level Practice 358 Reading Upper Level Practice 366

WRITING General Information 380 What Are Your Readers Looking For? 382 Creative or Formal? 383 Preparing a Creative Story 384 The Setup 386 The Confrontation 388 The Resolution 390 Preparing a Formal Essay 392 The Introduction 394 The Body 396 The Conclusion 398 Notes on Style 400 Evaluating Your Writing 403 Examples of Student Writing 404 Chapter Review 406 Writing Practice 408

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ANSWER KEY Test-Taking Fundamentals 418 Quantitative 418Arithmetic 418Arithmetic Practice 424 Algebra 425Algebra Practice 427 Geometry 428Geometry Practice 430 Synonyms 431Synonyms Practice 431 Analogies 432Analogies Practice 433 Reading Comprehension 434 Reading Comprehension Practice 436

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Explanation of Instructor’s Edition notation:

Additional problem - Indicates an additional question you could ask a student in order to further understanding or expand skills. It is not pertinent to solving the main problem.

Attractor - Indicates an obvious attractor answer choice. Watch out!

Solutions - Indicates a method or strategy that can be used to solve the problem. These are provided for questions that are particularly difficult or that can be used to reinforce certain strategies.

Answers - For multiple-choice questions, answers are shown at the bottom center of the page. For other questions, answers are shown beside the questions.

Try It Out - Indicates questions that are used to teach or reinforce concepts and strategies. They are not always representative of the types of questions seen on the SSAT. These should be used instructively, rather than diagnostically.

Put It Together - Indicates questions that are accurate representations of official SSAT material. These are useful for measuring student skill on the test.

?

h

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18 QUANTITATIVE

Plugging In Some SSAT math questions can be solved quickly by using the answer choices.

Questions involving algebraic equations can often be solved by plugging in theanswer choices for a variable.

− = =If 7 3 46, then x x

(A) 0(B) 1(C) 5(D) 7(E) 9

If you start with (C), you get − =7(5) 3 46, or 32 = 46 (not a true

statement). So, x must be bigger than 5, because 32 is too small.

Eliminate (A) and (B), because these will make your quantity smaller.

Try (D) and (E).

The correct answer is (D) because − =7(7) 3 46 .

When plugging in, start with answer choice (C).

Since numerical answer choices are presented in either ascending or descendingorder, choice (C) will be in the middle. If (C) isn’t right, you might be able to tell ifyou need a larger or smaller number. By starting in the middle, you can reduce thenumber of answer choices you plug in, which will save you time.

Plugging In can save time for all students. Advanced students may initially be reluctant to plug in, preferring to use algebraic methods. As you work through the text, walk your student through both methods to determine which method s/he prefers.

Make sure your student understands when it is appropriate to plug in the answer choices. Middle Level students can over-use this strategy, plugging in answers without reading the problem entirely and choosing attractors (e.g. plugging in for x when the problem asks for 2x). It can be helpful to walk your student through a practice test and identify which problems are good candidates for Plugging In.

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ARITHMETIC 127

27. A building has 47 floors, the first 7 of which are belowthe lobby. If an elevator starts on the third floor and goes6 floors up, which of the following best describes wherethe elevator is now?

(A) 2 floors below the lobby(B) the lobby(C) 1 floor above the lobby(D) 2 floors above the lobby(E) 9 floors above the lobby

28. Pat buys a piece of licorice 150 inches long. If she plansto give away all of the licorice by giving each of her 5friends an equal piece, how long should she cut eachpiece?

(A) 60 feet(B) 30 feet(C) 10 feet(D) 5 feet(E) 2.5 feet

29. .1 10 .2 5× × × =

(A) .5(B) 1(C) 1.5(D) 10(E) 50

30. What is the best estimate for759 9871 998

,,

?

(A) 40(B) 280(C) 400(D) 500(E) 4,000

h Draw a diagram.

h Pay attention to units.

Lobby+1+2+3+4+5

+7+6

‒1‒2‒3‒4‒5

‒7‒6

12345

76

910111213

1514

8

h (.1×10)×(.2×5) = (1×1)

h 800,0002,000

CEBC

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212 GEOMETRY

PUT IT TOGETHER

1. Find the perimeter of the irregular shape in Figure 8.

(A) 15 in. (B) 19 in. (C) 23 in. (D) 24 in. (E) 26 in.

2. In Figure 9, if UVWX is a square, the length of VY is 9, and the length of VW is 6, what is the area of rectangular region YUXZ?

(A) 15 (B) 18 (C) 27 (D) 36 (E) 54

3. In Figure 10, O is the center of the circle that has a radius of 5 meters. What is the area, in square meters, of square RSTU?

(A) 40 (B) 80 (C) 100 (D) 160 (E) 400

4. In Figure 11, X is a rectangular sheet of paper with a perimeter of 39 inches. Y shows the same sheet of paper after four squares, each with an area of 1 square inch, have been cut from the corners. What is the perimeter of the sheet of paper after it is cut?

(A) 31 inches (B) 35 inches (C) 39 inches (D) 43 inches (E) 47 inches

Figure 8

4 in.

3 in.

8 in.

Figure 9

U

V W

Y

X

Z

Figure 10

R

S

T

U

O 5

Figure 11

X Y

h This question is easier if you know that the radius or diameter of a circle is always the same, no matter the angle. If the radius of this circle is 5, its diameter is 10. Its diameter is the same length at a side of the square. So, the area of the square must be 10 × 10.

h Presenting the following series of shapes can help students see how perimeter stays constant in certain right-angle figures.

h Make sure that your student recognizes the meaning of the tick marks that show the length of the leftmost unknown side.

h Assume all angles are right angles.

DBCC

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224 GEOMETRY

Coordinate Plane

The coordinate plane is a grid made up of two number lines – a horizontal number line called the x-axis and a vertical number line called the y-axis. These two lines meet at a point called the origin. This is the point where both number lines are labeled zero.

The x-axis is used to measure the value of x at any point on the plane. Points to the right of the origin have positive values of x, and points to the left of the origin have negative values of x.

The y-axis is used to measure the value of y at any point on the plane. Points above the origin have positive values of y, and points below the origin have negative values of y.

We can describe the position of a point on the plane using a pair of numbers called an ordered pair. An ordered pair is also called the coordinates of the point.

The first number in the pair is the value of x at the point, called the x-coordinate.

The second number in the pair is the value of y at the point, called the y-coordinate.

In the figure above, P has coordinates ( )4,3 .

P ( ),x y

2

x

y

3 1 4 5

1

2

3

(+, +) (–, +)

(+, –) (–, –)

1

2

3

1 2 3 –1 –2 –3 –1

–2

–3

x

y

–x

–y

X is positive to the right of the origin and negative to the left, just like a number line. Y is positive going up and negative doing down, just like height.

If your student has trouble remembering which axis comes first (X,Y or Y, X), just remember that the order is alphabetical.

The following three modules on coordinate geometry cover concepts that might be too advanced for some students. These concepts don’t appear frequently on the SSAT, but they can be important for achieving competitive scores, particularly on the Upper Level SSAT.

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GEOMETRY 225

TRY IT OUT

1. Plot the following points on the graph below:

A: (2, 2) B: (–5, –1) C: (4, –4)

D: (–5, 3) E: (–4, –3) F: (–2, 4)

2. Find the coordinates of the following points:

K:____ L:____ M:____

N:____ P:____

Q:____ R:____ S:____

1

2

3

4

41 2 30–1 –2 –3–4

–4

–1

–2

–3

x

y

–x

–y

1

2

3

4

41 2 30–1–2–3–4

–4

–1

–2

–3

x

y

–x

–y

KL

M N

P

Q R S

D

CE

B

A

F

●

●●

●

●●

(0,4) (2,3) (4,2)

(-3,-2) (-1,-2) (2,-2)(-1,1) (3,0)

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256 SYNONYMS

Secondary Definitions

Sometimes, your definition of the stem word won’t fit the answer choices because asecondary definition (a less common meaning for the word) is being tested.

Note: Knowing the stem word’s part of speech will help you figure out whatdefinition is called for. Since parts of speech will always be consistent between thestem word and the answer choices, you can look to the answers to help you figureout what part of speech is being used.

Train Train can mean a locomotive, a part of a dress, or to teach.

Minute Minute can be used as a unit of time or as an adjective to mean very

small or tiny.

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SYNONYMS 257

TRY IT OUT

Think of at least two meanings for each of the following words:

set

run

stand

trail

pen

champion

moral

spring

hamper

revolution

TRY IT OUT

In the space provided, write at least two definitions for the stem word. Then try to complete the exercise.

1. BRIDGE:

(A) connect(B) suspend(C) elevate(D) fell(E) digest

2. PROMPT:

(A) timely(B) expelled(C) lax(D) candid(E) improvised

3. UNIFORM:

(A) authoritative(B) consistent(C) restrictive(D) unprepared(E) shapeless

AAB

to set in place, to set a price, to sink (sunset), a collection, a match (tennis)

to go quickly, to operate (machine), to unravel (stockings), to flow (river)

to be upright, to rise, to support a policy (“stand for”), a platform or booth

to drag behind, to follow, a path, a stream (smoke)

a writing instrument, to write

a winner, to support or defend

virtuous or honest, a principle of right or wrong conduct

to leap, to rise, a coiled wire, the season between winter and summer

to hold back or hinder, a basket

a radical change, a turn or rotation

a structure spanning a river, a nose ridge, a musical transition, to join

done without delay, to incite or move to action

an outfit or style of dress, identical

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READING COMPREHENSION 335

Process of Elimination

Eliminate answers which are too broad, too narrow, or simply incorrect.

As you read through the possible answers, eliminate answer choices that:

• cover more than the passage does.

• talk only about a portion of the passage.

• have nothing to do with the discussed topic.

Process of elimination is extremely effective on Reading Comprehension since you will usually have at least some understanding of the passage. Eliminate wrong answers and then make an educated guess.

What better way to show the values of a society than through its folklore? America is known for its rugged individuality, work ethic, and national pride. In its frontier legends, with heroes such as Paul Bunyan, Davy Crockett, and Pecos Bill, this American spirit shines brightly. The passage is primarily concerned with

(A) describing American traditions (B) evaluating the connection between myth and reality (C) explaining how folklore is a source for symbols of cultural values (D) summarizing the author’s favorite stories (E) examining how national pride is represented in stories With this question, it might be hard to anticipate the answer before looking at the answer choices, so it is best to use Process of Elimination.

(A) is not correct, because the passage is focused on folklore, not all American traditions: too broad.

(B) is not correct, because the passage is concerned with folklore and social values. “Myth and reality” is too broad.

(D) is not correct, because there is no mention of “favorite stories”: incorrect.

(E) is not correct, because the passage is concerned with all social values, not only “national pride.” This answer is too narrow. Through the Process of Elimination, we can reason that (C) is the best answer.

For an answer choice to be correct, it must be entirely correct. Do not get stuck on answer choices that are only partly right.

It is best for students to use process of elimination when they cannot effectively anticipate the answer. It is best used as a backup strategy, because it can be time-consuming. However, it is still a very valuable and often-needed SSAT skill.

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336 READING COMPREHENSION

TRY IT OUT

Give reasons for eliminating answer choices (e.g. too broad, too narrow, incorrect) and find the correct answers.

When groups of people live together, massive amounts of waste are produced. Some of the waste, such as paper, food scraps, and other natural materials, is biodegradable. Biodegradable materials can break down in a short time, degrading into useful nutrients and resources. However, some waste materials, like plastics, are not biodegradable. These can remain in their original form in the environment for hundreds of years. Scientists are working to replace many of the non-biodegradable materials with biodegradable ones, such as plastics made from potato starch. Also, scientists have discovered a fungus from the Amazon that is capable of breaking down and consuming plastic. This research could dramatically reduce the amount of non-biodegradable waste. However, this will not entirely solve the problem of waste, and the amount of available space where waste can be deposited is diminishing rapidly. Earth may soon become little more than a garbage dump, unless even more imaginative methods of dealing with waste materials are developed in the near future.

1. The purpose of the passage is to

(A) persuade readers to invest in research on plastics.

(B) show the connection between the environment and human civilization.

(C) describe the processes of biodegradation of different materials.

(D) demonstrate that even the most troubling problems can have simple solutions.

(E) present the problem of waste disposal and describe potential scientific solutions.

(A) _______________________________________

_______________________________________

(B) _______________________________________

_______________________________________

(C) _______________________________________

_______________________________________

(D) _______________________________________

_______________________________________

(E) _______________________________________

_______________________________________

2. Which of the following questions is fully answered by the passage?

(A) What type of waste is the most biodegradable?

(B) What are the consequences and effects of modern human society?

(C) Why is plastic less biodegradable than other materials?

(D) What are some solutions to the problem of non-biodegradable waste?

(E) How much waste is biodegradable?

(A) _______________________________________

_______________________________________

(B) _______________________________________

_______________________________________

(C) _______________________________________

_______________________________________

(D) _______________________________________

_______________________________________

(E) _______________________________________

_______________________________________

ED

no mention of “investing”

too broad; the passage is about waste

and biodegradability

too narrow and off-topic; the passage is

about the problem, not the process

too broad; the passage is about a

particular problem

incorrect: the passage lists materials, but

doesn’t say which is most biodegradable

too broad; the passage focuses on one

aspect of modern society

incorrect; the passage doesn’t explain

why plastic is less biodegradable

incorrect; the passage never specifies

how much waste is biodegradable

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342 READING COMPREHENSION

Detail / Supporting Idea Questions

Detail questions ask for specific facts from the passage.

Most of the questions that fit into this category could be called “find the fact” asthey rely on your ability to find a specific piece of information, often contained intwo or three sentences. Unlike main idea questions, which are more broad, thesequestions refer to a specific idea.

Common detail / supporting idea questions:

• According to the passage, which of the following is true of ____?

• According to the passage, if ____ occurs then…

• The passage states that ____ occurs because…

• The author believes…

• On line 10, the author compares pollution to…

Detail questions will often contain these words: states, mentions, specific, example

The answers to detail questions can be found in specific parts of the passage. Formost detail questions, you won’t remember the answer from the first reading.However, if you map the passage, you may remember where the detail appears inthe passage. Go to the appropriate place in the passage and search for the answer.

You should be able to support your answer with material in the passage. Practicedefending your answer choices.

Read above and below any line-numbers cited in the question to get the full contextof the sentence. Line numbers point you to the general area where the answer isfound. You will usually need the context around those lines to get the right answer.

Ask your student to write the evidential line number next to the correct answer.

Many students pick out key words in the passage without reading enough of the passage to understand the context.Many Reading Comprehension questions require a solid understanding of the whole passage, so it is often not enough to only read a small portion of the passage.

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READING COMPREHENSION 343

TRY IT OUT

Plato, it seems, was the first person to define the characteristics of the soul. Plato considered the soul to be divided into three distinct energies that are at the core of all human behavior. His reason for this view was based on the conflicting desires people often have; people are often attracted to and averse to something at the same time, such as when someone both wants to commit a crime and is reluctant to do it. Plato believe there must be multiple parts of the soul that control these contradictory motivations. According to Plato, the soul consists of three parts: 5 Reason, Emotion, and Appetite. Plato compared these, metaphorically, to the brain, the heart, and the stomach. He believed that each of these parts of the soul was essential and that they must work in balance in order to live in peace. He gave Reason the greatest value, arguing that a person who is virtuous and wise will use reason to control their passions and desires and that this is the only way to achieve true happiness. He believed so strongly in this idea of the soul that he designed social systems based on it, believing that the harmony of the soul could serve as a model 10 for harmony in the operation of an entire civilization.

1. According to the passage, Plato based his socialdesign on his concept of the soul because

_______________________________________

_______________________________________

2. According to the passage, Plato believed that themost influential part of the soul should be

(A) the heart(B) the stomach(C) Emotion(D) Reason(E) Appetite

3. The author mentions parts of the body (line 6) asan example of

(A) Plato’s knowledge of anatomy(B) the different energies of the soul as

theorized by Plato(C) factors that contribute to criminal behavior(D) opposing theories of the characteristics of

the soul(E) the modern understanding of biology

h line 8

–DB

he believed it was a fundamental formula

for peace

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