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In the complex plane, the horizontal axis is called the real axis and the vertical axis is called the imaginary axis. The complex number a + bi graphed in the complex plane is comparable to the point (a, b) graphed in the standard (x, y) coordinate plane. The modulus of the complex number a + bi is given by:
\[\sqrt{a^2 + b^2}\]
Question:
Which of the complex numbers z1, z2, z3, z4 and z5 below has the greatest modulus?
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Question:Consider the functions f(x) = sqrt(x) and g(x) = 7x + b. In the standard (x,y) coordinate plane, y = f(g(x)) passes through (4,6). What is the value of b?
A. 8 B. 8 C. 25 D. 26 E. 4  7. sqrt(6)
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Question:
N.B: This question is for SAT Subject Test Math Level 2
\[if \ log_a 5 = x \ and \ log_a 7 = y, \ then \ log_a \sqrt{1.4} = \]
(A) (xy)/2
(B) x/2  y (C) (x + y)/2 (D) (y  x)/2 (E) y/(2x)
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Two whole numbers have a greatest common factor of 8 and a least common multiple of 48. Which of the following pairs of whole numbers will satisfy the given conditions?
F. 4 and 9 G. 5 and 10 H. 10 and 16 J. 14 and 20 K. 16 and 24
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A group of students conducted several experiments using a variety of nonstick cookware, a spring scale, and several different weighted objects. Their goal was to determine which brand of cookware products had the best nonstick surface by measuring the coefficient of static friction, which is a measure of how resistant a stationary object is to movement. Experiment 1 A student connected the spring scale to a weighted object that was placed inside a piece of nonstick cookware as shown in Figure 1. The students planned to calculate the coefficient of static friction by determining the force required to disturb an object from rest. During the experiment, one student anchored the nonstick cookware be holding tightly to the handle while the other student attached a weighted, smooth steel object to the spring scale. The student pulled on the spring until the object began to move. A third student recorded the force in newtons, N, indicated on the spring scale at the moment the object began to move across the nonstick surface. This procedure was repeated for 3 different brands of cookware; each brand of cookware was tested with various weighted objects. The coefficient of static friction was calculated by dividing the average force required to move the object by its weight (mass × g, the gravitational constant). The results are shown in Table 1. Experiment 2
The students performed an experiment similar to Experiment 1, except three different brands of cooking spray were applied to the same cookware surface before the weights were put in place. The results are shown in Table 2.
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Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. Choose the alternative that you think is best, and fill in the corresponding bubble on your answer sheet. If you think that the original version is best, choose “NO CHANGE,” which will always be either answer choice A or F. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer. Questions:Need for Speed
As an avid skier and inline skater, I thought I had already achieved some incredible downhill speeds. On a recent trip to Quebec City, nevertheless [1], my concept of how fast humans can move was radically altered. It was Carnaval season, the time when people from across the province and the world flocking [2] to the old walled city for two weeks of food, drink, revelry, and winter sports. Normally, I go to Carnaval looking for the rare thrill, all the better if it requires a helmet and my signature on a release of liability. This time for me, it was fullcontact downhill iceskating. [3], [4] The course looked a lot like a bobsled run. From the top of the mountain a sturdy metal chute descended that wound left and right on its way down. About eight inches of icepack covered the metal surface, which was wetted twice daily to maintain an ideal slickness. If by the time you reach the end of the chute you still haven’t regained your footing, there’s a line of meterthick foam padding [4] to absorb your crash. [1]. A. NO CHANGE B. thus C. therefore D. though [2]. F. NO CHANGE G. flock H. flocked by J. are flocking [3]. A. NO CHANGE B. It was fullcontact for me this time, I was iceskating downhill. C. Iceskating downhill this time for me, it was fullcontact. D. This time, I was fullcontact iceskating downhill. [4]. At this point, the author wants to add a sentence to the paragraph that further illustrates his adventurous nature. Which of the options does this best? F. I certainly didn’t know what I had signed up for! G. Downhill iceskating sounded much more exciting than normal iceskating! H. I could easily have been injured, but the thrill I got was worth the risk! J. I normally wouldn’t sign up for such a thing, but anything goes at Carnaval! [5]. A. NO CHANGE B. footing; there’s a line of meterthick foam padding C. footing there’s a line of meterthick foam padding, D. footing; there’s a line of meterthick foam padding,
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ProblemA total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f , r, and m?
F. rm+5=f G. rm−5=f H. r+m+5=f J. rf = m + 5 K. rf = m − 5
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ProblemSamantha is making gluten free brownies for the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic?
N.B: Recipe is on the next page.
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Alexa was attempting to make muffins with blueberries. Her recipe required 3/4 cup of sugar and 1/8 cup of butter. Alexa accidentally put a whole cup of butter in the mix. Problem:A.
B. This got Alexa wondering how she could remedy similar mistakes if she were to dump in a single cup of some of the other ingredients. Assume she wants to keep the ratios the same.
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Problem:
An interior designer is creating a custom coffee table for a client. The top of the table is a glass triangle that needs to balance on a single support. If the coordinates of the vertices of the triangle are at (3, 6), (5, 2), and (7, 10), at what point should the support be placed?
