12.Practice.Tests.for.the.SAT_2015-2016_1128p

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310 12 Practice Tests for the SAT Practice Test Three Answers and Explanations Getting to the Answer: a + b +c= 180 7 c + 2c + c = 1 80 4. D lOc= 180 c= 18 Difficulty: Low Strategic Advice: Don't overthink this one-the x6 is on each side and can be subtracted from both sides. Getting to the Answer: Subtract x6 from both sides to get 4 = w. 5. c Difficulty: Medium Strategic Advice: Remember key triangle rules on Test Day: the sum of the interior angles is 1 80°, and triangles with two equal sides also have two equal angles. Getting to the Answer: OA and OB are radii of the circle, so they are equal. This means that angles OAB and ABO are equal as well. The interior angles of the triangle total 1 80°, and angle AOB is 70°. Therefore, ABO +ABO + 70° = 180°. 2ABO = 1 10° ABO = 55° 6. A Difficulty: Medium Strategic Advice: When you are presented with a new function, it might look complicated. As long as you plug in numbers carefully, these types of questions are easier than they appear. Getting to the Answer: Plug in the given numbers. 1,007 + 2(3.5) - 1,007 + 7 - 1,014 1,007 - 2(3.5) - 1,007 - 7 - 1,000 Change to the decimal equivalent, which is 1 .0 14, whic is (A). 7. E Difficulty: Medium Strategic Advice: Be sure to draw in any information that is given in the question stem but not included in the diagram. Getting to the Answer: If the whole side is 8, each smaller square has a side length of 2. The radius of the circle is formed by one and one-half diagonals of the square. Each diagonal is 2\/2, so the entire 2\/2 radius is 2\/2 + - 2 - = 3v'2. Area of circle = 7t(3V2)2 = 187t 8. c Difficulty: Medium Strategic Advice: Be sure to distinguish between the terms with, possibly, and without. Getting to the Answer: The shaded area includes all salads with onions and peppers. Some of these possibly have tomatoes as well, as the shaded region overlaps into the tomatoes region. 9. B Difficulty: Medium Strategic Advice: Take this carefully, step-by-step, as you translate from English to math. Getting to the Answer: She spends 350/o of $400 to pay bills; that is, x $400 = $ 140. That leaves her with $400 - $140 = 100 $260. She budgets 300/o of this for shopping; that is, _2Q_ x $260 = $78. That leaves $260 - $78 = $ 1 82. Of 100 this, she allots $130 for entertainment, leaving ' $182 - $ 130 = $52 to save. Finally, $52 as a percent of the original $400 is $52 x 1000/o = 130/o. $400
12 Practice Tests for the SAT Practice Test Three Answers and Explanations I 31 l 10. A Difficulty: Medium Strategic Advice: In complex geometry problems, look for parts in common between the various shapes. Getting to the Answer: Since angles of a triangle add up to 180 degrees, then 50 + h + g = 180 and 70 + z + g = 180. So, g= 130-h g= l lO-z 130-h= 110-z 11. c h = 20 +z Difficulty: Medium Strategic Advice: Use any diagram given to your full advantage. They're usually the key to a great score. Getting to the Answer: There are five tick marks between 0 and l. Therefore, l 3 . 3 l 2 p = - and q = - so p - q 1s - - - = -. s s ' s s s 12. c Difficulty: Medium Strategic Advice: Round up when the succeeding digit is 5 or above. Round down if the succeeding digit is less than 5. Getting to the Answer: Therefore, 16.763 rounds to 16.8 because 6 is greater than 5. 13. D Difficulty: Medium Strategic Advice: The square root of a negative number is undefined. Backsolving might let you solve this problem more quickly. Getting to the Answer: 0 ::;x2 - 4 4 ::;x2 2 ::;xor -2 x f (x) is undefined for any values of x that are not within the above range. Since 0 is not within the range, (D) is correct. 14. B Difficulty: High Strategic Advice: You are asked to Pick Numbers to plug into the function. Use the resulting information to confirm or eliminate each of the choices. Getting to the Answer: Pick Numbers to try to eliminate choices. Choice I says t > 0. If you select l for x, then y = 4, z = 0, and t = 0. Therefore, I is wrong. Eliminate (A), (C), and (E). The only difference between the remaining choices is whether or not Ill is correct, so test it first. Try using 4 for x. This means that y = 13, z = 14, and t = 7, which is odd. So Ill is not correct and (B) is the correct answer. Although you don't need to check II, it is correct because no matter what you get for y, z will always be even. If y is odd, then l is added to it to get z, which would always make z even. If y is even, then 4 is subtracted, and z is still even. Therefore, no matter what, z will always be even. 15. D Difficulty: High Strategic Advice: When you have multiple variables and multiple equations, use substitution or elimination to determine the answer. Often, one method is much easier than the other. Getting to the Answer: It is also important to note you are not being asked for a or b, but rather a - b. Very often in problems like this you do not need to solve for the individual variables; rather, you can manipulate the equations to find the desired expression. The easiest way to find a - b is through elimination. Multiply the second equation by -2, then add the equations together: 3a + Sb - 4c = 12 -2a - 6b + 4c = 8 a -b =20 By eliminating the variable c, the value of a - b was determined. (D) is the correct answer.
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