Algebra/Advanced Math
Convert to Standard to Slope-Intercept Form: 2x-3y=6
y= 2x/3 - 2
In percentage problems, when you see "what," "is," "of," and "percent," what symbols and/or phrases should you think of?
"What" means a variable (x)
"Is" means an equal sign (=)
"Of" means multiplied by (*)
"Percent" means divided by 100 (or multiplied by 0.01)
In coordinating conjuctions, what does FANBOYS stand for?
For, and, nor, but, or, yet, so
What's the difference between text structure and author's purpose?
Purpose is the why behind the passage. Why did the author write it? What did they want to accomplish? What’s the point?
Structure is how a passage works to achieve its purpose. How does the text flow from one idea to the next? Where does the author place particular emphasis?
I am an odd number. If you take away just one letter from my name, I become even. What number am I?
Seven
Explain how you would solve this problem using subsitution:
5x-4y=-6
y=2x+3
Step 1: Insert y into the first equation 5x4(2x+3)=-6
Step 2: Distribute 5x-8x-12=-6
Step 3: Simplify -3x-12=-6
Step 4: Solve for x (x=-2)
Step 5: Insert x into the second equation to find y, y=2(-2)+3 --> y=-1
The answer is (-2,-1)
A local zoo houses 13 penguins for every lion it houses. The zoo has 78 penguins. What is the ratio of lions to penguins? Using that information, how many lions does the zoo have total?
Ratio of lions to penguins - 1:13
Ratio of lions to total penguins - x:78
The proportion would be - 1/13=x/78
solve: x=6
Electric scooters offer a convenient way to travel across _____ riders should always wear helmets to reduce the risk of injury.
Which choice completes the text so that it conforms to the conventions of Standard English?
A) campus: however,
B) campus; however
C) campus, but
D) campus but
Answer: C)
C) connects these independent clauses by using a conjunction and a comma.
A) is wrong because A colon calls for an explanation of the scooters’ convenience, but the helmet warning doesn't give one. However means even so, which marks the warning as a contrast with the point about convenience rather than an explanation of it.
B) is wrong because The transition however is missing the comma after it. When however starts the second of two full sentences, a comma sets it off from the words that follow.
D) is wrong because it is missing the comma before the word but.
Rosa Linden never set out to make vases at all. Trained as a chemist, she first melted glass only to test how different minerals colored it, keeping careful notes on every batch. It was only when a visiting colleague admired one of her test pieces that she began shaping the molten glass into bowls and vases, and a second career took form almost by accident.
Which choice best describes the function of the underlined sentence in the text as a whole?
A) It identifies the specific techniques Linden used to color her glass.
B) It states the conclusion that the rest of the text works to establish.
C) It introduces a surprising claim about Linden that the rest of the text then explains
D) It offers an example that illustrates a general point made in the following sentence.
Answer: C)
Demonstrates a contradiction: if she never wanted to be one, how did she become one?
When you see a period and a semicolon in the answer choices, what should you automatically do?
Automatically assume both answer choices are wrong because a period and a semicolon are interchangeable. They both separate two complete, independent clauses.
Factor 10x2+80x+70
Step 1: Factor 10 out to get 10(x2+8x+7)
Step 2: Factor (x2+8x+7) to get (x+1)(x+7)
Answer: 10(x+1)(x+7)
A mixture contains 1,000 litres of seawater, 100 litres of Chemical X, and 50 litres of Chemical Y. Chemical Y forms what percent of the mixture?
A) 4.35%
B) 5%
C) 8.70%
D) 50%
Answer: A)
50/1150 = 4.35%
While examining a fifteenth-century manuscript from a Spanish convent, historian Mara Velázquez noticed that its final page contained an unusually detailed colophon, a note identifying the person who copied a text. According to the colophon, the manuscript was completed by _____ during a thunderstorm in 1427.
Which choice completes the text so that it conforms to the conventions of Standard English?
A) Elena of Salamanca a scribe whose notes sometimes described local events,
B) Elena of Salamanca; a scribe whose notes sometimes described local events,
C) Elena of Salamanca, a scribe whose notes sometimes described local events,
D) Elena of Salamanca, a scribe whose notes sometimes described local events;
Answer: C)
C) is correct because the description sits inside a continuing sentence. It needs the matching commas that this choice places at both ends.
A) is wrong because there is no ending comma. The single comma looks like an abrupt interruption instead.
B) is wrong because the semicolon is not placed between two independent clauses.
D) is wrong because the words after the semicolon can't stand alone.
Hired to design the signs for the city's new transit stations, the lettering artist Naomi Adeyemi produced a set that riders praised as unusually _______. Rather than crowding each sign with decorative flourishes, she kept the letters plain and well spaced, so that a traveler hurrying past could read a station's name without slowing down.
Which choice completes the text with the most logical and precise word or phrase?
A) intricate
B) legible
C) transparent
D) colorful
B) Legible
Adeyemi "kept the letters plain and well spaced," and the result is that "a traveler hurrying past could read a station's name without slowing down." Lettering you can read at a glance is legible lettering, so "legible" is the precise word needed.
I add six to eleven and get five. How is this correct?
Adding 6 to 11 refers to adding hours on a clock. After 12, the count resets, so 11 + 6 = 5 o’clock.
Describe the horizontal asymptote
For the graph of an exponential function, the value of y will always grow to positive or negative infinity on one end and approach, but not reach, a horizontal line on the other; The horizontal line that the graph approaches but never reaches
In a certain town, 500 residents commute to work. Of these residents, 30% bike to work. Of the residents who bike to work, 40% also own a car. How many of the 500 commuting residents both bike to work and own a car?
A) 50
B) 60
C) 90
D) 150
Answer: B)
Step 1: 30%*500=150
Step 2: 40%*150=60
To investigate whether early exposure to artificial light shapes later navigation, entomologist Priya Nanduri reared two groups of hawk moths, one beneath amber streetlamps and the other in darkness. During release trials, the moths that had developed beneath the lamps, unlike those raised in natural ______ toward a bright ultraviolet source even when moonlight was visible.
Which choice completes the text so that it conforms to the conventions of Standard English?
A) darkness, consistently flew
B) darkness consistently flew
C) darkness; they consistently flew
D) darkness. They consistently flew
Answer: A)
A) is correct because the comma after "lamps" opens the phrase beginning "unlike those raised," which ends before the main verb, flew. This choice adds a matching comma to close that extra information so the sentence about the moths can continue.
B) is wrong because it leaves the comma after "lamps" without an ending comma.
C) is wrong because a semicolon needs a full sentence on each side, and the first part has no main verb.
D) is wrong because the period leaves the first sentence unfinished.
In ecological studies of coral reef systems, scientists have long observed that reef biodiversity is closely linked to the presence of grazing herbivores such as parrotfish and surgeonfish. These species maintain algal populations in check, thereby allowing coral larvae to successfully settle and grow. In systems where herbivorous fish are removed—whether through overfishing or habitat degradation—algal overgrowth can lead to phase shifts in which coral-dominated ecosystems are replaced by algal-dominated ones. This transition has been associated with significant losses in biodiversity and is notoriously difficult to reverse once established. Recent research has focused on whether targeted interventions, such as the reintroduction of herbivorous fish species or artificial reef construction, can restore coral dominance, but results remain inconsistent due to variations in local nutrient levels, water temperature, and human activity.
Which choice best describes the function of the underlined sentence in the passage as a whole?
A) It presents the ecological consequence of removing a key functional group from reef ecosystems, thus establishing the urgency behind the restoration efforts discussed later in the passage.
B) It introduces an exception to the typical relationship between herbivorous fish and coral reefs in order to suggest that other factors may play a larger role in reef decline.
C) It defines a common feature of coral ecosystems that remains stable across environmental conditions, thereby framing the need for future research mentioned later in the text.
D) It summarizes the long-term goal of coral reef studies by identifying a desired state of ecosystem balance that is expanded upon in the remainder of the paragraph.
Answer: A)
The underlined sentence traces a cause and its damage: remove the herbivorous fish — “whether through overfishing or habitat degradation” — and “algal overgrowth can lead to phase shifts in which coral-dominated ecosystems are replaced by algal-dominated ones.” That is precisely the ecological consequence of pulling out a “key functional group,” the grazers the paragraph has just introduced to you as the fish that “maintain algal populations in check.”
Volcanic ash is rich in minerals such as potassium and phosphorus that growing plants draw on. When a thin layer of ash drifted down over the valley's farms one autumn and settled into the soil, ______ the next season's wheat came up noticeably taller and greener than the crops of recent years.
Which choice completes the text with the most logical transition?
A) for example,
B) as a result,
C) nevertheless,
D) subsequently,
Answer: B)
A word like subsequently would tell your reader only that the wheat came after the ash, leaving the growth a coincidence. But the passage went out of its way to tell you why ash helps: it carries potassium and phosphorus, so the timing is not the point, the causation is.
The volume of a right circular cone A is 4 cubic meters. What is the volume, in cubic meters, of a right circular cone with 2.5 times the radius and 7 times the height of cone A? The formula for a right circular cone is 1/3*pi*r2*h
VA=4m3=1/3*pi*r2*h
VB=1/3*pi*(2.5)2*(7)h
VB=6.25*7(1/3*pi*r2*h)
VB=6.25*7(4m3)
VB=175 m3
A market researcher selected a random sample of 250 subscribers to an online magazine and recorded how many of the magazine's articles each subscriber had read in the past week. The sample mean was 6.4 articles, with an associated margin of error of 0.5 at a given confidence level. Which of the following is the most appropriate conclusion?
A) Every subscriber to the magazine read between 5.9 and 6.9 of the magazine's articles in the past week.
B) The mean number of the magazine's articles read in the past week by all subscribers to the magazine is exactly 6.4.
C) It is plausible that the mean number of the magazine's articles read in the past week by all subscribers to the magazine is between 5.9 and 6.9.
D) It is plausible that the mean number of online-magazine articles read in the past week by all adults who read online magazines is between 5.9 and 6.9.
Answer: C)
A margin of error gives a plausible interval for the population mean, and only for the population you actually sampled. Keep both the “mean” and the “who” honest.
In a profile of a rapidly growing nonprofit that started in a cramped co-working space and now advises governments, the journalist noted that the founder, who had weathered early donor skepticism by publishing every grant and outcome online, often proclaimed "open data is the ______ an apt motto for an organization built on transparency and collaborative research.
Which choice completes the text so that it conforms to the conventions of Standard English?
A) future”; and
B) future” and
C) future”
D) future,”
Answer: D)
The phrase was introduced with a comma and needed to end with one. Quotation marks were needed for the quote.
Text 1
Astronomers have long wondered how tens of thousands of asteroids can persist in the main belt between Mars and Jupiter while orbiting the same star and drawing on the same material. According to conventional wisdom, gravity-driven accretion should let a few bodies sweep up the rest. So why do so many remain as separate objects after billions of years? Despite many proposed models, researchers still have not reached a fully satisfying explanation.
Text 2
Dynamical astronomer Leena Varma and colleagues connect the belt's diversity to orbital stirring. Because these rocky bodies are small and widely spaced, they rarely meet at gentle speeds. Jupiter's resonances continually jostle their paths, turning potential mergers into shattering impacts. In such conditions, direct growth by sticking probably happens far less than previously believed, which reduces the kind of head-to-head competition that the older picture assumed.
Based on the texts, how would Varma and colleagues (Text 2) most likely respond to the "conventional wisdom" discussed in Text 1?
A) By arguing that it rests on a misconception about how often asteroids can merge with one another in the stirred belt environment.
B) By asserting that it ignores the continual delivery of fresh fragments from comets that prevents competition among belt asteroids.
C) By suggesting that their own findings help clarify how asteroids are able to compete directly with Jupiter's powerful gravitational field.
D) By recommending that more astronomers examine how merger rates among asteroids are increased when their typical encounter speeds become higher.
Answer: A)
The question asks how Text 2 answers Text 1's "conventional wisdom" that "gravity-driven accretion should let a few bodies sweep up the rest." The "competition" Text 2 actually discusses is between asteroids — it says stirring "reduces the kind of head-to-head competition that the older picture assumed." So you can read Varma's response as arguing the old view rests on a misconception about how often asteroids merge with one another, with Jupiter as the cause of the stirring rather than the rival.
"To prepare for the international conference, the team invited several key speakers: Dr. Aris Thorne, a molecular biologist from London; Maria Santos, an environmental economist based in São Paulo; John Joe, a neurosurgeon from Frankfurt; Camila Itis, a veterinarian from Seattle; and Kenji Tanaka, a software engineer from Tokyo."
How many items are in this list?
Answer: five items