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100
Can be divided by 2.
What is an even number.
100
True or false, wrong answers count against your score?
What is False.
100
If 
and 
what is the value of 
What is 10.
There is more than one way to solve this problem. A student can apply standard techniques by rewriting the equation as 
and then factoring. Since the coefficient of 
is 14 and the constant term is 
factoring requires writing 51 as the product of two numbers that differ by 14. This is 
which gives the factorization 
The possible values of are 
and 
Since it is given that it must be true that Thus, the value of 
is 
A student could also use the quadratic formula to find the possible values of 
The possible values of are 
and 
Again, since it is given that it must be true that Thus, the value of is
There is another way to solve this problem that will reward the student who recognizes that adding 49 to both sides of the equation yields 
or rather 
which has a perfect square on each side. Since the solution 
is evident.
100
A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?
A) 1
B) 2
C) 3
D) 4
What is answer choice B.
The solutions to the system of equations are the points where the circle, parabola, and line all intersect. These points are 
and 
, and these are the only solutions to the system.
Choice A is not the correct answer. This answer may reflect the misconception that a system of equations can have only one solution.
Choice C is not the correct answer. This answer may reflect the misconception that a system of equations has as many solutions as the number of equations in the system.
Choice D is not the correct answer. This answer may reflect the misconception that the solutions of the system are represented by the points where any two of the curves intersect, rather than the correct concept that the solutions are represented only by the points where all three curves intersect.
100
The work of transportation planners generally includes evaluating current transportation needs, assessing the effectiveness of existing facilities, and improving those facilities or they design new ones. Most transportation planners work in or near cities, but some are employed in rural areas.
A) NO CHANGE
B) to design
C) designing
D) design
What is designing.
“designing” maintains parallelism with “evaluating,” “assessing,” and “improving.”
Choice A is not the best answer because “they design” does not maintain parallelism with “evaluating,” “assessing,” and “improving.”
Choice B is not the best answer because “to design” does not maintain parallelism with “evaluating,” “assessing,” and “improving.”
Choice D is not the best answer because “design” does not maintain parallelism with “evaluating,” “assessing,” and “improving.”
200
Orders of operation.
What is PEMDAS.
200
How long is the reading section?
What is 65 minutes.
OR
What is 52 multiple choice questions.
200
If 
what is one possible value of
What is any value greater than 
and less than 
.
Recognizing the structure of this inequality provides one solution strategy. With this strategy, a student will look at the relationship between 
and 
and recognize that the latter is −3 multiplied by the former.
Multiplying all parts of the inequality by −3 reverses the inequality signs, resulting in 
or rather 
when written with increasing values from left to right. Any value greater than 
and less than 
is correct.
200
If 
is a solution to the system of equations above, what is the value of 
A) -51
B) 3
C) 9
D) 144
What is answer choice C.
The second equation gives y in terms of x, so a student can use this to rewrite the first equation in terms of x. Substituting -4x for y in the equation 
gives 
This can be simplified to 
or 
Since the question asks for the value of 
not x, dividing both sides of 
by 17 gives the answer: 
Choice A is not the correct answer. This answer may result from neglecting to square the coefficient –4 in 
which would give 
Then the first equation would become 
which would give –51 as the value of 
Choice B is not the correct answer. This answer may result from finding the value for x, not the value of
Choice D is not the correct answer. This answer may result from finding the value of 
not
200
Mattie Silver had lived under Ethan’s roof for a year, and from early morning till they met at supper he had frequent chances of seeing her; but no moments in her company were comparable to those when, her arm in his, and her light step flying to keep time with his long stride, they walked back through the night to the farm. He had taken to the girl from the first day, when he had driven over to the Flats to meet her, and she had smiled and waved to him from the train, crying out, “You must be Ethan!” as she jumped down with her bundles, while he reflected, looking over her slight person: “She don’t look much on housework, but she ain’t a fretter, anyhow.” But it was not only that the coming to his house of a bit of hopeful young life was like the lighting of a fire on a cold hearth. The girl was more than the bright serviceable creature he had thought her. She had an eye to see and an ear to hear: 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.
It was during their night walks back to the farm that he felt most intensely the sweetness of this communion. He had always been more sensitive than the people about him to the appeal of natural beauty. His unfinished studies had given form to this sensibility and even in his unhappiest moments field and sky spoke to him with a deep and powerful persuasion. But hitherto the emotion had remained in him as a silent ache, veiling with sadness the beauty that evoked it. He did not even know whether any one else in the world felt as he did, or whether he was the sole victim of this mournful privilege.
A) fitness for farm labor.
B) vivacious youth.
C) receptive nature.
D) freedom from worry.
What is answer choice C.
Lines 4–8 mention many of Mattie’s traits: she is friendly (“smiled and waved”), eager (“jumped down with her bundles”), easygoing (“she ain’t a fretter”), and energetic (“like the lighting of a fire on a cold hearth”). However, the trait that appeals most to Ethan, as suggested by it being mentioned last in the paragraph, is her openness to the world around her: “She had an eye to see and an ear to hear: 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” (lines 11–13).
Choice A is not the best answer because the passage suggests that Ethan does not actually view Mattie as particularly well suited to farm labor. When first seeing Mattie, Ethan thinks to himself, after “looking over her slight person,” that “she don’t look much on housework” (lines 7–8).
Choice B is not the best answer because the passage suggests that Mattie’s youth is not what Ethan values most about Mattie. Although the passage does note that “the coming to his house of a bit of hopeful young life was like the lighting of a fire on a cold hearth” (lines 8–10), the narrator goes on to note that “the girl was more than the bright serviceable creature [Ethan] had thought her” (lines 10–11), indicating that Ethan values something more in Mattie than simply her vivacity.
Choice D is not the best answer because although Ethan acknowledges that Mattie “ain’t a fretter” (line 8), there is no evidence that Mattie’s freedom from worry is what Ethan values most about Mattie. The first paragraph lists several positive traits that Mattie has, with the most emphasis being placed on her openness to the world around her (see explanation for choice C).
300
The number that describes the direction and steepness of a figure.
What is the slope.
300
True or false, the most important sentences in the reading section are the first and last sentences of each paragraph?
What is True.
300
At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?
A)
B)
C)
D)
What is answer choice D.
The student must reason that because the mean of the males is lower than that of the females, the combined mean cannot be greater than or equal to that of the females, while also reasoning that because the mean of the females is greater than that of the males, the combined mean cannot be less than or equal to the mean of the males. Therefore the combined mean must be between the two separate means.
Choice A is not the correct answer. This answer results from a student finding the mean of the two means. This answer makes an unjustified assumption that there are an equal number of male and female primates.
Choice B is not the correct answer. This answer results from a student finding the mean of the two means and misapplying an inequality to the scenario. This answer makes an unjustified assumption that there are more females than males.
Choice C is not the correct answer. This answer results from a student finding the mean of the two means and misapplying an inequality to the scenario. This answer makes an unjustified assumption that there are more males than females.
300
The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
A)
B) 
C) 
D)
What is answer choice A is.
Multiplying the number of cups of milk by the amount of calcium each cup contains and multiplying the number of cups of juice by the amount of calcium each cup contains gives the total amount of calcium from each source. The student must then find the sum of these two numbers to find the total amount of calcium. Because the question asks for the calcium from these two sources to meet or exceed the recommended daily intake, the sum of these two products must be greater than or equal to 1,000.
Choice B is not the correct answer. This answer may result from a misunderstanding of the meaning of inequality symbols as they relate to real-life situations. This answer does not allow for the daily intake to meet the recommended daily amount.
Choice C is not the correct answer. This answer may result from a misunderstanding of proportional relationships. Here the wrong operation is applied, with the total amount of calcium per cup divided by the number of cups of each type of drink. These values should be multiplied.
Choice D is not the correct answer. This answer may result from a combination of mistakes. The inequality symbol used allows the option to exceed, but not to meet, the recommended daily value, and the wrong operation may have been applied when calculating the total amount of calcium intake from each drink.
300
For one month after they left the nest, I led my four young ravens at least once and sometimes several times a day on thirty-minute walks. During these walks, I wrote down everything in their environment they pecked at. In the first sessions, I tried to be teacher. I touched specific objects—sticks, moss, rocks—and nothing that I touched remained untouched by them. They came to investigate what I had investigated, leading me to assume that young birds are aided in learning to identify food from the parents’ example. They also, however, contacted almost everything else that lay directly in their own paths. They soon became more independent by taking their own routes near mine. Even while walking along on their own, they pulled at leaves, grass stems, flowers, bark, pine needles, seeds, cones, clods of earth, and other objects they encountered. I wrote all this down, converting it to numbers. After they were thoroughly familiar with the background objects in these woods and started to ignore them, I seeded the path we would later walk together with objects they had never before encountered. Some of these were conspicuous food items: raspberries, dead meal worm beetles, and cooked corn kernels. Others were conspicuous and inedible: pebbles, glass chips, red winterberries. Still others were such highly cryptic foods as encased caddisfly larvae and moth cocoons. The results were dramatic.
The four young birds on our daily walks contacted all new objects preferentially. They picked them out at a rate of up to tens of thousands of times greater than background or previously contacted objects. The main initial criterion for pecking or picking anything up was its novelty. In subsequent trials, when the previously novel items were edible, they became preferred and the inedible objects became “background” items, just like the leaves, grass, and pebbles, even if they were highly conspicuous. These experiments showed that ravens’ curiosity ensures exposure to all or almost all items in the environment.
A) edible.
B) plentiful.
C) conspicuous.
D) natural.
What is answer choice A.
The last paragraph of Passage 2 presents the results of an experiment in which the author scattered unfamiliar objects in the path of some ravens. According to the passage, the birds initially “contacted all new objects preferentially” but in “subsequent trials” only preferred those “previously novel items” that “were edible” (Passage 2, lines 18-24).
Choice B is not the best answer because the ravens studied by the author only preferred those “previously novel items” that “were edible,” whereas “the inedible objects became ‘background’ items, just like the leaves, grass, and pebbles” (Passage 2, lines 18-24). In other words, plentiful items did not continue to interest the ravens unless the items were edible.
Choice C is not the best answer because the ravens studied by the author only preferred those “previously novel items” that “were edible,” whereas “the inedible objects became ‘background’ items, just like the leaves, grass, and pebbles, even if they were highly conspicuous” (Passage 2, lines 18-24). In other words, conspicuous items did not continue to interest the ravens unless the items were edible.
Choice D is not the best answer because the ravens studied by the author only preferred those “previously novel items” that “were edible,” whereas “the inedible objects became ‘background’ items, just like the leaves, grass, and pebbles” (Passage 2, lines 18-24). In other words, natural items did not continue to interest the ravens unless the items were edible.
400
Number consisting of an integer and a proper fraction.
proper fraction - fraction less than one with a numerator less than the denominator.
What is a mixed number.
400
Which one of these statements is false?
1. Do not plug in '0'.
2. Do not use equations.
3. Do not plug in '1' for adding and subtraction.
4. Do easy questions first.
5. Plugging is for variables.
What is 3., Do not plug in 1 for adding and subtraction.
400
A company’s manager estimated that the cost C, in dollars, of producing nitems is 
. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?
A) 
B) 
C) 
D) 
What is answer choice C.
One method to find the correct answer is to create an inequality. The income from sales of n items is 12n. For the company to profit, 12n must be greater than the cost of producing n items; therefore, the inequality 
can be used to model the context. Solving this inequality yields 
Choice A is not the correct answer. This answer may result from a misunderstanding of the properties of inequalities. The student may have found the number of items of the break-even point as 70 and used the incorrect notation to express the answer, or the student may have incorrectly modeled the scenario when setting up an inequality to solve.
Choice B is not the correct answer. This answer may result from a misunderstanding of how the cost equation models the scenario. A student who uses the cost of $12 as the number of items n and evaluates the expression 7n will find the value of 84. A student who does not understand how the inequality relates to the scenario may think nshould be less than this value.
Choice D is not the correct answer. This answer may result from a misunderstanding of how the cost equation models the scenario. A student who uses the cost of $12 as the number of items n and evaluates the expression 7n will find the value of 84. A student who does not understand how the inequality relates to the scenario may think should be greater than this value.
400
The function f is defined by 
where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (-4,0), 
and 
What is the value of c?
A) -18
B) -2
C) 2
D) 10
What is answer choice A.
The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields 
or 
Alternatively, since –4, 
and p are zeros of the polynomial function 
it follows that 
Were this polynomial multiplied out, the constant term would be 
(We can see this without performing the full expansion.) Since it is given that this value is 8, it follows that 
or rather, 
Substituting 2 for p in the polynomial function yields 
and after multiplying the factors one finds that the coefficient of the x term, or the value of c, is –18.
Choice B is not the correct answer. This value is a misunderstood version of the value of p, not c, and the relationship between the zero and the factor (if is the zero of a polynomial, its corresponding factor is 
) has been confused.
Choice C is not the correct answer. This is the value of p, not c. Using this value as the third factor of the polynomial will reveal that the value of c is -18.
Choice D is not the correct answer. This represents a sign error in the final step in determining the value of c.
400
His fine brushwork conveys detailed street-level activity: a peanut vendor pushing his cart on the sidewalk, a pigeon pecking for crumbs around a fire hydrant, an old man tending to a baby outside a doorway. His broader brush strokes and sponge-painted shapes create majestic city skylines, with skyscrapers towering in the background, bridges connecting neighborhoods on either side of a river, and delicately painted creatures, such as a tiny, barely visible cat prowling in the bushes of a park. To art critics and fans alike, these city scenes represent the innovative spirit of twentieth-century urban Modernism.
A) NO CHANGE
B) exquisitely lettered street and storefront signs.
C) other details that help define Kingman’s urban landscapes.
D) enormous ships docking at busy urban ports.
What is answer choice D.
The phrase “enormous ships docking at busy urban ports” effectively continues the sentence’s series of details (“skyscrapers towering in the background” and “bridges connecting neighborhoods”) conveying the majesty of city skylines as depicted by Kingman.
Choice A is not the best answer because the phrase “delicately painted creatures, such as a tiny, barely visible cat prowling in the bushes of a park” does not convey a sense of the majesty of city skylines as depicted by Kingman and thus does not effectively continue the sentence’s series of details (“skyscrapers towering in the background” and “bridges connecting neighborhoods”).
Choice B is not the best answer because the phrase “exquisitely lettered street and storefront signs” does not convey a sense of the majesty of city skylines as depicted by Kingman and thus does not effectively continue the sentence’s series of details (“skyscrapers towering in the background” and “bridges connecting neighborhoods”).
Choice C is not the best answer because the phrase “other details that help define Kingman’s urban landscapes” is too vague and general to constitute a third example that conveys a sense of the majesty of city skylines as depicted by Kingman and thus does not effectively continue the sentence’s series of details (“skyscrapers towering in the background” and “bridges connecting neighborhoods”).
500
Integer for which the average of its positive divisors is also an integer.
What is an Arithmetic number.
500
Three steps used in the plugging in method.
What is to write down all variables.
What is to identify variable most seen.
What is pick a number for variable.
What is to solve for other variables or to solve the problem. .
What is to then to plug in numbers for the other variables that are on the same side if the last step was no possible.
What is to solve problem using your value.
What is to plug values into answer choices to find answer.
500
If the expression 
is written in the equivalent form 
what is A in terms of x?
A) 
B) 
C) 
D)
What is answer choice A.
The form of the equation suggests performing long division on 
Since the remainder 1 matches the numerator in 
it is clear that 
A short way to find the answer is to use the structure to rewrite the numerator of the expression as 
recognizing the term in parentheses as a difference of squares, making the expression equal to 
From this, the answer is apparent. Another way to find the answer is to isolate A in the form 
and simplify. As with the first approach, this approach also requires students to recognize as a difference of squares that factors.
Choice B is not the correct answer. The student may have made a sign error while subtracting partial quotients in the long division.
Choice C is not the correct answer. The student may misunderstand how to work with fractions and may have tried the incorrect calculation
Choice D is not the correct answer. The student may misunderstand how to work with fractions and may have tried the incorrect calculation
500
An architect drew the sketch below while designing a house roof. The dimensions shown are for the interior of the triangle.
What is the value of 
What is 2/3.
Because the triangle is isosceles, constructing a perpendicular from the top vertex to the opposite side will bisect the base and create two smaller right triangles. In a right triangle, the cosine of an acute angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. This gives 
which can be simplified to 
500
During his career, Kingman exhibited his work internationally. He garnered much acclaim. In 1936, a critic described one of Kingman’s solo exhibits as “twenty of the freshest, most satisfying watercolors that have been seen hereabouts in many a day.”
The writer wants to conclude the passage with a sentence that emphasizes an enduring legacy of Kingman’s work. Which choice would best accomplish this goal?
A) Although Kingman’s work might not be as famous as that of some other watercolor painters, such as Georgia O’Keeffe and Edward Hopper, it is well regarded by many people.
B) Since Kingman’s death in 2000, museums across the United States and in China have continued to ensure that his now-iconic landscapes remain available for the public to enjoy.
C) The urban landscapes depicted in Kingman’s body of work are a testament to aptness of the name chosen for Kingman when he was just a boy.
D) Kingman’s work was but one example of a long-lasting tradition refreshed by an innovative artist with a new perspective.
What is answer choice B.
It concludes the passage with a sentence that emphasizes the enduring legacy of Kingman’s work by indicating that museums continue to make Kingman’s iconic paintings accessible to the public.
Choice A is not the best answer because it concludes the passage with a sentence that acknowledges that other painters’ work is more famous than Kingman’s (which downplays, rather than emphasizes, the enduring legacy of Kingman’s work) and offers only a general assertion that Kingman’s work is “well regarded by many people.”
Choice C is not the best answer because instead of referring to the enduring legacy of Kingman’s work, it concludes the passage with a sentence that recalls a detail the passage provides about Kingman’s early life.
Choice D is not the best answer because it concludes the passage with a sentence that is too vague and general to emphasize effectively an enduring legacy of Kingman’s work. It is not clear what the idea of refreshing a long-lasting tradition is intended to mean or how (or even whether) this represents an enduring legacy. Moreover, referring to Kingman’s work as “but one example” downplays the significance of any potential legacy that might be suggested.