Answers to Newsletter Practice Questions
April 2024
Answer: C
Choice C is correct. The equation y = (2x − 4)(x − 4) can be written in vertex form, y = a (x − h ) 2 + k, to display the vertex, (h, k ), of the parabola. To put the equation in vertex form, first multiply: (2x − 4)(x − 4) = 2x 2 − 8x − 4x + 16. Then, add like terms, 2x 2 − 8x − 4x + 16 = 2x 2 − 12x + 16. The next step is completing the square. y = 2x 2 − 12x + 16 y = 2(x 2 − 6x ) + 16 Isolate the x 2 term by factoring. y = 2(x 2 − 6x + 9 − 9) + 16 Make a perfect square in the parentheses. y = 2(x 2 − 6x + 9) − 18 + 16 Move the extra term out of the parentheses. y = 2(x − 3)2 − 18 + 16 Factor inside the parentheses. y = 2(x − 3)2 − 2 Simplify the remaining terms. Therefore, the coordinates of the vertex, (3, −2), are both revealed only in choice C. Since you are told that all of the equations are equivalent, simply knowing the form that displays the coordinates of the vertex will save all of these steps—this is known as “seeing structure in the expression or equation.” Choice A is incorrect; it is in standard form, displaying the y-coordinate of the y-intercept of the graph (0, 16) as a constant. Choice B is incorrect; it displays the y-coordinate of the y-intercept of the graph (0, 16) as a constant. Choice D is incorrect; it displays the x-coordinate of one of the x-intercepts of the graph (2, 0) as a constant.
February 2024
Answer: D
D) The speaker addresses a criticism leveled against him, then announces a great ambition of his.
January 19, 2024
Answer: D
Choice D is correct. When an equation is written in the form y = mx + b, the coefficient of the x-term (in this case 0.8636) is the slope of the graph of this equation in the xy-plane. The slope of the graph of this linear equation gives the amount that the average number of students per classroom (represented by y) changes per year (represented by x). The slope is positive, indicating an increase in the average number of students per classroom each year. Choice A is incorrect and may result from a misunderstanding of slope and y-intercept. The y-intercept of the graph of the equation represents the estimated average number of students per classroom in 2004. Choice B is incorrect and may result from a misunderstanding of the limitations of the model. You may have seen that x ≤ 10 and erroneously used this statement to determine that the model finds the average number of students in 2014. Choice C is incorrect and may result from a misunderstanding of slope. You may have recognized that slope models the rate of change but thought that a slope of less than 1 indicates a decreasing function.
December 15, 2023
Answer: D
As a strategy, we recommend making a prediction for the underlined word, as if it is a blank we need to fill in. How about “naturally.” We then compare our prediction to the answer choices, within which spontaneously, involuntarily and intuitively all have some merit.
The problem with spontaneously is that it involves “sudden impulse without premeditation”, which can verge on “randomly,” which is not what we want. Involuntarily involves doing something “without will or conscious control”, like a muscle reflex—our knee would jerk on being struck whether we wanted it to or not. This verges on “forced” which is not what we want for differentiating smiles without thinking about it. This while intuitively invokes “instinct.” While based on definition all seem close, “intuitively” most invokes a natural ability which is what the sentence calls for in “not [consciously] looking for” various cues, but being able to differentiate nonetheless.
July 2023
Answer: D
We must utilize the equation distance = rate * time. In fact we need to use it 3 times. First 400 miles = 225mph * total time. Total time = 1.77 hrs. Save this number. Then the first “slower” leg: 90 miles = 125 mph * time1. Time1 = .72 hours. Then, total time = time1 + time2. So 1.77 = .72 + time2. Time 2 = 1.057 hours. Finally, the last leg: the remaining distance = rate2 * time2. So 310 = rate2 * 1.057. Rate2 = 293 mph.
June 2023
Answer: B
For “word in context” questions, our strategy is as follows:
1) Re-read the sentence.
2) Treat the word in question as a blank.
3) Make a prediction for what you would insert in that blank.
4) Compare your prediction to the answer choices to narrow down.
Read your likely answer choice back into the sentence. An appropriate prediction for “intense” in the sentence might be “focused”. This prediction in fact helps us get away from trap answer choices that relate to common uses of “intense”. Given our prediction, “concentrated” looks good, as in more “intensive.” We read it in: The coming decades will likely see more “concentrated” clustering of jobs, innovation, and productivity in a smaller number of bigger cities and city-regions. This works as it focuses on the physical clustering.
May 2023
Answer: A
From table 2, Sample 1 has a blue spot with 0.6 Rf and a yellow spot with 0.78 Rf. Rf is defined earlier as the percentage distance the ion travels relative to the solvent. So the blue ion travels 60% as far as the solvent while the yellow travels 78% as far. Choice A best estimates these percentages visually.
April 25, 2023
Answer: C
This is a classic SAT and ACT grammar topic relating to an introductory dependent clause: “By re-creating snowflake formation,”. We must first note that any dependent clause “depends” on what comes immediately after the comma. In this case, there is no subject identified in the dependent clause. Who recreated snowflake formation? Grammatically, this requires that we state the subject immediately following the comma, that is the scientists or names of the people who recreated snowflake formation. Note that choice C is the only one that states a subject immediately.
March 31, 2023
Answer: C
First, what is the question asking for? What deems “success” in this probability question?
P(G AND Y) OR P(Y AND G).
Basic probability rules we teach: for independent events, “and” means multiply and “or” means add.
Imagine doing the draw one M&M at a time.
P (G) = 30/92
Now with one fewer M&M, P(Y) = 15/91.
So P (G AND Y) = .0537, by multiplying the above probabilities.
But there’s one more way to reach “success”: P (Y THEN G)
P (Y) = 15/92
Now with one fewer M&M, P(G) = 30/91.
So P (Y AND G) = .0537 (again multiplying to achieve “and”)
Add the two ways to reach “success” (i.e. “or”): 0.0537 + 0.0537 = 0.1075.
February 23, 2023
Answers:
1) C
2) D
This is a regularly occurring two-part question on the SAT, pairs of which occur roughly 10 times across the Reading section.
As a method:
Scan ahead to see if you are completing a two-part question. Approach the two parts together, that is let the evidence for the second part inform your thinking for the first part.
The question in the first part is as informative as the answer. Here, a key part of the question is “values most.”
Scanning the various evidence choices (question 2), we go back to the text to find key pieces of evidence. “No moments in her company were comparable to those when..” stands out as superlative, but the issue is the narrator only declares “the walks” as the product of this sentence. But what about the walks does Ethan “value most”. It is not until the end of the paragraph that we find the best evidence: “he could show her things and tell her things and taste the bliss of feeling that all he imparted left long reverberations and echoes he could wake at will.”
Again we look for evidence of what Ethan values most. We must interpret the metaphor “taste the bliss of feeling” as a good or great feeling, that is, something he values. Additionally, the “reverberations and echoes he could wake at will” suggest a lasting impact, which again is indicative of something he would value.
In tandem, we choose D for the second question to link to “values most” and then C for the first question as a summary of what he values, that is “an eye to see and an ear to hear,” which creates the bliss of feeling and reverberations.
January 23, 2023
Answer: B
Let’s use our 2 step method to begin any math problem: 1) what is the question asking for, and 2) how do I get there? The key is to get your pencil moving in both respects. How do we write down “divisible by 2x+3”? On our paper, let’s write:
(polynomial)
-----------------
2x + 3
Now let’s go back to the problem and simply each function:
f(x) = 2x (x^2 + 3x + 2) . We could factor further, but let’s stop for a moment because we see an “aha”. The second portion of the above is identical to g(x). In other words:
f(x) = 2x (g(x)).
Now we backsolve to create the following polynomials:
2x (g(x)) + g(x)
2x (g(x)) + 3 * g(x)
2* 2x (g(x)) + 3* g(x)
3* 2x (g(x)) + 2* g(x)
In all of these, we can factor out g(x). In B, we are left with
g(x) * (2x + 3). This is divisible by (2x + 3) when we substitute into our “polynomial” above.
October 24, 2022
Answer: C
We must use the introduction text as well as Scientist 2’s text. If Earth’s glaciers are meant to be similar to Europa’s surface features, then we are likely to see features identified as present on Europa: pressure ridges, cracks, and dark bands (see intro text). By elimination, we are least likely to see meteorite craters.
September 24, 2022
Answer: 0
Remember that “you don’t have to know how to end a problem to start a problem.” To get started then, draw a hypothetical W in and see what the triangles reflect. Label the new angles x and y, for example. What do we know about x and y? They are complementary. So why not bring out our calculator and do some pseudo-backsolving for Cos (x) - Sin (y). How about Cos (45) - Sin (45). 0. What about Cos (30) - Sin (60). 0. Cos (60) - Sin (30). 0. We have our answer.
August 23, 2022
Answer: B
This is a classic subject/verb trap. Remember that for a sentence to be a sentence it must have a verb. To gauge whether we are using the correct verb, we must ensure it corresponds to the subject in number, gender, tense, etc. So 1) what is the verb? “Are”. And 2) who or what is doing the verb: the committee. Note: “Of architects, engineers, urban planners, and developers” is simply describing “the committee”. As “The committee” is singular, and later in the sentence we see present tense, the verb should be “is”. Useful trick: put parentheses around any portion of a subject that can be removed, such as a descriptor. This will help reduce distance between a subject and verb. For ex: The committee (of architects, engineers, urban planners, and developers) IS meeting as we speak (to vote on the zoning change proposal).
May 25, 2021
Answer: C
This is a classic SAT and ACT grammar topic relating to an introductory dependent clause: “By re-creating snowflake formation,”. We must first note that any dependent clause “depends” on what comes immediately after the comma. In this case, there is no subject identified in the dependent clause. Who recreated snowflake formation? Grammatically, this requires that we state the subject immediately following the comma, that is the scientists or names of the people who recreated snowflake formation. Note that choice C is the only one that states a subject immediately.
April 7, 2021
Answer: C
First, what is the question asking for? What deems “success” in this probability question?
P(G AND Y) OR P(Y AND G).
Basic probability rules we teach: for independent events, “and” means multiply and “or” means add.
Imagine doing the draw one M&M at a time.
P (G) = 30/92
Now with one fewer M&M, P(Y) = 15/91.
So P (G AND Y) = .0537, by multiplying the above probabilities.
But there’s one more way to reach “success”: P (Y THEN G)
P (Y) = 15/92
Now with one fewer M&M, P(G) = 30/91.
So P (Y AND G) = .0537 (again multiplying to achieve “and”)
Add the two ways to reach “success” (i.e. “or”): 0.0537 + 0.0537 = 0.1075.
October 2, 2020
Answer: 0
Remember that “you don’t have to know how to end a problem to start a problem.” To get started then, draw a hypothetical W in and see what the triangles reflect. Label the new angles x and y, for example. What do we know about x and y? They are complementary. So why not bring out our calculator and do some pseudo-backsolving for Cos (x) - Sin (y). How about Cos (45) - Sin (45). 0. What about Cos (30) - Sin (60). 0. Cos (60) - Sin (30). 0. We have our answer.
September 1, 2020:
Answer: B
This is a classic subject/verb trap. Remember that for a sentence to be a sentence it must have a verb. To gauge whether we are using the correct verb, we must ensure it corresponds to the subject in number, gender, tense, etc. So 1) what is the verb? “Are.” And 2) who or what is doing the verb: the committee.
Note: “Of architects, engineers, urban planners, and developers” is simply describing “the committee.” As “The committee” is singular, and later in the sentence we see present tense, the verb should be “is.”
Useful trick: put parentheses around any portion of a subject that can be removed, such as a descriptor. This will help reduce distance between a subject and verb. For ex: The committee (of architects, engineers, urban planners, and developers) IS meeting as we speak (to vote on the zoning change proposal).
July 29, 2020:
Answer: D
We must utilize the equation distance = rate * time. In fact we need to use it 3 times. First 400 miles = 225mph * total time. Total time = 1.77 hrs. Save this number. Then the first “slower” leg: 90 miles = 125 mph * time1. Time1 = .72 hours. Then, total time = time1 + time2. So 1.77 = .72 + time2. Time 2 = 1.057 hours. Finally, the last leg: the remaining distance = rate2 * time2. So 310 = rate2 * 1.057. Rate2 = 293 mph.
April 2020:
Answer: C
First, what is the question asking for? What deems “success” in this probability question?
P (G THEN Y) OR P (Y THEN G). Imagine doing the draw one M&M at a time.
P (G) = 30/92
Now with one fewer M&M, P(Y) = 15/91.
So P (G THEN Y) = .0537
But there’s one more way to reach “success”: P (Y THEN G)
P (Y) = 15/92
Now with one fewer M&M, P(G) = 30/91.
So P (Y THEN G) = .0537
Add the two ways to reach “success”: 0.0537 + 0.0537 = 0.1075.
March 2020:
Answer: E
Let’s explore two methods; think about which one suits you better.
1) Hopefully you’ll have learned the method for approaching half-life problems. If not, we can quickly teach it. In 1600 years, 1/2 of the Radium will have decayed. Form a table for yourself.
