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The passage is adapted from Ngonghala CN, et. al’s “Poverty, Disease, and the Ecology of Complex Systems” © 2014 Ngonghala et al. In his landmark treatise, An Essay on the Principle of Population, Reverend Thomas Robert Malthus argued that population growth will necessarily exceed the growth rate of the means of subsistence, making poverty inevitable. The system of feedbacks that Malthus posited creates a situation similar to what social scientists now term a “poverty trap”: i.e., a self-reinforcing mechanism that causes poverty to persist. Malthus’s erroneous assumptions, which did not account for rapid technological progress, rendered his core prediction wrong: the world has enjoyed unprecedented economic development in theensuing two centuries due to technology-driven productivity growth. Nonetheless, for the billion people who still languish in chronic extreme poverty, Malthus’s ideas about the importance of biophysical and biosocial feedback (e.g., interactions between human behavior and resource availability) to the dynamics of economic systems still ring true. Indeed, while they were based on observations of human populations, Malthus's ideas had reverberations throughout the life sciences. His insights were based on important underlying processes that provided inspiration to both Darwin and Wallace as they independently derived the theory of evolution by natural selection. Likewise, these principles underlie standard models of population biology, including logistic population growth models, predator-prey models, and the epidemiology of host-pathogen dynamics. The economics literature on poverty traps, where extreme poverty of some populations persists alongside economic prosperity among others, has a history in various schools of thought. The most Malthusian of models were advanced later by Leibenstein and Nelson, who argued that interactions between economic, capital, and population growth can create a subsistence-level equilibrium. Today, the most common models of poverty traps are rooted in neoclassical growth theory, which is the dominant foundational framework for modeling economic growth. Though sometimes controversial, poverty trap concepts have been integral to some of the most sweeping efforts to catalyze economic development, such as those manifest in the Millennium Development Goals. The modern economics literature on poverty traps, however, is strikingly silent about the role of feedbacks from biophysical and biosocial processes. Two overwhelming characteristics of under-developed economies and the poorest, mostly rural, subpopulations in those countries are (i) the dominant role of resource-dependent primary production—from soils, fisheries, forests, and wildlife—as the root source of income and (ii) the high rates of morbidity and mortality due to parasitic and infectious diseases. For basic subsistence, the extremely poor rely on human capital that is directly generated from their ability to obtain resources, and thus critically influenced by climate and soil that determine the success of food production. These resources in turn influence the nutrition and health of individuals, but can also be influenced by a variety of other biophysical processes. For example, infectious and parasitic diseases effectively steal human resources for their own survival and transmission. Yet scientists rarely integrate even the most rudimentary frameworks for understanding these ecological processes into models of economic growth and poverty. This gap in the literature represents a major missed opportunity to advance our understanding of coupled ecological-economic systems. Through feedbacks between lower-level localized behavior and the higher-level processes that they drive, ecological systems are known to demonstrate complex emergent properties that can be sensitive to initial conditions. A large range of ecological systems—as revealed in processes like desertification, soil degradation, coral reef bleaching, and epidemic disease—have been characterized by multiple stable states, with direct consequences for the livelihoods of the poor. These multiple stable states, which arise from nonlinear positive feedbacks, imply sensitivity to initial conditions. While Malthus’s original arguments about the relationship between population growth and resource availability were overly simplistic (resulting in only one stable state of subsistence poverty), they led to more sophisticated characterizations of complex ecological processes. In this light, we suggest that breakthroughs in understanding poverty can still benefit from two of his enduring contributions to science: (i) models that are true to underlying mechanisms can lead to critical insights, particularly of complex emergent properties, that are not possible from pure phenomenological models; and (ii) there are significant implications for models that connect human economic behavior to biological constraints. World Population, 1990-2015
The above table plots the world population, in billions of people, from 1990 through 2015 Percent of Population Living in Extreme Poverty
The table above shows the percentage of people in each region that lived in extreme poverty, as defined by the World Bank, for each of the years plotted. The seventh region, North America, is not shown, as its extreme poverty rate fell below the minimum rate for tracking in this study.
Which of the following conclusions is best supported by the two tables?
Correct answer: As of 2015, less than 3.5 billion people in the world lived in extreme poverty. Explanation: To answer this question, we need to compare the answer options to the two tables. When you are looking at the answer options, keep in mind that the correct answer must be supported by both tables, not just one. Let’s start with “in 1999, there were more people living in extreme poverty in South Asia than in East Asia and the Pacific”. Note that the table that compares regions only deals with percents (percentage of people in that region living in poverty) but not with actual numbers of people. Without an idea of how many people live in each region, we can’t compare total numbers. Next, “fewer people in Latin America & the Caribbean lived in poverty in 2008 than in 2002” has the same problem - without knowing how many people are in each region, we can’t draw conclusions about the total number of people (for example, if one region has one billion people and another has one hundred, you could take the same percentage of each region and get wildly different actual numbers). Answer choice “extreme poverty is not a major concern in Europe & Central Asia” is interesting in that it offers a value judgment - from the numbers you might think “only 1% of people in this region live in extreme poverty, and 1% isn’t a big number” but ask yourself: if it’s 1% of 500 million people, isn’t it possibly a major concern to those 5 million people? Value judgments like this are very hard to prove, and when you’re asked to draw a conclusion on the SAT you need to be able to prove your answer. This leaves us with, “as of 2015, less than 3.5 billion people in the world lived in extreme poverty”. Without even having to go back and reference the tables you should notice that this choice mentions a population size- which is discussed in the first table- and poverty level- which is covered in the second table. To double check, we can look at the first table and see that is 2015 there are 7.3 billion people in the world- which makes 3.5 billion people about half of the population. Looking at the second table in 2015 we can see that all poverty rates are substantially below 50%, so we can draw this conclusion. Page 2
The passage is adapted from Ngonghala CN, et. al’s “Poverty, Disease, and the Ecology of Complex Systems” © 2014 Ngonghala et al. In his landmark treatise, An Essay on the Principle of Population, Reverend Thomas Robert Malthus argued that population growth will necessarily exceed the growth rate of the means of subsistence, making poverty inevitable. The system of feedbacks that Malthus posited creates a situation similar to what social scientists now term a “poverty trap”: i.e., a self-reinforcing mechanism that causes poverty to persist. Malthus’s erroneous assumptions, which did not account for rapid technological progress, rendered his core prediction wrong: the world has enjoyed unprecedented economic development in theensuing two centuries due to technology-driven productivity growth. Nonetheless, for the billion people who still languish in chronic extreme poverty, Malthus’s ideas about the importance of biophysical and biosocial feedback (e.g., interactions between human behavior and resource availability) to the dynamics of economic systems still ring true. Indeed, while they were based on observations of human populations, Malthus's ideas had reverberations throughout the life sciences. His insights were based on important underlying processes that provided inspiration to both Darwin and Wallace as they independently derived the theory of evolution by natural selection. Likewise, these principles underlie standard models of population biology, including logistic population growth models, predator-prey models, and the epidemiology of host-pathogen dynamics. The economics literature on poverty traps, where extreme poverty of some populations persists alongside economic prosperity among others, has a history in various schools of thought. The most Malthusian of models were advanced later by Leibenstein and Nelson, who argued that interactions between economic, capital, and population growth can create a subsistence-level equilibrium. Today, the most common models of poverty traps are rooted in neoclassical growth theory, which is the dominant foundational framework for modeling economic growth. Though sometimes controversial, poverty trap concepts have been integral to some of the most sweeping efforts to catalyze economic development, such as those manifest in the Millennium Development Goals. The modern economics literature on poverty traps, however, is strikingly silent about the role of feedbacks from biophysical and biosocial processes. Two overwhelming characteristics of under-developed economies and the poorest, mostly rural, subpopulations in those countries are (i) the dominant role of resource-dependent primary production—from soils, fisheries, forests, and wildlife—as the root source of income and (ii) the high rates of morbidity and mortality due to parasitic and infectious diseases. For basic subsistence, the extremely poor rely on human capital that is directly generated from their ability to obtain resources, and thus critically influenced by climate and soil that determine the success of food production. These resources in turn influence the nutrition and health of individuals, but can also be influenced by a variety of other biophysical processes. For example, infectious and parasitic diseases effectively steal human resources for their own survival and transmission. Yet scientists rarely integrate even the most rudimentary frameworks for understanding these ecological processes into models of economic growth and poverty. This gap in the literature represents a major missed opportunity to advance our understanding of coupled ecological-economic systems. Through feedbacks between lower-level localized behavior and the higher-level processes that they drive, ecological systems are known to demonstrate complex emergent properties that can be sensitive to initial conditions. A large range of ecological systems—as revealed in processes like desertification, soil degradation, coral reef bleaching, and epidemic disease—have been characterized by multiple stable states, with direct consequences for the livelihoods of the poor. These multiple stable states, which arise from nonlinear positive feedbacks, imply sensitivity to initial conditions. While Malthus’s original arguments about the relationship between population growth and resource availability were overly simplistic (resulting in only one stable state of subsistence poverty), they led to more sophisticated characterizations of complex ecological processes. In this light, we suggest that breakthroughs in understanding poverty can still benefit from two of his enduring contributions to science: (i) models that are true to underlying mechanisms can lead to critical insights, particularly of complex emergent properties, that are not possible from pure phenomenological models; and (ii) there are significant implications for models that connect human economic behavior to biological constraints. World Population, 1990-2015
The above table plots the world population, in billions of people, from 1990 through 2015 Percent of Population Living in Extreme Poverty
The table above shows the percentage of people in each region that lived in extreme poverty, as defined by the World Bank, for each of the years plotted. The seventh region, North America, is not shown, as its extreme poverty rate fell below the minimum rate for tracking in this study.
Which of the following best describes how the data in the two tables supports Malthus’s prediction that population growth will necessarily exceed the growth rate of the means of subsistence, making poverty an inevitable consequence?
Correct answer: It contradicts Malthus’s prediction, because it shows that poverty is decreasing even while the population is increasing. Explanation: If we look at the first table, we can see that from 1990 to 2015 the world population did grow, which does support part of Malthus’s prediction. However, if we look at the second table, we see that from 1990-2015 the percentage of people living poverty actually decreases across each world region (and dramatically so in those regions that were >50% in 1990). Thus, as population increased, poverty decreased. This contradicts Mathus’s prediction overall so we can eliminate answer choices that claim to support his prediction: “ it supports Malthus’s prediction, because it shows that poverty is still a major problem in the world “ and “it supports Malthus’s prediction, because it demonstrates that poverty is a problem that can be solved in certain regions”. Looking at the remaining options, “it contradicts Malthus’s prediction, because it demonstrates that poverty remains highest in the same regions of the world year after year” is a true statement based on the second table; however, this has nothing to do with Mathus’s prediction so we can eliminate it. This leaves us with, “it contradicts Malthus’s prediction, because it shows that poverty is decreasing even while the population is increasing” as the correct answer. This statement is supported by both of the tables and does contradict Malthus’s overall prediction because that tables show that as population increased, poverty decreased. Page 3
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AB and CD are two parrellel lines intersected by line EF. If the measure of angle 1 is Possible Answers:
Correct answer: Explanation: The angles are equal. When two parallel lines are intersected by a transversal, the corresponding angles have the same measure.
Figure not drawn to scale.
In the figure above, APB forms a straight line. If the measure of angle APC is eighty-one degrees larger than the measure of angle DPB, and the measures of angles CPD and DPB are equal, then what is the measure, in degrees, of angle CPB? Possible Answers:
Explanation: Let x equal the measure of angle DPB. Because the measure of angle APC is eighty-one degrees larger than the measure of DPB, we can represent this angle's measure as x + 81. Also, because the measure of angle CPD is equal to the measure of angle DPB, we can represent the measure of CPD as x. Since APB is a straight line, the sum of the measures of angles DPB, APC, and CPD must all equal 180; therefore, we can write the following equation to find x: x + (x + 81) + x = 180 Simplify by collecting the x terms. 3x + 81 = 180 Subtract 81 from both sides. 3x = 99 Divide by 3. x = 33. This means that the measures of angles DPB and CPD are both equal to 33 degrees. The original question asks us to find the measure of angle CPB, which is equal to the sum of the measures of angles DPB and CPD. measure of CPB = 33 + 33 = 66. The answer is 66.
One-half of the measure of the supplement of angle ABC is equal to the twice the measure of angle ABC. What is the measure, in degrees, of the complement of angle ABC? Possible Answers:
Explanation: Let x equal the measure of angle ABC, let y equal the measure of the supplement of angle ABC, and let z equal the measure of the complement of angle ABC. Because x and y are supplements, the sum of their measures must equal 180. In other words, x + y = 180. We are told that one-half of the measure of the supplement is equal to twice the measure of ABC. We could write this equation as follows: (1/2)y = 2x. Because x + y = 180, we can solve for y in terms of x by subtracting x from both sides. In other words, y = 180 – x. Next, we can substitute this value into the equation (1/2)y = 2x and then solve for x. (1/2)(180-x) = 2x. Multiply both sides by 2 to get rid of the fraction. (180 – x) = 4x. Add x to both sides. 180 = 5x. Divide both sides by 5. x = 36. The measure of angle ABC is 36 degrees. However, the original question asks us to find the measure of the complement of ABC, which we denoted previously as z. Because the sum of the measure of an angle and the measure of its complement equals 90, we can write the following equation: x + z = 90. Now, we can substitute 36 as the value of x and then solve for z. 36 + z = 90. Subtract 36 from both sides. z = 54. The answer is 54.
In the diagram, AB || CD. What is the value of a+b? Possible Answers:
None of the other answers.
Explanation: Refer to the following diagram while reading the explanation: We know that angle b has to be equal to its vertical angle (the angle directly "across" the intersection). Therefore, it is 20°. Furthermore, given the properties of parallel lines, we know that the supplementary angle to a must be 40°. Based on the rule for supplements, we know that a + 40° = 180°. Solving for a, we get a = 140°. Therefore, a + b = 140° + 20° = 160°
In rectangle ABCD, both diagonals are drawn and intersect at point E. Let the measure of angle AEB equal x degrees. Let the measure of angle BEC equal y degrees. Let the measure of angle CED equal z degrees. Find the measure of angle AED in terms of x, y, and/or z. Possible Answers:
Correct answer: 180 – 1/2(x + z) Explanation: Intersecting lines create two pairs of vertical angles which are congruent. Therefore, we can deduce that y = measure of angle AED. Furthermore, intersecting lines create adjacent angles that are supplementary (sum to 180 degrees). Therefore, we can deduce that x + y + z + (measure of angle AED) = 360. Substituting the first equation into the second equation, we get x + (measure of angle AED) + z + (measure of angle AED) = 360 2(measure of angle AED) + x + z = 360 2(measure of angle AED) = 360 – (x + z) Divide by two and get: measure of angle AED = 180 – 1/2(x + z)
A student creates a challenge for his friend. He first draws a square, the adds the line for each of the 2 diagonals. Finally, he asks his friend to draw the circle that has the most intersections possible.
How many intersections will this circle have? Possible Answers:
Correct answer: Explanation: The answer to this problem is 12. This can be drawn as shown below (intersections marked in red). We can also be sure that this is the maximal case because it is the largest answer selection. Were it not given as a multiple choice question, however, we could still be sure this was the largest. This is because no line can intersect a circle in more than 2 points. Keeping this in mind, we look at the construction of our initial shape. The square has 4 lines, and then each diagonal is an additional 2. We have thus drawn in 6 lines. The maximum number of intersections is therefore going to be twice this, or 12.
Two pairs of parallel lines intersect:
If A = 135o, what is 2*|B-C| = ? Possible Answers:
Explanation: By properties of parallel lines A+B = 180o, B = 45o, C = A = 135o, so 2*|B-C| = 2* |45-135| = 180o
Lines Possible Answers:
Correct answer: Explanation: Since we know opposite angles are equal, it follows that angle Imagine a parallel line passing through point
If Possible Answers:
Correct answer: Explanation: When the measure of an angle is added to the measure of its supplement, the result is always 180 degrees. Put differently, two angles are said to be supplementary if the sum of their measures is 180 degrees. For example, two angles whose measures are 50 degrees and 130 degrees are supplementary, because the sum of 50 and 130 degrees is 180 degrees. We can thus write the following equation: Subtract 40 from both sides. Add The answer is
In the following diagram, lines Possible Answers:
Correct answer: Explanation: When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°. Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.
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Which of the following conclusions is best supported by the second image?
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