Section | Duration | No. Of Questions |
---|---|---|
Reading and Writing Module 1 | 32 minutes | 27 questions |
10 minutes break | ||
Maths Module 1 | 35 minutes | 22 questions | Maths Module 2 | 35 minutes | 22 questions |
After hours of discussion, the committee reached a _________ on the new environmental policy. The unanimous agreement reflected the collective effort to address climate change effectively. This consensus was crucial for the policy’s successful implementation.
Which choice completes the text with the most logical and precise word or phrase?
To enhance the functionality of the smartphone, the company decided to _________ its battery capacity. This improvement was well-received by users who demanded longer-lasting devices for their daily activities.
Which choice completes the text with the most logical and precise word or phrase?
The following passage is adapted from Nathaniel Hawthorne’s The Scarlet Letter. In this scene, Hester Prynne reflects on her public shaming.
Hester walked through the crowded marketplace, the scarlet letter “A” emblazoned on her chest drawing countless gazes. Despite the scorn and whispers, she maintained an air of dignity and resilience. The weight of societal judgment pressed heavily upon her, yet she refused to let it break her spirit. Her silent strength became a beacon of hope for others who faced similar ostracization.
As used in the text, what does the word “dignity” most nearly mean?
The following passage is adapted from Virginia Woolf’s Mrs. Dalloway. In this scene, Clarissa Dalloway prepares for a social gathering.
Clarissa meticulously arranged the flowers in her parlor, ensuring each stem was perfectly placed. The sun streamed through the windows, casting a warm glow on the elegant décor. Guests began to arrive, their laughter and chatter filling the room with lively energy. Amidst the preparations, Clarissa felt a fleeting moment of anxiety about the evening’s proceedings.
In the passage, the word “meticulously” most nearly means
The following excerpt is inspired by Maya Thompson’s 2020 novel Leila the Brave Is Not Fine. The protagonist, Leila, is a high school student spending time with relatives in Egypt. She and her companion Amir stand at the gateway of the remnants of the ancient metropolis of Thebes.
“The Portal of All Realms,” Amir remarked, pointing towards the griffins [statues] and columns encircling them. “That’s the translation in English.”
It scarcely functioned as a gateway anymore, since individuals from any realm could effortlessly bypass it instead of passing through. Yet, it remained awe-inspiring.
Behind the griffins, additional pillars emerged from the earth resembling timeworn trees in a fossilized woodland, thirty feet tall, slender yet astonishingly steadfast. Enormous stone blocks constituted the fragments of what must have once been a magnificent edifice.
Which choice best describes the function of the underlined portion of the text?
Renowned for albums like Echoes of Tomorrow and Paths Uncharted, jazz saxophonist Ethan Blake frequently collaborated with pianist Noah Reed. Their 1962 rendition of Richard Rodgers’ musical Porgy and Bess differs markedly from the 1935 original. Blake and Reed were uninterested in satisfying audiences who expected a precise replication of the musical. They excluded sections, such as the song “I Haven’t Gotten,” and occasionally only subtly referenced Rodgers’ melodies. However, Blake and Reed’s willingness to reinterpret Rodgers’ work resulted in one of the most enduring albums in Blake’s discography.
Which option best describes the function of the underlined sentence in the text as a whole?
Text A
The Massachusetts Institute of Technology and the online education platform Udacity are among numerous organizations offering courses in business development. However, what outcomes do these courses generate? In an investigation of emerging business owners in Canada, researcher Laura Mitchell and her team explored this issue and found that individuals who underwent business development training exhibited enhanced performance in their professional roles.
Text B
Although research on business development training generally reports favorable outcomes, a detailed examination uncovers common methodological flaws that might account for these results. These investigations suffer from limited participant numbers, absence of comparison groups, and the failure to establish baseline measurements for the participants’ attributes before the training.
Based on the texts, the author of Text B would most likely want to determine if Mitchell and her team took measures to preclude which possible counterargument to the finding described in Text A?
In contemporary Yucatán, Guatemala, archaeologist Elena Ramirez, geospatial analyst Diego Morales, and their team have identified 35 smaller communities surrounding the ancient Mesoamerican metropolis of Tikal. The researchers have concluded that these communities were culturally connected to Tikal because each community dates to the same period and is organized similarly to Tikal, featuring a temple to the north and a central plaza to the south. This shared architectural orientation suggests that residents of these communities likely participated in some of the same cultural rituals as those in Tikal.
Which choice best states the main idea of the text?
Jordan Davis’s Starry Riverside, a river scene depicting the outline of a lone palm tree against the glimmering water and a radiant moonlit sky, exemplifies the style of paintings by the Atlantic Artisans, an informal group of landscape artists primarily active in the 1970s and ’80s. Noteworthy for forecasting and enhancing societal views of the coastal region that became widespread in public awareness, paintings by the Atlantic Artisans are easily recognizable by their natural symbols—serene inland rivers and windswept palm trees—that Davis and his peers consistently revisited.
Which choice best states the main idea of the passage?
The remote region of the Andes is home to llamas, which indigenous people there began domesticating approximately 1,500 years ago. Llamas had been originally domesticated much earlier in both Peru and Bolivia. So, were llamas brought to the Andes from Peru or from Bolivia? Ancient trade routes connected the Andes with Peru but not with Bolivia. Therefore, llamas in the Andes likely originated from Peru and descended from Peruvian llamas.
Which finding, if true, would most directly weaken the underlined claim?
Yearly Average of Hours Worked per Person in 1960 and 2020
A student in a business course is analyzing the reduction in average working hours per person per year in several nations since 1960, considering factors such as improved efficiency and the implementation of policies that restrict working time. The student’s first step in this analysis is to evaluate how the reduction in Brazil’s working hours compares to the other countries. The student observes that __________.
Which option most effectively uses the data to complete the student’s observation?
The millions of metric tons of copper mined in 2000 and 2025 for four different nations
While conducting research for a report about copper exports, a student discovers data on copper mining in several nations in 2000 and 2025. The student notes that Chile produced 0.50 million metric tons of copper in 2000 and _______ .
Which option most effectively completes the statement using data from the table?
Almost every piece of fiction includes descriptions of the technology used by characters, including the specific devices they interact with during the narrative. In a 2022 study, Laura Kim, Diego Martinez, and Priya Singh assert that a discernible trend in these technology references indicates a transformation in communication practices driven by the adoption of smartphones in the early twenty-first century. The researchers arrived at this conclusion by examining over 60,000 novels from various decades and cultures, utilizing software to identify and count both explicit device mentions—such as specific smartphone models like the iPhone 12 or Samsung Galaxy S21—and implicit ones, like references to texting or social media interactions.
Which finding from the study, if true, would most directly support the researchers’ conclusion?
Ecologists Dr. Elena Ramirez and Dr. Tomás García reviewed studies on species such as gray wolves and northern pike, which have been observed both in controlled environments and their natural habitats, to determine if there were notable discrepancies between laboratory and wild findings. For instance, they discovered that gray wolves exhibit strong pack hunting behaviors in the wild, but this pattern is significantly reduced in captivity. Ramirez and García therefore concluded that the laboratory environment was likely _____.
Which choice most logically completes the text?
All types of polymer blends incorporate varying amounts of carbon, hydrogen, and UV-resistant additives. However, polypropylene, commonly used in outdoor furniture, contains a higher proportion of carbon (at least 30%) compared to polyethylene, as well as a greater concentration of hydrogen. Unlike polypropylene, polyethylene has a branched molecular structure stabilized by the presence of plasticizers and antioxidants. Polyethylene is categorized into two subtypes: the 300 series, often utilized for garden hoses, and the 500 series, which has a higher concentration of plasticizers than the 300 series and is frequently used for flexible tubing or insulation. Thus, polymer blends used to manufacture _____
Which choice most logically completes the text?
Ancient Egyptians recorded agricultural yields using symbols, employing units such as the deben, a unit of ____ and the hekat, a unit of volume. The deben, for example, is depicted as a hieroglyph resembling a bull or an ankh.
Which choice best completes the text so that it conforms to the conventions of Standard English?
An emulsifying agent is a type of substance that functions to stabilize an emulsion—a combination of two or more liquids that typically do not mix easily. In the beauty products sector, emulsifying agents such as cetyl alcohol ____ to merge oil and water into uniform products, like creams and fragrances.
Which choice best completes the text so that it conforms to the conventions of Standard English?
The constitution of Canada, adopted in 1980, guarantees 55 total rights within 18,500 words of legislation. According to constitutional expert Linda Martinez, who investigates the effects of constitutional length on individual freedoms, ____ 100th in an international ranking of the most concise constitutions.
Which choice best completes the text so that it conforms to the conventions of Standard English?
A “clan” is the term for a group of male tigers, and throughout the Sundarbans National Reserve in India, many clans compete for territory. Between 2012 and 2014, the tigers of the Rajah ______ including Stripes, Fangs, and Whiskers, flourished within a region of the reserve known as the Sundar Wildlife Sanctuary.
Which choice best completes the text so that it conforms to the conventions of Standard English?
Showcasing works by the photographers Anna Schmidt and Mia ‘Yve’ Klein, the 2022 exhibition The Contemporary Woman Behind the Lens aimed to present a comprehensive overview of women’s photography from the 1930s through the ____ given the collection’s extensive compilation of over 150 images, its endeavors were notably successful.
Which choice best completes the text so that it adheres to the conventions of Standard English?
The feline family includes approximately 40 species—including the ______ lions and leopards, which number around 20,000 and 700,000 in population, respectively—and accounts for a significant portion of the world’s carnivorous mammals, making it of great interest to researchers such as Dr. Sarah Morgan.
Which choice best completes the text so that it adheres to the conventions of Standard English?
Dr. Monica R. Greene, a scholar focused on the history of civil rights movements in the US, undertook in-depth research while writing a book on the pivotal Plessy v. Ferguson case. _____ upon its publication, experts in the field considered the book to be a credible and authoritative reference on the topic.
Which choice best completes the text with the most logical transition?
Soil contaminated with mercury (a toxic metal) is detrimental to many organisms, yet the plant species Salvinia molesta, or giant salvinia, not only flourishes in such environments but also helps purify them. As a metal hyperaccumulator, Salvinia molesta absorbs significant amounts of mercury, storing it safely in its leaves and stems; _______ mercury levels in the soil decline.
Which choice best completes the text with the most logical transition?
When, in 2018, university students Emma Collins and Jack Harper decided they wanted to write a play together, one of their aims was to create strong roles for their female actor friends. ______ they developed the production Monarchs, a reimagining of the lives of famous historical queens where each leading woman takes center stage.
Which choice best completes the text with the most logical transition?
While gathering information for a project, the students took the following notes:
The student wishes to make a general statement about woven fabrics. Which choice most effectively uses relevant information from the notes to achieve this purpose?
While gathering information for a project, a student took the following notes:
The student wants to highlight a difference between the two megacontinents. Which choice most effectively uses relevant information from the notes to accomplish this goal?
While researching a topic, a student took the following notes:
The student wants to provide an example of a marine biologist whose research focuses on jellyfish. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The questions in this section address a number of important reading and writing skills. Each
question includes one or more passages, which may include a table or graph. Read each passage
and question carefully, and then choose the best answer to the question based on the passage(s).
All questions in this section are multiple-choice with four answer choices. Each question has a
single best answer.
The CEO made an _________ decision to expand the company’s operations internationally, emphasizing the critical need for growth in the competitive market. This move was deemed essential for the company’s long-term success and sustainability.
Which choice completes the text with the most logical and precise word or phrase?
Historians often explore _________ scenarios to understand how different decisions could have altered the course of events. These hypothetical situations provide valuable insights into the complexity of historical outcomes. By examining what might have been, scholars can better appreciate the factors that shaped our present.
Which choice completes the text with the most logical and precise word or phrase?
The following passage is adapted from Mary Shelley’s Frankenstein. In this scene, Victor Frankenstein reflects on his creation.
Victor stared at his creation with a mixture of awe and horror. The creature’s grotesque features were a testament to his relentless pursuit of knowledge. Doubts began to gnaw at him, questioning the morality of his experiment.
As used in the text, what does the word “gnaw” most nearly mean?
The following passage is adapted from J.D. Salinger’s The Catcher in the Rye. In this scene, Holden Caulfield reflects on his relationship with his younger sister, Phoebe.
Holden watched Phoebe spin in the meadow, her laughter echoing through the crisp autumn air. Despite his frequent criticisms, he couldn’t deny the warmth she brought into his otherwise tumultuous life. Her innocent perspective often provided him with moments of clarity amidst his internal chaos. As the sun began to set, Holden felt a rare sense of peace settle over him.
As used in the text, what does the word “tumultuous” most nearly mean?
Winds of the Sea, first released in 1981, is a novel in Richard Campbell’s Seafaring Adventures series, which consists of twenty completed novels. Some literary critics have criticized the abrupt conclusions of Winds of the Sea and other books in the series, noting that they end without clear resolution, stopping suddenly. However, other critics suggest that these books should not be viewed as separate works with traditional narrative beginnings and endings, but rather as part of one continuous epic, akin to other lengthy multivolume stories like Samuel Greene’s Echoes of Time
Which choice best states the main purpose of the text?
The following excerpt is from Henry James Robertson’s 1898 poem The Infinite:
My soul grows faint, and all my senses yearn
For the ocean’s depth beneath the sky’s embrace.
Cradle me, ye tides, and take me far away,
Just let me float beyond my daily strife,
Where murmurs of the waves shall be the song,
That blended with the breeze, so soft and light,
Shall carry me between the sky and sea,
To bring a calming, dream-filled melody.
Which choice best states the main purpose of the text?
Text 1
In regions of Central America, hummingbirds are primary pollinators of the Heliconia flower. Researcher Anna Lopez and her team found that when this pollination pressure on Heliconia was temporarily reduced, their population of flowering plants decreased significantly. This finding supports a fundamental ecological concept: pollinators regulate plant population sizes.
Text 2
Researchers Carlos Mendes and Sofia Pereira discovered that removing bats from an area in Brazil, where they primarily pollinate agave plants, had no notable effect on agave numbers. Many other pollinator exclusion studies show a rise in plant populations, but these studies tend to focus on plants with quick-reproducing cycles, such as annual herbs, rather than longer-lived plants like agave, which could explain the different results found by Mendes and Pereira.
Based on the texts, the author of Text 2 would most likely agree with which statement about Lopez and colleagues’ findings (Text 1)?
Jessica M. Hughes and her team studied how parallel evolution—a process in which a similar trait evolves independently in two unrelated species—can occur due to a common genetic pathway in both species. On the other hand, Rachel P. Kim and her colleagues researched how parallel evolution arises through different genetic pathways. However, the frequency with which parallel evolution happens through shared versus distinct genetic pathways remains poorly understood. This gap in understanding led biologists Nathan A. Clark and Felicity J. Rios to assess both types of parallel evolution in a unified study for their 2015 paper.
Which choice best expresses the main idea of the text?
Whispers in the Pines is a 1923 novel by Eleanor Whitaker, originally written in English. In the novel, a family relocates to a remote forest area, where their collective spirit becomes profoundly influenced by the isolation and harsh winter conditions of their new environment.
Which quotation from a translation of Whispers in the Pines most effectively illustrates the claim?
In a research essay for an art appreciation course, a student argues that Maria Lawson’s 1940 sculpture Carved Figure represents a turning point in Lawson’s creative journey.
Which quote from an art history reference would best support the student’s argument?
In a 2019 study, Emily Thompson and Jacob Rivera found that employees’ proficiency in advanced software tools had no effect on the likelihood that the employees would receive promotions within their companies. Since this study was based on research among mid-level managers in a single multinational corporation, however, doubts have been raised about how reliable and representative the findings are. To better understand the issue, Mei Ling and colleagues analyzed the results of 60 studies on software proficiency and career advancement, such as a 2019 study from Australia that included 1,200 participants and a 2019 study from Canada with 250 participants. Taking all 60 studies together, Ling and colleagues found a significant positive effect of software proficiency on promotion rates, suggesting that ______
Which choice most logically completes the text?
Scholars consider The Tales of Forgotten Kingdoms, the 1969 novel by Turkish author Mehmet Alkan, as a pivotal work in the genre of mystical realism, a style of Middle Eastern fiction where fantastical plot elements—often influenced by the myths and legends of ancient civilizations—are combined with a realistic portrayal typical of modern novels. This genre has had a profound impact on writers globally, including Helena Kowalska, whose 1998 novel Voices of the Mountains mirrors classic mystical realist novels in blending literary realism with the folklore of Eastern Europe.
Which quote from a literary critic would most strongly support the claim made in the underlined section of the text?
The Atlantic Ridge Zone (ARZ) is a broad region of deep-sea plains and underwater peaks between Bermuda and the Canary Islands, where mining is allowed but the area’s biodiversity remains largely unexplored. The vast majority of marine invertebrate species discovered in a recent ARZ study were previously unknown to researchers, and animal life sampling has primarily focused on the western portion of the zone. Some species, such as Cystella maritima, were identified using both physical characteristics and genetic analysis, while others, including Borealia maritimus and species for which genetic sampling was unfeasible, were identified solely through their physical features. Since genetic analysis does not rely on subtle physiological distinctions, it is ___________.
Which choice most logically completes the text?
Scholars are increasingly examining how Indigenous songs serve to communicate and preserve ecological knowledge (e.g., songs from the Maori about natural landmarks and those of the Inuit about wildlife interactions). In one study, ethnobiologist Sarah Mitchell and her team gained valuable insights from Nainoa Makai, a song keeper for the Hawaiian people, regarding songs that reference the cultivation of fish in man-made ponds in coastal areas of the Pacific Islands. Archaeological evidence indicating a significant rise in fish size and population during the period when this technique, as described in the songs, was employed supports the conclusion that ______.
Which option best completes the text?
Sunnybrook Library and Riverdale Library are two of several local _______ large mural of a tree decorates the exterior of Sunnybrook Library, while a mural of a river flows along the side of Riverdale Library.
Which choice best completes the text so that it conforms to the conventions of Standard English?
When Greenland became part of GlobalPol—the Global Criminal Investigation _______ in 1985, the Greenland National Security Bureau gained access to the collective resources of law enforcement agencies from around the world.
Which choice best completes the sentence so that it conforms to conventions of Standard English?
The size of reptile eggs varies greatly among species, and a scientific ___ that compared the sizes of eggs produced by different reptile species found Python molurus eggs to be larger, on average, than Chrysemys picta eggs.
Which choice best completes the sentence so that it conforms to conventions of Standard English?
The connection between genetic codes and epigenetic markers explains how cells with the same DNA develop different ______ whereas the genetic code in each cell contains a full DNA sequence, the epigenetic markers consist of chemical modifications that dictate which traits from the sequence will be activated.
ro
Which choice best completes the sentence so that it conforms to conventions of Standard English?
A recent study of asteroid 2021 ZL3—an object in the outer solar system orbiting between Mars and Saturn—has identified its color as gray, which may indicate an icy surface. However, these conclusions are ultimately ______ as the gray color could be the result of radiation, solar wind, or collisions with other celestial bodies rather than a reflection of its actual composition.
Which choice best completes the sentence so that it conforms to conventions of Standard English?
That the geographic center of Europe was located within the borders of Poland was agreed by all _______ pinpointing its exact coordinates sparked considerable debate.
Which choice best completes the sentence to conform to conventions of Standard English?
The equatorial line, marking zero degrees latitude and established in the late 19th century, was initially set based on astronomical observations. _______ as years went by, more accurate measurements would be made, but the equatorial line remained the same; it wasn’t until the 1970s, with advancements in satellite data, that the equator’s position was officially adjusted—by about a hundred meters south.
Which choice best completes the sentence with the most logical transition?
James Marlow likely arrived in New York as early as 1875, at the age of 25, to begin a career in the performing arts. Very little is known about his initial years there, but by 1883 he was gaining recognition for productions such as The King’s Revenge. ______ in 1889, he would captivate audiences with The Last Laugh, which is considered by some to be one of his finest works.
Which choice best completes the sentence with the most logical transition?
In the East Asian country of Vietnam, the proportion of residents living in urban areas grew from 45.5% to 49.3% between 2014 and 2019; this rise in urbanization was observed throughout the region. ______ from 2014 to 2019, the total percentage of the East Asian population residing in cities increased from 46.1% to 48.7%.
Which choice best completes the sentence with the most logical transition?
The city has been expanding its public parks over the last few years. These green spaces provide residents with places to relax and play. _____ the initiative has had the unexpected benefit of attracting more tourists to the area.
Which choice best completes the sentence with the most logical transition?
The medieval castle has stood for centuries as a testament to architectural ingenuity. It has survived numerous battles and natural disasters. _____ recent neglect and lack of maintenance have left it in a precarious state.
Which choice best completes the sentence with the most logical transition?
While researching a topic, a student has taken the following notes:
Which choice most effectively incorporates information from the notes to emphasize the scope of Delgado’s body of work?
While researching a topic, a student has taken the following notes:
The student wants to compare the efficiency ratios of the two factories. Which option most effectively uses relevant information from the notes to achieve this goal?
The questions in this section address a number of important reading and writing skills. Each
question includes one or more passages, which may include a table or graph. Read each passage
and question carefully, and then choose the best answer to the question based on the passage(s).
All questions in this section are multiple-choice with four answer choices. Each question has a
single best answer.
If 5x + 13 = 31, what is the value of $\mathbf{\sqrt{5x+31}}$
At Maprang’s nuts a $\mathbf{2\frac{1}{4}}$ pound bag of pistachio nuts costs \$6.00. At this rate, what is the cost, in cents, of a bag weighing 9 ounces? (Note: 1 pound = 16 ounces)
What is the sum of 4y + 3 and 2y – 1?
A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where 𝑥 represents the number of 1-point questions and 𝑦 represents the number of 3-point questions?
The function 𝑔 is defined by g(x) = $ \mathbf{x^{2}+9}$ For which value of 𝑥 is g(x) = 25 ?
Right triangles LMN and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has a measure of 53°. What is the measure of angle Q?
For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function 𝑚 models the number of minutes it will take Juan to ride
𝑥 miles at this rate?
For line ℎ, the table shows three values of 𝑥 and their corresponding values of 𝑦. Line 𝑘 is the result of translating line ℎ down 5 units in the xy-plane. What is the 𝑥-intercept of line 𝑘?
The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is $\mathbf{k\sqrt{3}}$ centimeters, where 𝑘 is a constant. What is the value of 𝑘?
Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A?
Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation?
Each side of a square has a length of 45. What is the perimeter of this square?
5X+7y = 1
ax+by = 1
In the given pair of equations, 𝑎 and 𝑏 are constants. The graph of this pair of equations in the 𝑥𝑦-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines?
For the exponential function 𝑓, the value of 𝑓(1) is 𝑘, where 𝑘 is a constant. Which of the following equivalent forms of the function 𝑓 shows the value of 𝑘 as the coefficient or the base?
The three candidates who ran for a city council position in Memphis in 2020 received a total of 120,000 votes. The ratio of votes for the first candidate to votes for the second candidate was approximately 4 to 1. The ratio of votes for the first candidate to votes for the third candidate was approximately 100 to 13. Based on this information, which of the following is closest to the number of votes received by the first candidate?
The function 𝑝 is defined by 𝑝(𝑛) = $ \mathbf{7n^{3}}$. What is the value of 𝑛 when 𝑝(𝑛)is equal to 56?
A square base on pyramid have total surface area equal to 54,080 and area of 4 lateral face equal to 28,480. Find the answer of the height of the pyramid?
Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2?
The total cost, in dollars, to rent a surfboard consists of a \$25 service fee and a \$10 per hour rental fee. A person rents a surfboard for 𝑡 hours and intends to spend a maximum of \$75 to rent the surfboard. Which inequality represents this situation?
A small business owner budgets \$2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays \$4.90 per candle to purchase small candles and \$11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?
A circle on the X-Y Plane has a center of (-2,-5). Line K is tangent to the circle on the point (-4,1). What is the slope of line K? (The answer is fraction only)
A quadratic function is used to model the height of an objective and have (x,y) which x is time(second) and y is the height (ft), having (0,0) and (8 , 1,024) respectively. What height (ft) when time 10 second?
If you find more than one correct answer, enter only one answer.
ㆍ You can enter up to 5 characters for a positive answer and up to 6 characters (including the
negative sign) for a negative answer.
ㆍIf your answer is a fraction that doesn’t fit in the provided space, enter the decimal
equivalent.
ㆍIf your answer is a decimal that doesn’t fit in the provided space, enter it by truncating or
rounding at the fourth digit.
ㆍIf your answer is a mixed number (such as 3늘), enter it as an improper fraction (7/2) or its
decimal equivalent (3.5).
ㆍ Don’t enter symbols such as a percent sign, comma, or dollar sign.
The questions in this section address a number of important math skills.
Use of a calculator is pernitted for all questions. A reference sheet, calculator, and these directions
can be accessed throughout the test.
Unless otherwise indicated:
All variables and expressions represent real numbers.
ㆍ Figures provided are drawn to scale.
ㆍAll figures lie in a plane.
ㆍ The domain of a given function fis the set of all real numbers x for which f(x) is a real
number.
For multiple-choice questions, solve each problem and choose the correct answer from the
choices provided. Each multiple-choice question has a single correct answer.
For student-produced response questions, solve each problem and enter your answer as
described below.
3x = 12
-3x + y = -6
The solution to the given system of equations is (𝑥,𝑦). What is the value of 𝑦?
In the xy-plane, the graph of the equation 𝑦 = $ \mathbf{-x^{2}+9x-100}$ intersects the line 𝑦 = 𝑐 at exactly one point. What is the value of c?
The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is 𝑘 times the 2015 population, what is the value of 𝑘 ?
Which expression is equivalent to $\mathbf{a^{\frac{11}{12}}}$ where 𝑎 > 0?
A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?
$$\mathbf{f(t)= 8000(0.65)^{t}}$$
The given function𝑓 models the number of coupons a company sent to their customers at the end of each year, where 𝑡 represents the number of years since the end of 1998, and 0 ≤ t ≤ 5. If 𝑦 = 𝑓(𝑡)is graphed in the 𝑡𝑦-plane, which of the following is the best interpretation of the 𝑦-intercept of the graph in this context?
A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is $\mathbf{(x-2)^{2}+(y-k)^{2}= r^{2}}$, where r is a positive constant. What is the value of 𝑟?
$$\mathbf{\frac{1}{7b}=\frac{11x}{y}}$$
The given equation relates the positive numbers 𝑏,𝑥, and 𝑦 . Which equation correctly expresses 𝑥 in terms of 𝑏 and 𝑦
The area of triangle is $\mathbf{x^{2}}$. The height of the triangle is (2x+22) and the base length is (x-10). What is the value of x?
Which is sufficient to prove that \(\Delta ABC\) is congruent to \Delta DEF?
I) \(\measuredangle B\) = \(\measuredangle C \)
II) AC = DF
III) BC = EF
The graph of the equation y = $\mathbf{-x^{2} + 40x – 256}$ is shown. Which of the following equivalent forms of the equation shows the maximum value of y as a constant or coefficient?
$$\mathbf{5x^{2}+10x+16=0}$$
How many distinct real solutions does the given equation have?
Two data sets of 23 integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to 10, but less than 20. The second interval represents the frequency of integers greater than or equal to 20, but less than 30, and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B?
Gold has always been coveted for its aesthetic qualities. However, due to its malleability, it also has many industrial and electronic applications. Gold can be stretched so thinly that a single ounce can cover 100 square yards of surface. How many square feet can be covered with 2.5 ounces of gold?
A supermarket chain received an average grade of 65% customer satisfaction from 10 recent customer surveys. The chain manager wants to earn at least an 80% rating from its first 20 customer surveys. What is the lowest score the 17th survey can receive and still achieve the 80% satisfaction rate from its first 20 surveys? (Omit the percent sign.)
y = m(x+3)(x-5)
In the quadratic function below, m is a nonzero constant. The graph of the equation in the xy-plane has the vertex (e, f). Which of the following is the value of f?
If $\mathbf{\left | 2x+3 \right | = 5}$ and$\mathbf{\left | 3y-3 \right | = 6}$, what is one possible value of $\mathbf{\left | xy \right |}$?
Rectangle X has a length of 12 centimeters (cm) and a width of 2.5 cm. Right triangle Y has a base of 10 cm. The area of rectangle X is three times the area of right triangle Y. What is the height, in cm, of right triangle Y?
There are 8 men basketball teams and 6 women basketball teams joining a competition. In each men team, 7 players are 6 feet or taller, and 3 players are shorter than 6 feet. In each women team, 6 players are 6 feet or taller, and 3 players are shorter than 6 feet. One of these players is selected at random. What is the probability of selecting a male player,given that the player is shorter than 6 feet?
The width of a rectangle is 7 centimeters.The length of the rectangle is 40 centimeters longer than the width. What is the area, in square centimeters, of the rectangle?
A circle has center O, and points A and B lie on the circle. Line segments AC and BC are tangent to the circle at points A and B. If the radius of the circle is 120 inches and the area of quadrilateral ACBO is 25,080 square inches. What is the distance, in inches, between points O and C?
The table shows values of x and their corresponding values of g(x), where g(x) = $\mathbf{\frac{f(x)}{x+2}}$. If f is a linear function, what is the y-intercept of y = f(x)?
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The questions in this section address a number of important math skills.
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