GACE Program Admission Assessment
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GACE Program Admission
GACE Program Admission Overview
GACE Program Admission Reading
GACE Program Admission Mathematics
GACE Program Admission Writing
GACE Program Admission
The Georgia Assessments for the Certification of Educators (GACE) is Georgia’s stateapproved assessment program for P12 public school educators. The GACE assessments are computerbased tests which determine whether you have the aptitude to work in Georgia’s public schools.
Your GACE Program Admission assessment will consist of three tests: the GACE Program Admission Reading test, the GACE Program Admission Mathematics test, and the GACE Program Admission Writing test.
You’ve got some options here. You can take the three GACE Program Admission tests individually or take the three tests in one combined session. Every test includes selectedresponse (SR) questions; some tests include constructedresponse (CR) questions, as well. Take a look at the chart below for details:
Test  Questions Type & Number  Testing Time*  Test Duration** 

Test I: Reading

56 SR questions  85 Minutes  2 Hours 
Test II: Mathematics

56 SR questions  85 Minutes  2 Hours 
Test III: Writing

40 SR questions, 2 CR questions 
100 Minutes  2 Hours 
Combined Test:

152 SR questions, 2 CR questions 
4 Hours 30 Minutes  5 Hours 
*Timed part of the test.
**Includes testing time as well as tutorials and directions.
The Program Admission Reading test includes both fiction and nonfiction passages. This test will cover your knowledge of three subareas:
 Key Ideas and Details (30%)
 Craft, Structure, and Language Skills (35%)
 Integration of Knowledge and Ideas (30%).
You’ll encounter the following content while taking this test:
Paired passages (approximately 100 words each), followed by 47 questions
 Long passages (approximately 200 words each), followed by 47 questions
 Short passages (approximately 100 words each), followed by 23 questions
 Brief statements followed by single questions
The Program Admission Mathematics test includes questions in four subareas:
 Number and Quantity (30%)
 Algebra and Functions (30%)
 Geometry (20%)
 Statistics and Probability (20%).
You will answer the following types of questions while taking this test:
 Singleanswer
 Stimulusbased
 Cluster
The Program Admission Writing test includes two main subareas:
 Text Types, Purposes, and Production (60%)
 Language and Research Skills for Writing (40%).
Be prepared to see each of the following sections while completing this test:
 A section containing 40 selectedresponse questions. You will have about 40 min. for this part.
 An Argumentative essay question which will require you to use evidence to support a position. Prepare to spend about 30 min. on this part.
 An Informative/Explanatory essay question which will require you to draw information from two provided sources to identify major ideas. You can expect to spend about 30 min. on this section.
GACE Program Admission Quick Facts
Quick Facts
Cost: The GACE Program Admission assessment includes both a $25 registration fee and a $28 test center fee – these fees are included in the prices below:
Program Admission (combined tests I, II, and III): $128
Program Admission (any two tests): $103
Program Admission (single test): $78
Study Time: The amount of time you will need to spend preparing for the GACE Program Admission depends on your knowledge of the content covered. It is important to know that you must pass each of the three tests because there is not a composite score option for passing the assessment.
Scoring: Scores range from 100 to 300. A passing score for the Program Admission is 250.
What test takers wish they would’ve known:
 Testtakers tend to overestimate their abilities to perform well on GACE assessments. Many students regret not putting more time and effort into preparing for GACE assessments beforehand. Fortunately, it’s easy to avoid this mistake by using test preparation materials.
 It’s a great strategy to track your time while taking the GACE Program Admission. You can monitor your time by periodically checking the timer in the upper righthand corner of your screen.
 Because time management is crucial, skip questions you find extremely difficult and move forward to questions you find easier to answer. Don’t worry, you can mark the questions you skip as you take the test. Try to finish the other questions with 10 to 15 minutes remaining and use that extra time to return to the more challenging questions. If you are unsure of an answer, it is better to guess than to leave a question blank.
 When answering the selectedresponse questions, you should read all possible answers before marking the correct one. You don’t want to miss out on the best answer by not reading all of the responses!
 Always check your answer before moving to the next question. Many testtakers are surprised by how they’re able to find overlooked errors in their work by using this strategy.
Information obtained from the Georgia Assessments for the Certification of Educators website: https://gace.ets.org/
GACE Program Admission: Reading
You will have 1 hour and 25 minutes to answer 56 multiplechoice questions.
The Reading subtest can be neatly divided into three sections:
 Key Ideas and Details (35%)
 Craft, Structure, and Language Skills (30%)
 Integration of Knowledge and Ideas (35%)
So, let’s start with Key Ideas and Details.
Key Ideas and Details
This section tests your knowledge on the ability to both draw inferences from the text and to identify what the text explicitly states. You should be able to determine central ideas and themes as well as describe how they develop throughout the course of the text. You must also analyze how details in the text support the main ideas and then use those details to identify appropriate summaries.
Let’s discuss some concepts that will more than likely appear on the test.
Making Inferences
When you make an inference, you use background knowledge, as well as what the text explicitly states, to come to a logical conclusion. Remember that authors don’t include all of the information for us when they write a text – they allow us to use our inferencing skills to fill in the details and make inferences.
Consider the following passage:
Backstage, the speaker shuffled through her notes a final time, occasionally pausing to adjust her hair or check the time on her watch. As 2:00 p.m. drew nearer, the air seemed to grow warmer. She began to tap her shoe against the floor. Finally, she heard her name announced. This was it…
When reading this passage, you can draw a couple of inferences. The author does not state that the subject is about to speak in front of a crowd or that she feels anxious; however, your own life experiences, as well as your experience as a reader, allow you to infer both what will happen next and how the subject of the passage is feeling.
Central Ideas and Themes
Finding a central idea or theme in a text is all about getting to the point. As you read, think about the “big picture” created by the details in the text in order to determine the author’s overall message. Is the author trying to make a general statement about life or help you understand a major concept?
Let’s take a moment to think about Aesop’s fable, The Tortoise and the Hare. In the story, the hare is overconfident that he will win the race and, therefore, does not bother to try his best. During the race, the hare stops to boast, to tease the tortoise, and even to take a nap. The tortoise, however, continues the race at his own slow, steady pace. In the end, the turtle is the victor.
So, what central message about life is Aesop trying to get us to understand? Aesop uses the details in the story to tell us that it is better to be determined and hardworking instead of arrogant and careless. This overall message is the theme of The Tortoise and the Hare.
Supporting Ideas and Details
The use of details, such as descriptions, reasons, explanations, and comparisons, helps to support themes, opinions, and main ideas in a text. While you read, try to ask yourself what ideas the details in a story may support. Remember, authors include details for a reason. Thinking back to The Tortoise and the Hare, you might say that the detail that the hare stops to take a nap helps to support the idea that the hare is overconfident.
As another example of how to use supporting details, imagine a scene which includes two characters, Joe and Chris, walking around at a fair and eating popcorn. Chris is accidentally nudged by a passerby, and he drops his bag of popcorn. In response to the incident, Joe invites Chris to share his bag of popcorn. The detail that Joe shares his popcorn with Chris can be used to support the idea that Joe is an unselfish and considerate character.
Craft, Structure, and Langauge Skills
This section tests your ability to use context clues to determine the meaning of words and to analyze how the author’s word choice contributes to the tone or the author’s attitude towards a subject. You should be able to identify transitional words and phrases and how they contribute to the overall structure of the text.
While completing this section, you will identify text structures such as cause and effect, compare and contrast, problem and solution, and sequence of events. Prepare to recognize figurative language (and its purpose) and to differentiate between facts and the author’s opinion.
Here are some concepts that you may see on the test.
Figurative Language
Figurative language, as opposed to literal language, has a different meaning than what the words themselves actually state. You know that if someone says, “It’s raining cats and dogs,” the weather outside has nothing to do with pets — it’s just raining hard! “It’s raining cats and dogs” is an example of a type of figurative language called an idiom. Other types of figurative language include personification, similes, metaphors, and puns.
So, how might figurative language appear on the test? Let’s say that you see the statement, “That cat is as big as a horse.” You would know that the author is using figurative language because a cat wouldn’t really be as large as a horse. And, because the phrase includes extreme exaggeration, it is an example of hyperbole. Also, the phrase is an example of a simile, a comparison which uses “like” or “as.” What is the author’s intention for using this phrase? He or she wants to let you know that the cat is really big!
Using Context Clues
When you read, you often must use context clues to determine the meaning of an unfamiliar word or to decide which definition of a multiplemeaning word an author is using. Using context clues just means that you are making an educated guess about the meaning of a word based on the text around it.
For example, the word “reservations” is a multiple meaning word. If you encounter this word in a passage, you’ll need to use context clues to determine how the word is being used in the text. Consider the following passage:
Although John was having reservations about asking Carla on a second date, he called City Pizza to find out whether the restaurant allowed customers to make reservations.
If you can tell which definition of “reservations” the author uses in each instance, you are using context clues!
Point of View
A text might be written in the firstperson (uses pronouns like “I” and “my”), secondperson (uses pronouns like “you” and “your”), or thirdperson (uses pronouns like “he” and “their”) point of view. You should be able to determine from which point of view a passage is written, as well as to determine what, if any, opinions the speaker is expressing. Remember that the viewpoint of a passage might be nonbiased (based on fact) or biased (based on opinions).
For example, “Iguanas, such as mine, are the best pets” is written in the firstperson point of view because it uses the word “mine.” It is also an example of a biased statement because it is based on an opinion which cannot be proven true or false. Considering the viewpoint from which a passage is written, ask yourself what reasoning and evidence a speaker uses to support ideas.
Integration of Knowledge and Ideas
This section tests your ability to draw conclusions, identify textural evidence upon which arguments are based, and determine whether the evidence presented strengthens or weakens an argument. You will analyze how content compares in two or more texts or other media formats, such as visual representations. Be prepared to analyze how ideas in a text relate to one another.
Here are some things you may see on the test.
Drawing Conclusions
While you complete this portion of the Reading test, you will draw conclusions based on what you read as well as your analysis of visual and quantitative content. You will need to identify which arguments and claims are being presented. You’ll also consider the validity of an author’s reasoning and point out what evidence the author includes to support his or her point.
For example, imagine that you are reading a passage about type 2 diabetes and lifestyle. What conclusion does the author want you to make about the relationship between these two ideas? The author might argue that lifestyle choices contribute to the development of type 2 diabetes. Alternatively, the author might be presenting the case that lifestyle changes can help people with type 2 diabetes. Is any evidence, such as statistics, included to prove the author’s point? If so, decide if the evidence is logical and relevant or if it is weak and/or unrelated to the author’s point.
Comparing Texts
During this section, you’ll analyze how two or more texts address similar ideas or themes. You will be asked to integrate the information in the texts and to compare and contrast the authors’ evidence, viewpoints, and/or central messages.
As an example, let’s say that you are given two nonfiction passages: one is an unbiased historical passage about the Suffragette movement in the United States; the other is an article which encourages contemporary American women to vote.
How might you compare and contrast these two texts? You might decide that the author of the second article uses a persuasive tone and that the author of the first article uses a scholarly tone. Your analysis might also include that the author of one text writes for the purpose of motivating the audience to take action and that the author of the other text writes to inform the audience. A connection that you might make between the two texts is that women’s right to vote is a topic which many Americans have felt strongly about for a long time.
And that’s some basic info about the Reading subtest.
GACE Program Admission Reading Practice Questions and Answers
Question 1
Which of the following statements best expresses the main idea of paragraph 1 of the selection?
 Homelessness is a serious issue
 The problem of homelessness can be solved
 People should take action to solve the problem of homelessness
 Homelessness happens only in the United States
Correct answer: 1. This is correct because the author makes it clear that “homelessness is a serious issue” by calling it an epidemic, and by mentioning how widespread it is.
Question 2
Which of the following is the best definition of the expression handtomouth as it is used in line 3 of the selection?
 Having more than necessary
 Having nothing to spare
 Eating more than they should
 Spending too much money on food
Correct answer: 2. “Having nothing to spare” is correct. The author uses the phrase “living from paycheck to paycheck” as a context clue to help the reader understand the colloquial expression.
Question 3
The author uses the question “Have you ever seen a homeless person?” to begin the selection in order to:
 prompt readers to take a specific action
 establish the author’s position on homelessness
 connect with the reader on a topic he assumes they are familiar with
 challenge preconceived ideas about homelessness
Correct answer: 3. By opening with a rhetorical question, the author directly addresses the reader, simultaneously engaging the reader and introducing the topic of the selection. The next line of the passage, “chances are, you have,” provides a response to his question.
Question 4
Which of the following best defines the word epidemic as it is used in line 2 of the selection?
 Contagious
 Restrained
 Widespread
 Limited
Correct answer: 3. “Widespread” is correct.
Use the following passages to answer questions 58.
Passage 1 is by Dorothy Sayers; Passage 2 is adapted from a work by Raymond Chandler.
Passage 1
The detective story does not and cannot attain the loftiest level of literary achievement. Though it deals with the most desperate effects of rage, jealousy, and revenge, it rarely touches the heights and depths of human passion. It presents us with an accomplished fact and looks upon death with a dispassionate eye. It does not show us the inner workings of the murderer’s
mind—it must not, for the identity of the criminal is hidden until the end of the book. The most successful writers are those who contrive to keep the story running from beginning to end at the same emotional level, and it is better to err in the direction of too little feeling that too much.
Passage 2
I think what was really gnawing at Dorothy Sayers in her critique of the detective story was the realization that her kind of detective story was an arid formula unable to satisfy its own implications. If the story started to be about real people, they soon had to do unreal things to conform to the artificial pattern required by the plot. When they did unreal things, they ceased to be real themselves. Sayers’ own stories show that she was annoyed by this triteness. Yet she would not give her characters their heads and let them make their own mystery.
Question 5
Which of the following best paraphrases the main idea in Passage 1?
 Detective stories are not great literature
 Detective stories have plots without direction
 Detective stories may someday be improved upon
 Detective stories don’t have relatable characters
Correct answer: 1. Passage 1 makes the argument that detective stories “cannot attain the loftiest level of literary achievement.” In other words, detective stories “are not great literature.” So, this choice is correct.
Question 6
Which of the following statement would the author of Passage 2 most likely agree with?
 Detective story writers should ensure that the characters are not too deeply developed
 Dorothy Sayers’ writings have inspired a new type of detective story
 Detective writers should hold on tightly to their plots and characters’ actions
 Dorothy Sayers writes formulaic and predictable detective stories
Correct answer: 4. The author in Passage 2 makes it clear that the reason why Dorothy Sayers (author of Passage 1) finds fault with the detective genre is that she comes to it with the assumption that it is prescribed. Thus, this choice is correct.
Question 7
Which of the following best describes the relationship between the two passages?
 Passage 1 discusses the limitations of the genre; Passage 2 discusses the uniqueness of the genre
 Passage 1 focuses on the uniqueness of the genre; Passage 2 focuses on its weaknesses
 Passage 1 highlights the merits of the genre; Passage 2 downplays its faults
 Passage 1 relates the details the particulars of the genre; Passage 2 generalizes the limitations
Correct answer: 1. This is the best answer because the first passage focuses on the limitations of writing in the detective genre, while Passage 2 focuses on how the detective genre is unique and has merit.
Question 8
Which of the following would the author of Passage 1 most likely agree with?
 The plot of a detective story is formulated
 Detective story writers will soon be known as worldclass writers
 The characters in detective stories are welldeveloped and have deep inner worlds
 The detective genre involves a creative and unpredictable writing style
Correct answer: 1. This is the correct answer because Dorothy Sayers, author of Passage 1, describes the predictable, strict, and formulaic writing style that characterizes the detective genre, in her opinion.
Use the following passage to answer questions 910.
Harold Washington’s acceptance speech. In 1983, Harold Washington was the first African American elected mayor of Chicago.
1 Tonight we are here. Tonight we are here to celebrate a resounding victory. We, we have fought a good fight. We have finished our course. And we have kept the faith. We fought that good fight. We fought it, with unseasoned weapons and with a phalanx of people who mostly have never been involved in a political campaign before. This has truly been a pilgrimage. Our government will be moving forward as well, including more people. And more kinds of people, than any government in the history of Chicago. Today… today… today, Chicago has seen the bright daybreak for this city and for perhaps this entire country. The whole nation is watching as Chicago is so powerful in this! Oh yes, they’re watching.
2 Out of the crucible… Out of the crucible of this city’s most trying election, carried on the tide of the most massive voter turn out in Chicago’s history. Blacks. Whites. Hispanics. Jews. Gentiles. Protestant and Catholics of all stripes. Have joined hands to form a new democratic coalition. And… and to begin in this place a new democratic movement.
3 The talents and dreams of our citizens and neighborhoods will nourish our government the way it should be cherished and feed into the moving river of mankind. And we have kept the faith in ourselves as decent, caring people who gather together as a part of something greater than themselves. We never stopped believing that we were a part of something good and something that had never happened before.
4 We intend to revitalize and rebuild this city. To open its doors and be certain that its babies are healthy! And its old people are fed and wellhoused. We intend, we intend that our city will grow again and bring prosperity to ALL of its citizens.
Question 9
In paragraph 1 of the selection, the repetition of the word “we” has the effect of:
 uniting the people and reminding them of their collective efforts in a singular cause.
 reminding the people of all the work that they still need to do.
 singling out the ones who did not join in the movement.
 addressing the governing body correctly in the plural tense.
Correct answer: 1. In this historic speech, Washington is repeating the word “we” to honor the collective efforts of the people in working together on this cause.
Question 10
In paragraph 3, the speaker employs what figurative language device in the first sentence?
 Paradox
 Hyperbole
 Personification
 Understatement
Correct answer: 3. In the sentence, the “talents and dreams” of the people are “nourishing” and “feeding” the “river of mankind”. Here, Washington employs personification—he gives inhuman objects human qualities. He brings to life the people’s talents and dreams to show how they “feed” all mankind.
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GACE Program Admission: Mathematics
You will have 1 hour and 25 minutes to answer 56 multiplechoice questions.
The Mathematics subtest can be neatly divided into four sections:
 Number and Quantity (30%)
 Algebra and Functions (30%)
 Geometry (20%)
 Statistics and Probability (20%)
So, let’s start with Number and Quantity.
Number and Quantity
This section tests your knowledge of ratio concepts, proportional relationships, the multiplication and division of fractions, and rational numbers. You will be asked to work with both radicals and integer exponents, to use quantitative reasoning to solve problems, and to find common factors and multiples.
Let’s discuss some concepts that will more than likely appear on the test.
Dividing Fractions by Fractions
When presented with a question that asks you to divide one fraction by another fraction, keep in mind that dividing fractions is just multiplying with reciprocals (reverse). Once your multiplication problem is set up, you will multiply your numerators then your denominators.
What might this look like on the test? Here’s an example:
(8/6)/(2/3)
You’ll set up your multiplication problem:
(8/6)(2/3)
And multiply to find your answer:
24/12 or 2
Integer Exponents
Remember that an exponent is the power to which a number is raised. For example, 4^{3} is the same as 4 x 4 x 4. In this example, 3 is the exponent.
What might this look like on the test? You may, for example, be asked to compare two base/exponent combinations (such as 4^{4} and 6^{3}) and decide which of the two is greater or if they are equivalent.
Common Factors and Multiples
To prepare for this section of your test, you should review both common factors and multiples, including least common multiples (LCMs) and greatest common factors (GCFs). The LCM of two numbers is the smallest number, excluding zero, that is a multiple of both numbers. The GCF is the greatest factor that can be used to divide two numbers. In order to determine the GCF of two numbers, list the prime factors of each of the two numbers. Then, multiply the prime factors which the numbers have in common in order to find your answer.
On the test, you may be asked to determine the greatest common factor of 18 and 24 (which is 6).
Algebra and Functions
This section tests your knowledge on the connections between proportional relationships and linear equations, as well as your ability to interpret and build functions.
You need to be able to apply arithmetic to algebraic expressions and use operations to generate equivalent expressions. You will also be asked to represent and solve equations and inequalities.
Here are some concepts that you may see on the test.
Solving for x
While completing the Algebra and Functions portion, you’ll need to work with some variables. Variables don’t have to be scary! Just remember that a variable is a standin for a number. Most variables are represented with letters, like “x.”
You’ll be asked to solve equations to find out the value of variables. Here’s an example of the type of problem that you might find in this section of the test:
Solve for x:
4x – 2 = 2x + 8
To solve this equation, you would bring like terms to one side:
4x – 2x = 2 + 8
Add and subtract on each side:
2x = 10
And divide each side by 2 to find the value of x:
x = 5
Equivalent Expressions
Equivalent expressions have the same solution, but they may be written differently. To solve for equivalent expressions, you’ll need to combine like terms and use the distributive property. Just remember that the distributive property will require you to use the order of operations to find the correct answer!
Here’s an example of two equivalent expressions:
2x^{4} + 2x and 2(x^{4} + x).
The second example has the same value as the first. If you just distribute the 2 in the second equation, it will look like the first equation.
Geometry
This section tests your knowledge of congruence, right triangles, similarity, trigonometry, volume, area, surface area, angles, circles, and the Pythagorean theorem. You will be asked to apply geometric concepts in order to construct, compare, and describe the relationships between figures and to work with transformations in the plane.
Here are some things you may see on the test.
Geometrical Figures
You need to know about parallel and perpendicular lines, as well as geometrical figures, including circles, quadrilaterals, and triangles. While you complete this portion, you will be asked to compare figures and to describe the relationships between them. You’ll also identify examples of congruence and interact with coordinate planes.
Here’s an example question (with answer) regarding a geometrical figure:
The given figure is a(n) equilateral triangle because each of its angles measures 60°.
Volume
Volume is how much space an object takes up. You’ll use your knowledge of volume formulas to solve problems like the one below:
Your neighborhood swimming pool is 30’ wide and 35’ long. It measures 6’ in depth. When filled to capacity, what is the volume of the pool?
To solve this problem, think of the pool as a rectangular prism. To find the volume of a rectangular prism, all you need to do is multiply the length, width, and height:
V = l x w x h
30 x 35 x 6 = 6,300
The volume of the pool is 6,300 cubic feet.
Pythagorean Theorem
Questions about the Pythagorean theorem will test your knowledge of right triangles and your ability to use these shapes to solve equations, make comparisons, and draw conclusions.
According to this theorem, side c is the side of the triangle opposite the right angle; side a and side b are the other two sides of the right triangle. You will use the Pythagorean equation (a^{2} + b^{2 }= c^{2}), to solve related questions. Here’s an example of what a related question might look like on the test:
A piece paper has been folded into a right triangle. Side a is 4 inches and side b is 3 inches. If side c is the hypotenuse, what is the length of side c?
To solve this problem, just plug the numbers into the Pythagorean equation:
4^{2} + 3^{2 }= c^{2}
Apply the exponents:
16 + 9 = c^{2}
Add the values on the left:
25 = c^{2}
And find the square root of c:
5 = c
So, the hypotenuse of the little origami craft must be 5 inches!
Statistics and Probability
This section tests your knowledge of linear and probability models, bivariate data patterns, statistical variability, and the use of probability to evaluate outcomes. You should also be prepared to describe distributions and make inferences about populations based on random samples.
Let’s discuss some concepts that will more than likely appear on the test.
Measures of Center
The Mathematics test will require you to work with measures of central tendencies, such as mean, median, and mode. For an example, take a look at the following question:
This list shows the price of jackets in a store last month: $34, $45, $46, $48, $56
This is the current list of jacket prices: $4, $45, $44, $48, $56
In the second list, which price is the outlier? Does the outlier change the mean, the median, or the mode?
In this example, the $4 price is the outlier, because it is drastically different from the other prices. The outlier does not affect the mode (frequency of appearance) of the prices. It also does not affect the median (midpoint) price, because the number of prices remains the same on both lists. It does, however, affect the mean (average) price. The mean price of the jackets in the first list is $45.80, and the mean price of jackets in the second list is $39.40. You can find the mean of each list by adding the price of each jacket and then dividing the sum by the number of items in the list (5).
Distributions
In statistics, a probability distribution is used to describe the likelihood of an outcome.
A discrete probability distribution may appear as a formula or a table listing all values that a discrete variable could be. Discrete variables have a finite and countable number of values and continuous variables do not.
Cumulative probability distributions describe the probability that the value of a variable will fall within a specific range.
A uniform probability distribution describes a situation in which every value of a random variable has an equal chance of occurring. For example, flipping a coin would have a uniform probability distribution. Each of the two outcomes (heads or tails) is equally likely to occur. Here’s an example.
Imagine that you will flip a coin twice.
Number of “heads”  Probability 
0 1 2 
.25 a .25 
What value would correctly replace a in the distribution table?
The value .5 would correctly replace a because the probability values would then equal 100%.
And that’s some basic info about the Mathematics subtest.
Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.
GACE Program Admission Mathematics Practice Questions and Answers
Now, let’s look at a few practice questions in each area to see how these concepts might actually appear on the real test.
Question 1
Which of the following expressions is equivalent to a/3 + b/5?
 (a + b)/8
 (5a + 3b)/15
 (3a + 5b)/15
 (5a + 3b)/30
Correct answer: 2. To add fractions, a common denominator must be used. In this case, the denominators of “3” and “5” are prime (have no common factors except for 1). Therefore, the ideal common denominator for “3” and “5” is the product of 3 × 5, which is 15. In order to scale the fraction a/3 up to have a denominator of 15, that fraction must be multiplied by 5/5, resulting in 5a/15. In order to scale the fraction b/5 up to have a denominator of 15, the fraction must be multiplied by 3/3, resulting in 3b/15. Finally, the two fractions that now share a denominator of 15 can be added straight across the numerators while the denominator of the sum remains 15: 5a/15 + 3b/15 = (5a + 3b)/15.
Question 2
The recipe for Grammy Jane’s breakfast muffins calls for ⅙ cup of flour per muffin. Right now, there are 2⅚ cups of flour available for baking. How many muffins can be made?
 23
 17
 16
 11
Correct answer: 2. If each muffin requires ⅙ cup of flour, and there are 2⅚ cups of flour available, then 2⅚ must be divided by ⅙ to see how many muffins can be made. 2⅚ ÷ ⅙ should be transformed to 17/6 ÷ ⅙ because mixed numbers should be converted to improper fractions in order to divide. Then, the expression should be rewritten as and then to 17/6 × 6/1 because division of a fraction is the equivalent of multiplication by its reciprocal. Because “6” appears in the numerator of one fraction and the denominator of the other, the answer is just 17/1, or 17.
Question 3
What is the digit in the hundreds place in the product of 63 × 31?
 3
 1
 5
 9
Correct answer: 4. The product of 63 × 31 = 1,953. The digit that occupies the hundreds place is 9.
Question 4
Solve the following equation and present your answer in fullyreduced fraction form:
3(4x – 5) + 8 = 9(2x – 1)
 1/3
 8/3
 1/15
 23/6
Correct answer: 1. The first step in solving this equation is to simplify each side completely. The first step of simplification requires distributing into each set of parentheses to get 12x – 15 + 8 = 18x – 9. Next, like terms on each side are combined to the extent possible to get 12x – 7 = 18x – 9. Finally, solving can begin. While several steps would be valid at this point, the smaller variable part is often moved to join the larger and so 12x can be subtracted from each side to get 7 = 6x – 9. Now, the variable can be isolated by adding 9 to each side (2 = 6x) and dividing by the coefficient of x, 6, on each side. The resulting solution, 2/6 = x should be reduced completely by the common factor of 2 in the numerator and denominator of the fraction, yielding the best answer: 1/3.
Question 5
Marty gets an allowance of $5 each week from his parents. He also can earn extra money by doing additional chores outside of his usual household responsibilities for $1.50 per chore. He has been working on saving his money to buy a new game and thinks he will be close this week. If he would like to get at least $20 from his parents at the end of the week, what is the minimum number of additional chores Marty needs to complete?
 13
 10
 14
 17
Correct answer: 2. Let c = number of additional chores Marty must complete. Because Marty will earn $1.50 for each chore, the expression 1.5c represents the money Marty will earn from doing c additional chores. Marty gets $5 each week automatically from his parents, so the expression 5 + 1.5c represents the total amount of money that Marty can get from his parents at the end of the week. Marty wants to have at least $20, and so 5 + 1.5c ≥ 20 expresses Marty’s goal of attaining at least $20. To solve this inequality statement, subtract 5 on each side to get 1.5c ≥ 15. Then, divide both sides of the inequality statement by 1.5 in order to isolate c. Neither of these steps require a change in direction of the inequality symbol because neither one is multiplication or division by a negative number. The final result, therefore, is c ≥ 10, indicating that Marty must complete at least 10 additional chores over the course of the week in order to get at least $20 from his parents at week’s end.
Question 6
The graph of the function f(x) is shown above. For what value(s) of x does f(x) = 1?
 0, 1, and 2
 None
 4, 1, and 4
 2
Correct answer: 3. The expression “f(x)” means “the value of the function,” which is the ycoordinate of the function. Accordingly, “f(x) = 1” means that the ycoordinate equals 1. Therefore, the question is asking for the xvalue(s) on this graph that have a corresponding ycoordinate of 1. This question is answered with a simple look from left to right across the function for intersection with the horizontal line y = 1. The xvalues that have a ycoordinate of 1 are 4, 1, and 4.
Question 7
Which of the following expressions (in square units) is the most reasonable estimate for the area of the circle in the graph shown above?
 23
 128
 41
 27
Correct answer: 3. The area, A, of a circle with radius r is found using the formula A = πr². The radius of the circle in the diagram must be estimated as slightly larger than halfway between 3 and 4 units. Radius equals 3.6 is a reasonable approximation. Using 3.6 for r and using 3.14 as a decimal approximation for the irrational number π in the area formula leads to the calculation of A = 3.14(3.6)². Following the order of operations leads to a simplified equation of A = 3.14(12.96) and then A = 40.6944. The value 40.6944 becomes 41 when rounded to the nearest whole number because the tenths place digit is 6 (which is at least 5, and so requires rounding up).
Question 8
A pole broke 15 feet from its base. The base remains perpendicular to the ground. The break was not complete, however, so the top portion of the pole extends to the ground while still remaining attached to its base, as shown in the diagram above. The top portion of the pole hits the ground 8 feet from the place where the base of the pole enters the ground. How tall, in feet, was the pole before it broke?
 25
 23
 17
 32
Correct answer: 4. Because the pole is perpendicular to the ground, the pieces of the pole form one leg and the hypotenuse of a right triangle. The space on the ground between the base of the pole and the (former) top of the pole is the other leg of the right triangle. The two legs of the right triangle, then, are 15 feet and 8 feet. Therefore, the length of the top portion of the pole is the length of the hypotenuse of the right triangle and can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle will equal the square of the hypotenuse of that triangle. The formula for the Pythagorean Theorem is written a² + b² = c², where a and b are the leg lengths and c is the length of the hypotenuse. In this case, then, the equation to solve is 8² + 15² = c². Following the order of operations correctly makes the equation 64 + 225 = c², and then 289 = c². The equation is solved for c by taking the square root of each side and using only the positive version of the square root of 289, which is 17. [Also note that “8, 15, 17” is a Pythagorean Triple, and so the missing side could have been found without actually making the calculations for the Pythagorean Theorem.] Because the top portion of the pole has a length of 17 feet, the total height of the pole before it broke would have been the 15foot portion still in the ground, plus the additional 17 feet, or 15 + 17 = 32 feet.
Question 9
A change purse contains 4 pennies, 3 nickels, 2 dimes, and the rest of the coins are quarters. If a person has a 1/3 probability of selecting a penny when randomly selecting a coin from the change purse, how many quarters are there?
 12
 4
 2
 3
Correct answer: 4. Because drawing a penny when randomly selecting a coin from the change purse has a probability of 1/3, the 4 pennies known to be in the change purse must represent onethird of the total number of coins in the change purse. Because 1/3 = 4/x is solved by crossmultiplication to get 1x = 12, there must be 12 coins in the change purse. The change purse contains 4 + 3 + 2 = 9 coins that are not quarters. The difference between the total number of coins and the number of coins that are not quarters, 12 – 9, must be equal to the number of quarters in the change purse. Therefore, there are 3 quarters in the change purse.
Question 10
The scatter plot above shows data that is best described as having:
 a strong negative linear correlation between x and y.
 a very weak negative linear correlation between x and y.
 a strong positive linear correlation between x and y.
 a very weak positive linear correlation between x and y.
Correct answer: 1. Though not all of the data is perfectly lined up, this data does show a relatively strong linear correlation because of the relatively tight clustering of the data in the rough shape of a line. If a line of fit were attempted here, almost all of the data would be close to the line. The correlation is negative because the path of the cluster of points appears to aim downwards as the graph is viewed from the left to the right. That is, the data points show decreasing yvalues as xvalues increase, like a line with a negative slope.
Getting the Help You Need
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GACE Program Admission: Writing
You will have 1 hour and 40 minutes to answer 40 multiplechoice questions and 2 constructedresponse questions.
The Writing subtest can be neatly divided into two sections:
 Text Types, Purposes, and Production (60%)
 Language and Research Skills for Writing (40%)
So, let’s start with Text Types, Purposes, and Production.
Text Types, Purposes, and Production
This section will require you to write two essays to test your ability to create both argumentative and informative/explanatory texts. Your work will be evaluated in terms of your ability to coherently express ideas using correct grammar and appropriate structure, to develop and maintain a clear focus, and to provide relevant evidence and details.
A. Argumentative Essay section:
For this portion of the Writing test, you’ll use sufficient, pertinent evidence to successfully support a claim. Be sure to use reasonable examples and details which logically support your position and to follow the general guidelines of standard English. Focus on writing a strong introduction and include a thesis statement; you will want your position on the topic to be clear to the reader.
B. Informative/Explanatory Essay section:
While completing this section of the Writing test, you will draw evidence from informational text which will be provided for you. You will use this evidence to support explanations of complex ideas presented in the text. However, be sure to avoid plagiarism! Remember to write with clarity, maintain a clear focus, and demonstrate your ability to use appropriate diction and a variety of sentence structures.
Language and Research Skills for Writing
While you complete this portion of the test, you’ll recognize and correct grammatical errors, structural issues, and misused vocabulary words. You will also analyze sources in terms of relevance and credibility and appropriately cite those sources.
Here are some concepts that you may see on the test.
PronounAntecedent Agreement
Pronouns, like “he,” are used to replace more specific nouns like “George.” If a more specific noun, like “George,” occurs first in the text, then that noun is an antecedent. Consider this information as you read the following sentence:
“If that giraffe could speak, he would probably tell you that the leaves of the acacia tree are his favorite treat.”
In the example, “giraffe” is the antecedent and “he” is the pronoun. Pronouns should agree with their antecedents in terms of number and gender. Consider how the same sentence becomes confusing when the pronoun doesn’t agree with the antecedent:
“If that giraffe could speak, he would probably tell you that the leaves of the acacia tree are their favorite treat.”
Misplaced and Dangling Modifiers
A modifier is a word, phrase, or clause that describes another word. Usually, modifiers are adjectives, like “friendly” or “personable.” Sometimes, a modifier is included in the wrong part of a sentence. Consider this example:
“The live bowl of fish looks great in her office.”
Since the fish are alive and the bowl is not, “live” is a misplaced modifier. You could revise the sentence by moving the modifier:
“The bowl of live fish looks great in her office.”
A dangling modifier is a modifier which does not have a clear subject. The word that a dangling modifier is meant to describe is missing. Consider this example:
“Staring over the fields, a storm was approaching.”
“Staring” is a modifier but who or what is staring here? There are multiple ways to revise this sentence. Here is one example:
“He was staring over the fields as a storm was approaching.”
Elements of a Citation
Be prepared to recognize elements of citations and to determine what type of source a citation references. Also, remember that direct quotations belong in quotation marks and need internal citations. An internal citation occurs in parentheses in the body of the text.
Let’s test your knowledge now with an MLA citation for an imaginary source. As you read the citation, decide what type of source it references (print book, newspaper, website, etc.):
Doe, Jane. “How I Stood up to Cancer.” Natural Health Oct. 2018: 101104. Print.
If you determined that the citation refers to an article in a print magazine, you are correct!
And that’s some basic info about the Writing subtest.
GACE Program Admission Writing Practice Questions and Answers
Practice Questions and Answers
Question 1
Both₁ of Janet’s children became a concert pianist₂ after they went to Julliard; she was unbelievably₃ proud of them.
Which of the following parts of the sentence is grammatically incorrect?
 No error
 2
 1
 3
Correct answer: 2. Nouns that refer to the same item must agree in number: they must both be singular, or they must both be plural. Because the sentence states that Janet has two children, the number of concert pianists should be plural. The corrected sentence should read, “Both of Janet’s children became concert pianists.”
Question 2
It bothers me when Casey₁ says that she₂ is inarticulate, because she₃ is more articulate than me₄.
Which part of the sentence contains an error in pronoun usage?
 3
 4
 2
 1
Correct answer: 2. Pronouns must agree in case. Problems of case can occur with comparisons because they are really shorthand sentences which usually omit words. Complete the above comparison in your head, and you can choose the correct case for the pronoun. You wouldn’t say, “She is more articulate than me is,” you would say, “She is more articulate than I am.”
Question 3
Famine and close living quarters₁ in cities was₂ to blame for the rapid spread of the Black Death₃ in Italy.
Which part of the sentence contains a grammatical error?
 1
 3
 No error
 2
Correct answer: 4. The subject of the sentence is “famine and close living quarters.” Because this is a compound subject made up of two singular nouns joined by and, a plural verb is required. Therefore, “was” should be changed to “were.”
Question 4
My band has been rehearsing daily₁. Because we have a concert in two weeks₂. It is our first paid gig, so we are all looking forward to it₃.
Which part of the passage is a fragment?
 1
 3
 No error
 2
Correct answer: 4. A sentence is a group of words that has a subject, a verb, and expresses a complete thought; a sentence fragment is a group of words that does not express a complete thought. The word “because” makes “2” a fragment. The corrected sentence would read, “My band has been rehearsing daily because we have a concert in two weeks.”
Question 5
Trying to fall asleep in the uncomfortable bunk₁, the sheets felt uncomfortably hot₂ and the breeze refused to blow₃.
Which part of the sentence contains a misplaced modifier?
 2
 3
 1
 No error
Correct answer: 3. “Trying to fall asleep…” is a dangling modifier or a modifier that appears to modify the wrong word or phrase because the word or phrase that it should modify is missing from the sentence. A corrected version of the sentence would read, “Trying to fall asleep in the uncomfortable bunk, I felt uncomfortably hot in the sheets and the breeze refused to blow.”
Question 6
Mark₁ your music is so poignant₂ and original, and I love how it reflects your passion. We will probably hear you on the radio₃ someday!
Where should a comma be inserted to make the sentence grammatically correct?
 After “poignant”
 After “Mark”
 After “radio”
 No comma is needed
Correct answer: 2. Use commas to separate the name of a person being spoken to from the rest of the sentence. The name “Mark” at the beginning of the sentence should be followed by a comma.
Correct answer: 3. The expression “f(x)” means “the value of the function,” which is the ycoordinate of the function. Accordingly, “f(x) = 1” means that the ycoordinate equals 1. Therefore, the question is asking for the xvalue(s) on this graph that have a corresponding ycoordinate of 1. This question is answered with a simple look from left to right across the function for intersection with the horizontal line y = 1. The xvalues that have a ycoordinate of 1 are 4, 1, and 4.
Question 7
I had buyer’s remorse when a newer version of my phone came out just weeks after I purchased the old one. My regret increased when I discovered that the newer version had more storage capabilities and cost only slightly more than I paid.
The underlined word “remorse” means:
 regret
 guilt
 embarrassment
 anticipation
Correct answer: 1. Synonyms are words that mean the same thing or almost the same thing. When you see a word you don’t know, you can use synonyms as context clues to help figure out an unfamiliar word’s meaning. In the passage, the synonym “regret” helps you understand the meaning of “remorse.”
Question 8
Which of the following internal citation is NOT written correctly?
 Biographer Joe Smith correctly asserts that Emily Dickinson’s poetry is “a deep reflection of her true life” (14).
 Emily Dickinson’s poetry is a “deep reflection of her true life” (Smith 14).
 Emily Dickinson’s poetry is a “deep reflection of her true life” (Joe Smith, 14).
 All of the above are correctly written
Correct answer: 3. Emily Dickinson’s poetry is a “deep reflection of her true life” (Joe Smith, 14) is incorrectly written. Within an internal citation, only include the writer’s last name and pagination within the parenthesis.
Question 9
This weekend, I will go to basketball practice on Saturday morning₁, have dinner with my girlfriend on Saturday night₂, and then I am excited to be going to the movies on Sunday₃.
Which part of the sentence contains an error in parallel structure?
 3
 No error
 1
 2
Correct answer: 1. Parallel structure is a pattern which involves two or more words, phrases, or clauses that are similar in length and form. Because the writer established a parallel pattern at the beginning of the sentence with “go to basketball” and “have dinner,” which are in the future tense, he cannot switch to future continuous tense with “to be going.” To maintain parallel structure, the last part of the sentence should read, “and then go to the movies on Sunday.”
Question 10
When I walk₁ my dog at night, she₂ barks at everyone we pass, she₃ must not like strangers.
Which part of the sentence above contains an error?
 2
 3
 1
 No error
Correct answer: 2. This sentence is a runon with a comma splice. The comma between “pass” and “she” should be replaced with either a period to make a new sentence or a coordinating conjunction such as “so” to connect the two independent clauses.
Getting the Help You Need
Feeling overwhelmed? Don’t worry! We have you covered.
Go to 240tutoring.com and sign up for our GACE Program Admission study guide.
It comes with a 48 hour no questions asked refund policy, so if you don’t like it, you can request a full refund within 48 hours.
Also, it comes with the 240Tutoring Guarantee. If you score a 90% or higher on our practice test, but fail the real exam, you’re entitled to a moneyback refund.