TheoryFree DAT Practice Test
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DAT Questions
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Q1Which S<sub>N</sub>2 reaction would proceed the fastest?
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✓ Correct answer: 1-bromopentane and sodium iodide
S<sub>N</sub>2 reactions involve a backside nucleophilic attack on an electrophilic carbon. As a result, less steric congestion for this backside attack results in a faster reaction, meaning that S<sub>N</sub>2 reactions proceed fastest for primary carbons. In addition, beta-branching next to a primary carbon results in a slower reaction, as does a poorer leaving group (i.e. chloride instead of bromide).<br/><br/>1-bromopentane has a good leaving group (bromine) attached to a primary carbon with no beta-branching, meaning it will proceed the fastest.
Q2What is the hybridization of carbon in C<sub>2</sub>H<sub>2</sub>?
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✓ Correct answer: <em>sp</em>
The carbon is bonded to two other atoms (C and H), which means that it needs two hybrid orbitals.
Q3In a jar of candy there are 127 red candies, 92 orange ones, 108 yellow ones, 77 green ones, and 13 blue candies. If a person reaches into the jar without looking and grabs one piece of candy, what is the probability of that piece being red?
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✓ Correct answer: 30%
A person reaching into the candy jar would have a 30% chance of pulling out a piece of red candy. There are 417 pieces of candy in the jar altogether, which means the person has 127 chances in 417 to pull out a piece of red candy (or 127/417 if the candy is red). To convert that to a percentage, divide the number of chances to get a red candy (127) by the total number of pieces (417), then multiply the quotient by 100.
Q4If <tex>x = i - 1</tex>, then <tex>x2 + 2x + 2 =</tex>
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✓ Correct answer: 0
You're dealing with imaginary numbers here, so your calculator won't be much use. To solve this problem, just plug (i - 1) into the expression in place of x and do the math.
Q5<img src="asset:assets/questions/bc253b706121c5ec.png"/><br/><br/>Quantity A: Area of the larger circle<br/><br/>Quantity B: 2×area of the smaller circle
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✓ Correct answer: The two quantities are equal.
Consider the length of the square side is a. To find the length of the diagonal of the square, multiply the length of one side by the square root of 2:<br/><br/><img src="asset:assets/questions/5c4eaed1189287e6.png"/><br/><br/><img src="asset:assets/questions/ed4d6e21a93bf65a.png"/><br/><br/>As can be seen, the half of the diagonal of the square is the radius of the larger circle and the length of the square side is equal to the radius of the smaller circle. Therefore,<br/><br/>The area of the larger circle: <img src="asset:assets/questions/ebca89c7ee7b7a0a.png"/><br/><br/>The area of the smaller circle: <img src="asset:assets/questions/6df6b45c3f9a2116.png"/>
Q6What is the point of intersection of the line that passes through the points (1,5)and (3,9) and the line perpendicular to that line that passes through the point (0,-2)?
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✓ Correct answer: (-2,-1)
Determine the equation of the line through the points (1,5) and (3,9). The slope is which is 2. Find the y-intercept, b: 5 = 2(1) + b, so b = 3. The equation of the line is y = 2x + 3. The line perpendicular to this line has a slope that is the negative reciprocal, namely and the y-intercept is -2, because the given point is (0,-2). Now, find the intersection of these lines.
Q7Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle.
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✓ Correct answer: 1,331.41 ft2
The area of the triangle is 1,331.41 ft<sup>2</sup>.<br/><br/>Solution<br/><br/>Use the formula <i>A </i>= 1/2<i>bh</i><br/><br/>Where A = area<br/><i>b</i> = base<br/><i>h</i> = height<br/><br/>A = ½ (42.20 ft) (63.10 ft) = 1,331.41 ft<sup>2<br/></sup>
Q8Convert 75.2228° to degrees, minutes, and seconds.
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✓ Correct answer: 75°13’22”
One minute is defined as 1/60 of a degree (1° = 60 minutes).<br/><br/>One second is defined as 1/60 of a minute (one minute = 60 seconds).<br/><br/>Therefore, 1° = (60 minutes per degree) (60 seconds per minute) = 3600 seconds.<br/><br/>Convert the decimal part of the angle reading (0.2228°) to minutes: (0.2228°)(60 minutes per degree) = 13.368 minutes.<br/><br/>Convert the decimal part of 13.368 minutes to seconds:(0.368 minutes) (60 seconds per minute) = 22 seconds.<br/><br/>Add together to obtain DMS 75°13’22”.
Q9In a plane there are 8 points, no three of which are collinear. How many lines do the points determine?
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✓ Correct answer: 28
Since no three points are collinear, every pair of points determines a distinct line. There are such lines.
Q10The length, width, and height of a rectangular solid are 5 cm, 3 cm, and 7 cm, respectively. What is the length of the longest segment whose endpoints are vertices of the rectangular solid?
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