GACE
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GACE
Which symbol most accurately reflects the relationship between the two numbers below?<br/><br/><tex>1.2</tex> ☐ <tex>\frac{9}{10}</tex>
Correct — B. Option A: Since the numerator (9) is less than the denominator (10) of the fraction, it is less than 1. Therefore, 1.2 is greater than <tex>\frac{9}{10}</tex>.<br/><br/>Option C: Since the numerator (9) is less than the denominator (10) of the fraction, it is less than 1.0. -
GACE
Shane’s Softball Production Company can produce 12 softballs in an hour. How many softballs can they produce in 14 hours?
Correct — A. Although this is not a difficult problem, and could be calculated mentally, perhaps by multiplying 14 by 10 (140), then adding 2 more 12s to the answer.<br/><br/>However, there is a trick that allows you to multiply numbers close to ten together within seconds.<br/><br/>First, consider the problem: 14 x 12<br/>Using the 2 in 12, add it to 14: 16 (these are the first two digits of the answer).<br/>Using the 2 in 12, multiply it by the 4 in 14: 8 (this is the last digit of the answer).<br/>Thus, the answer to 14 x 12 is 168.<br/><br/>It works for larger numbers in the teens, but those involve “carrying”.<br/>Consider the problem: 17 x 14.<br/>Using the 4 in 14, add it to 17: 21<br/>Using the 4 in 14, multiply it by the 7 in 17 (28). The 8 is the last digit of the answer. Carry the 2 over, and add it to the 21 from the previous step to get 23. The answer to 17 x 14 is 238.<br/><br/><b>Key Takeaway:</b> Sometimes you will find it necessary to multiply numbers in the teens together. With practice, this strategy will allow you to perform that calculation mentally, both quickly and accurately.<br/><br/>Again, this is a trick that requires lots of practice that works for some, and doesn’t work for others. -
GACE
Students are plotting points on a coordinate plane. Rudy plots the point <tex> (-6, 3) </tex> in the second quadrant. Frank plots the same point in the third quadrant. Who plotted the point correctly?
Correct — D. When writing coordinate pairs, we always write the <tex> x- </tex>coordinate first, then the <tex> y- </tex>coordinate. <tex> (x, y)</tex> Quadrants on a graph are numbered <em>counter-clockwise</em> as shown here:<br/><br/><img src="asset:assets/questions/50f583651cc758df.jpeg"><br/><br/><em>Retrieved from: https://openstax.org/books/prealgebra-2e/pages/11-1-use-the-rectangular-coordinate-system</em> The point <tex> (x, y) </tex> falls in the first quadrant, where both the points are <em>positive</em>. In the second quadrant, the <tex> x- </tex>coordinate is <em>negative</em> and the <tex> y- </tex>coordinate is <em>positive</em> ( <tex> (-x,y) </tex>). In the third quadrant, the <tex> x- </tex>coordinate is <em>negative</em> and the <tex> y- </tex>coordinate is also <em>negative</em> ( <tex> (-x,-y) </tex>). In the fourth quadrant, the <tex> x- </tex>coordinate is <em>positive</em> and the <tex> y- </tex>coordinate is <em>negative</em> ( <tex> (x,-y) </tex>). The point <tex> (-6,3) </tex> is in the second quadrant since the <tex> x- </tex>coordinate is negative and the <tex> y- </tex>coordinate is positive. Thus, <em>Rudy</em> plotted the point correctly. -
GACE
Sharon bought an equal number of $65, $55, and $40 tickets for a concert. She spent $640 for all the tickets. How many of each did she buy?
Correct — B. Let's use <em>x</em> to represent the number of tickets bought at each price. Then we can say 65<em>x</em> + 55<em>x</em> + 40<em>x</em> = 640. If we add the numbers on the left side of the equation, we get 160<em>x</em> = 640. To find the value of <em>x</em>, divide both sides of the equation by 160. <em>x</em> = 4. -
GACE
The price of a shirt is increased by 20%, and the price of a $40 pair of shoes is decreased by 40%. If the new price of the shirt now equals the new price of the shoes, what was the original price of the shirt?
Correct — C. First, determine the new price of the shoes: 40% of $40 is (40/100) · $40 = $16, so the new price of the shoes is $40 − $16 = $24. At this point, we can work with the answers to figure out which one is correct: increase each answer by 20% until we get $24. The correct answer is B since 20% of $20 is $4 and $20 + $4 = $24. -
GACE
What is the term for the distance around a circle?
Correct — D. The distance around a circle is its circumference. -
GACE
Which of the following is a prime number?
Correct — C. 23 is a prime number. A prime number is a number that can only be divided by itself and by the number 1, without a remainder. 50, 25, and 6 can all be divided by numbers other than itself and 1. Even numbers greater than 2 are never prime. -
GACE
Which diagram shows the graph of y = | x – 3 | ?<br/><br/>A. B.<br/><br/><img src="asset:assets/questions/9d4e383766f561ed.gif"> <img src="asset:assets/questions/6fae00e1255e23ef.gif"><br/><br/>C. D.<br/><br/><img src="asset:assets/questions/8e57fd686e8936df.gif"> <img src="asset:assets/questions/1dc92697f16f39c1.gif">
Correct — C. The graph of y = | x – 3 | is the same as the graph of y = x – 3 for values of x ≥ 3, but is a reflection in the x axis of y = x – 3 for values of x ≤ 3. <br/><br/>We know then, that the graph will have a V shape, since all values of y are positive (never going below the x axis).<br/><br/>We can also calculate that when y = 0, x =3 (0 = x-3; x = 3) so the bottom point of the V will be at x = 3. ∴Graph C shows y = | x – 3 |. -
GACE
A radius of a circle is 3 cm. What is its area?
Correct — C. A circle with a radius of 3 cm has an area of 28.26 cm<sup>2</sup>. The formula for the area of a circle is 3.14 (?) multiplied by the radius squared. 3² = 9, so 3.14 x 9 is 28.26 cm<sup>2</sup>. -
GACE
The population of the town of Homeville increased by approximately 0.5% last year. If the population at the beginning of the year was 2,460, what was the approximate population by the end of the year?
Correct — E. This problem is asking you to find ½ of 1 percent change of 2,460. To do this mentally, first determine what 1 percent of the original number is, then half that. In this case, 1% of 2,460 is 24.6, and half of that is 12.3. Since you can’t have 3/10 of a person, we can approximate the population increase as 12 people. Add that to the initial 2,460 to find that the new population is 2,472.<br/><br/><b>Key takeaway:</b> There are many types of percent problems you may encounter. It will be helpful to you if you know that you find 10% of a number by moving the decimal one place to the left and 1% of a number by moving the decimal point two places to the left. -
GACE
Which of the following is an example of an ordered pair?
Correct — E. An ordered pair is defined as a set of coordinates shown as two numbers inside parentheses. -
GACE
Which strategy is the most helpful in having students ask questions after reading?
Correct — D. When students talk with each other about a book they have both read, they often naturally begin asking each other questions about the book. This enhances comprehension and also allows them to enjoy the social dimension of literacy. -
GACE
The word embrace has a few different meanings and can be used as a noun or a verb. What does it mean in this segment of the attached passage and is it used as a noun or a verb? “A purpose that is large enough to embrace the wellbeing of the planet and all of its inhabitants.”
Correct — D. The word <em>to</em> before the word <em>embrace</em> is a context clue indicating that the word is a verb. No one can <em>hug</em> the wellbeing of the planet and <em>comprehend</em> does not make sense in this sentence. -
GACE
Text features, such as bold-faced and capitalized words, are important in directions because <code>________</code>.
Correct — C. Text features highlight important words and phrases in a set of directions. When words are in bold-faced lettering or in all capital letters, the reader should take note because those words or phrases are probably important in the steps they are following. These features do not add to the engagement factor, make the steps easier to follow, or indicate any knowledge about the writer. -
GACE
Which of the following is a vowel?
Correct — E. Only five of our letters are vowels, which are the letters a, e, i, o, and u. -
GACE
Highlighting, underlining, and using post-it notes while reading are examples of <code>________</code>.
Correct — A. Highlighting, underlining, and using post-it notes while reading are examples of active reading strategies. By actively engaging with the text, the reader is more focused and has a higher chance of fully comprehending the directions being read. -
GACE
From the following, choose the best title for this passage.
Correct — C. Chocolate, Nepal, and Switzerland are talked about, but not in a way that signifies emphasis and are not the best choices. Cheese is emphasized and is the best choice for a title. -
GACE
Which of the following does this author believe a mature writer does when it comes to being original and truly imaginative?
Correct — D. Choices A, B and D are incorrect as they are not the quote explaining what a mature writer does concerning imagination.<br/><br/>Choice C is correct as it is the exact quote from the author. -
GACE
The Black Death, or, as it has been known, the Oriental plague, the bubonic plague, or in England, simply the plague, and in Italy, "la mortalega" (the great mortality) derived its name from the Orient; its inflammatory boils, tumors of the glands, and black spots, indicative of putrid decomposition, were such as have been seen in no other febrile disease. All the symptoms were not found in every case, and in many cases one symptom alone preceded death. Although afflicted with all the manifestations of the plague, some patients recovered.<br/><br/>According to Hecker the symptoms of cephalic affliction were seen; many patients were stupefied and fell into a deep sleep, or became speechless from palsy of the tongue, while others remained sleepless and without rest. The fauces and tongue were black and as if suffused with blood; no beverage could assuage the burning thirst, so that suffering continued without alleviation until death, which many in their despair accelerated with their own hands. Contagion was evident, for attendants caught the disease from their parents and friends, and many houses were emptied of their inhabitants.<br/><br/>The passage suggests that the Black Death was hard to detect because:
Correct — D. Option B: The passage explains the difficulties in diagnosis because "all of the symptoms were not found in every case."<br/><br/>Option C: The Plague was very contagious but this did not make it hard to detect. -
GACE
Which of the following statements is the best example of a simile?
Correct — A. Similes are comparisons of seemingly unlike things using comparatives such as <em>like</em> or <em>as</em>. The other answer options are examples of a metaphor (The black bicycle seat was a sizzling hot iron after sitting in the sun all day.), an idiom (The early bird gets the worm.), and personification (The hyena laughed.). -
GACE
Which is an example of a high-frequency word?
Correct — B. High-frequency words are those that appear often in print and do not follow normal phonemic clues. A student probably could not sound out a word like the, so they have to memorize these words. -
GACE
Spanish in the U.S.<br/><br/>Did you know that the United States has the second largest Spanish-speaking population in the world? With over 37 million speakers the age of five and older the U.S. alone has more inhabitants that speak Spanish than the whole country of Venezuela.<br/><br/>Spanish students don’t have to study abroad to get a good look into Latin-American culture. There are many cities here in the U.S. with (1) thriving Latino (2) districts that any student of Spanish can visit to practice speaking. Miami, for example, is home to a multitude of diverse Hispanics from all over Latin America and Europe. When walking down the streets of Little Havana (one of the predominantly Hispanic <i>barrios</i>, or neighborhoods) you will hear the Cuban Spanish (3) language variety. In Chicago, the place to hear Mexican Spanish is <i>La Villita.</i><br/><br/>Since Spanish-speaking U.S. citizens are the fastest growing linguistic group in the United States, it is common to find Spanish-language television channels (such as Univisión and Telemundo) in larger cities. In fact, it’s thanks to these mass media that there are people (although few) that spend their whole lives in the United States without ever having to learn or speak English. The governor of California, Arnold Schwarzenegger, even commented once that Hispanics in the U.S. need to “turn off the TV in Spanish” in order to learn English more quickly.<br/><br/>But Governor Schwarzenegger ought to know that, according to linguistic research on (4) bilingualism, families of Hispanic heritage (as well as other non-English speaking families) produce English dominant (or English only) speakers by the third generation after their immigration. That means, it is more common than not that the grandchildren of the Mexican immigrant cannot communicate with their grandparent in Spanish. Thus, the Spanish language does not seem to (5) pose a threat in the U.S. society, contrary to what many politicians often suggest in their political rhetoric.The word “bilingualism”, in bold after the (4) in paragraph 4, can best be defined as
Correct — D. The word “bilingualism” can best be defined as the ability to communicate in two languages. Answer B, although possible, is too specific, since someone who is bilingual could communicate in French and Mandarin. Answer C is false, because being able to communicate with your grandparents doesn’t make you necessarily bilingual. Answers D is misleading in two ways: first, someone who speaks a language other than English isn’t necessarily bilingual, and second, like answer B, being able to speak English isn’t a necessary component to being bilingual. -
GACE
(1) Determining which foods are junk and which aren't can be confusing. Is fast food junk? What about high-calorie or convenience-store foods? Think of it this way: If the food has very few vitamins, minerals, (3) and other nutrients that you need to be healthy, <u>it's</u> probably junk. The main <u>principle</u> to remember is that food classified as junk will have a lot of sugar, fat, and/or salt.<br/><br/>(5) The effects of junk food are <u>no laughing matter</u>. Junk food can lead to obesity, heart disease, and diabetes. But you may not realize how much it can immediately make you feel like, well, junk. The fat in (7) those foods can build up on your blood vessel walls, Dr. Harold Jayne explains, which "makes it harder for your blood vessels to circulate blood around your body." That buildup can quickly <u>effect</u> how<br/><br/>(9) well you are able to perform during sports and other exercise.<br/><br/>Which of the following statements best expresses the main idea of paragraph 1 of the selection?
Correct — A. Option B: The main point of paragraph 1 is that junk foods have low nutritional content and high amounts of sugar, fat, or salt. The author includes this point to show the reader how to determine if a food should be classified as junk.<br/><br/>Option D: Even though it is true that nutritious foods contain vitamins and minerals, the paragraph focuses on junk foods, not nutritious foods. -
GACE
Anthropology has taught us that in many primitive societies religion—a sense of man's dependence on a power higher than himself—is preceded by a stage of magic—a belief in man's own power to influence by occult means the action of the world around him. That the ancestors of the Roman community passed through this stage seems clear, and in surviving religious practice we may discover evidence of such magic in various forms. There is, for instance, what anthropology describes as 'sympathetic magic'—the attempt to influence the powers of nature by an imitation of the process which it is desired that they should perform. Of this we have a characteristic example in the ceremony of the <em>aquaelicium</em>, designed to produce rain after a long drought.<br/><br/>Which best summarizes the main idea of this passage?
Correct — A. Option B: This passage notes that societies believe first in magic, then in a higher power; it goes on to explain how ancient Rome was no different.<br/><br/>Option D: This passage defines magic as being based on occult means, but this is not the main purpose. -
GACE
Which word is most closely synonymous with organization in writing?
Correct — C. Organization is the aspect of writing that deals with how a piece of work is structured. Teaching organization requires students to think about structure and how the way their work is crafted and built contributes to its overall purpose. -
GACE
Which word is NOT spelled correctly?
Correct — A. Option C: "Annually" is spelled correctly.<br/><br/>Option D: The correct spelling is "publicly." -
GACE
Which sentence below contains a prepositional phrase?
Correct — A. Option B: Prepositions are specific words that show time, place, direction, or manner. Prepositional phrases begin with a preposition and end with a noun or pronoun. This sentence contains a <em>relative clause</em> "<em>who just started in our class today," </em>not a prepositional phrase.<br/><br/>Option D: Prepositions are specific words that show time, place, direction, or manner. Prepositional phrases begin with a preposition and end with a noun or pronoun. <em>"In after-school tutoring" </em>is a prepositional phrase that indicates <em>place.</em> -
GACE
Select the answer choice that corrects an error in the underlined portion. If there is no error, choose D indicating that no change is necessary. Mr. Alvarez said it was (A) <u>all right</u> for us to have a yard sale. (B) <u>Hoards</u> of people came to it as they (C) <u>always</u> do.
Correct — A. To hoard is to amass a collection of valuables, often hidden. Therefore it is not the proper word to use in talking about a group of people. This group is a “horde.” -
GACE
How does using published paragraphs as models help students learn to write their own paragraphs?
Correct — D. Modeling is an important technique for the teaching of writing paragraphs because it meets students where they are, demonstrating how paragraphs work for students at their level and identifying strategies that are both helpful and detrimental to readers. -
GACE
Which course of action most improves the following sentence?<br/><br/>The short story, that <i>Stand By Me</i> was based on, was written under an alias.
Correct — B. The sentence is most improved by removing the commas. The clause “that <i>Stand By Me</i> was based on” is essential and should not be set off with commas. This is clear both because it specifies which short story is being discussed and by the use of <i>that</i> instead of <i>which</i> at the beginning of the clause.
GACE sample questions
Tap any question below to reveal the answer and a plain-English explanation.
GACE (1) Determining which foods are junk and which aren't can be confusing. Is fast food junk? What about high-calorie or convenience-store foods? Think of it this way: If the food has very few vitamins, minerals, (3) and other nutrients that you need to be healthy, <u>it's</u> probably junk. The main <u>principle</u> to remember is that food classified as junk will have a lot of sugar, fat, and/or salt.<br/><br/>(5) The effects of junk food are <u>no laughing matter</u>. Junk food can lead to obesity, heart disease, and diabetes. But you may not realize how much it can immediately make you feel like, well, junk. The fat in (7) those foods can build up on your blood vessel walls, Dr. Harold Jayne explains, which "makes it harder for your blood vessels to circulate blood around your body." That buildup can quickly <u>effect</u> how<br/><br/>(9) well you are able to perform during sports and other exercise.<br/><br/>Which of the following statements best expresses the main idea of paragraph 1 of the selection?
A. Junk foods have low nutritional content and high amounts of sugar, fat, or salt. ✓
B. It is easy to tell which foods are junk and which foods are nutritious.
C. All fast food can be classified as junk food.
D. Nutritious food contains vitamins and minerals.
Correct — A. Option B: The main point of paragraph 1 is that junk foods have low nutritional content and high amounts of sugar, fat, or salt. The author includes this point to show the reader how to determine if a food should be classified as junk.<br/><br/>Option D: Even though it is true that nutritious foods contain vitamins and minerals, the paragraph focuses on junk foods, not nutritious foods.
GACE Anthropology has taught us that in many primitive societies religion—a sense of man's dependence on a power higher than himself—is preceded by a stage of magic—a belief in man's own power to influence by occult means the action of the world around him. That the ancestors of the Roman community passed through this stage seems clear, and in surviving religious practice we may discover evidence of such magic in various forms. There is, for instance, what anthropology describes as 'sympathetic magic'—the attempt to influence the powers of nature by an imitation of the process which it is desired that they should perform. Of this we have a characteristic example in the ceremony of the <em>aquaelicium</em>, designed to produce rain after a long drought.<br/><br/>Which best summarizes the main idea of this passage?
A. Primitive religions believe in magic and then a higher power, and ancient Rome was no exception. ✓
B. Ancient Roman religion was based on occult means.
C. The ancestors of the Roman community did not believe in a higher power.
D. 'Sympathetic magic' only occurs in the most primitive religions.
Correct — A. Option B: This passage notes that societies believe first in magic, then in a higher power; it goes on to explain how ancient Rome was no different.<br/><br/>Option D: This passage defines magic as being based on occult means, but this is not the main purpose.
GACE Which word is most closely synonymous with organization in writing?
A. Outline
B. Graphic
C. Structure ✓
D. Process
Correct — C. Organization is the aspect of writing that deals with how a piece of work is structured. Teaching organization requires students to think about structure and how the way their work is crafted and built contributes to its overall purpose.
GACE Which word is NOT spelled correctly?
A. publically ✓
B. hecticly
C. annually
D. practically
Correct — A. Option C: "Annually" is spelled correctly.<br/><br/>Option D: The correct spelling is "publicly."
GACE Which sentence below contains a prepositional phrase?
A. The teacher taught us a new word game in after-school tutoring. ✓
B. My teacher asked, "Have you met the new student?"
C. Our parents refused to let us attend the ballgame even when we begged.
D. I finally finished searching my brother's gross room.
Correct — A. Option B: Prepositions are specific words that show time, place, direction, or manner. Prepositional phrases begin with a preposition and end with a noun or pronoun. This sentence contains a <em>relative clause</em> "<em>who just started in our class today," </em>not a prepositional phrase.<br/><br/>Option D: Prepositions are specific words that show time, place, direction, or manner. Prepositional phrases begin with a preposition and end with a noun or pronoun. <em>"In after-school tutoring" </em>is a prepositional phrase that indicates <em>place.</em>
GACE Select the answer choice that corrects an error in the underlined portion. If there is no error, choose D indicating that no change is necessary. Mr. Alvarez said it was (A) <u>all right</u> for us to have a yard sale. (B) <u>Hoards</u> of people came to it as they (C) <u>always</u> do.
A. Hordes ✓
B. No change is necessary.
C. all ways
D. alright
Correct — A. To hoard is to amass a collection of valuables, often hidden. Therefore it is not the proper word to use in talking about a group of people. This group is a “horde.”
GACE How does using published paragraphs as models help students learn to write their own paragraphs?
A. Students can see how paragraphs exist in the 'real world' at their reading and writing levels.
B. Students can see what bad strategies authors use that distract them as readers.
C. Students can see what good strategies authors use that help them as readers.
D. All answer choices are correct. ✓
Correct — D. Modeling is an important technique for the teaching of writing paragraphs because it meets students where they are, demonstrating how paragraphs work for students at their level and identifying strategies that are both helpful and detrimental to readers.
GACE Which course of action most improves the following sentence?<br/><br/>The short story, that <i>Stand By Me</i> was based on, was written under an alias.
A. Fix the tense shift.
B. Remove the commas. ✓
C. Change alias to pen name.
D. Insert a conjunction.
Correct — B. The sentence is most improved by removing the commas. The clause “that <i>Stand By Me</i> was based on” is essential and should not be set off with commas. This is clear both because it specifies which short story is being discussed and by the use of <i>that</i> instead of <i>which</i> at the beginning of the clause.
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