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College Board, SAT, and the acorn logo are registered trademarks of the College Board. 5LSA07  \nSection 3: Math Test — No Calculator  \nQUESTION 1.  \nChoice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4. Dividing both sides of 5x = 4 by 5 yields x = . The value of x can now be substituted into the expression 10x + 3, giving 510 ( ) + 3 = 11.  \nAlternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and 10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.  \nChoices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10, contradicting the given equation, 5x + 6 = 10. For example, choice A is incorrect because if the value of 10x + 3 were 4, then it would follow that x = 0 . 1, and the value of 5x + 6 would be 6 .5, not 10.  \nQUESTION 2.  \nChoice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0. Then, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives 5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting 2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Therefore, the solution to the given system of equations is (2, −2) .  \nAlternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. The value of y can then be found in the same way as before.  \nChoices A, C, and D are incorrect because when the given values of x andy are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the equations are not true. These answers may result from sign errors or other computational errors.  \nQUESTION 3.  \nChoice A is correct. The price of the job, in dollars, is calculated using the expression 60 + 12nh, where 60 is a fixed price and 12nh depends on the number of landscapers, n, working the job and the number of hours, h, the job takes those n landscapers. Since nh is the total number of hours of work done when n landscapers work h hours, the cost of the job increases by $12 for each hour a landscaper works. Therefore, of the choices given, the best interpretation of the number 12 is that the company charges $12 per hour for each landscaper.  \nChoice B is incorrect because the number of landscapers that will work each job is represented by n in the equation, not by the number 12. Choice C is incorrect because the price of the job increases by 12n dollars each hour, which will not be equal to 12 dollars unless n = 1. Choice D is incorrect because the total number of hours each landscaper works is equal to h. The number of hours each landscaper works in a day is not provided.  \n23  \nQUESTION 4.  \nChoice A is correct. Ifa polynomial expression is in the form (x)2 + 2(x)(y) +(y)2, then it is equivalent to (x + y)2. Because 9a4 + 12a2b2 + 4b4 = (3a2)2 + 2(3a2)(2b2) + (2b2)2, it can be rewritten as (3a2 + 2b2)2.  \nChoice B is incorrect. The expression (3a + 2b)4 is equivalent to the product (3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b) . This product will contain the term 4(3a)3 (2 b) = 216a3b. However, the given polynomial, 9a4 + 12a2b2 + 4b4, does not contain the term 216a3b. Therefore, 9a4 + 12a2b2 + 4b4 ≠ (3a + 2b)4. Choice C is incorrect. The expression (9a2 + 4b2)2 is equivalent to the product (9a2 + 4b2)(9a2 + 4b2) . This product will contain the term (9a2)(9a2) = 81a4. However, the given polynomial, 9a4 + 12a2 b2 + 4b4, does not contain the term 81a4. Therefore, 9a4 + 12a2 b2 + 4b4 ≠ (9a2 + 4b2)2. Choice D is incorrect. The expression (9a + 4b)4 is equivalent to the product (9a + 4b)(9a + 4b)(9a + 4b) (9a + 4b) . This product will contain the term (9a)(9a)(9a)(9a) = 6,561a4. However, the given polynomial, 9a4 + 12a2b2 + 4b4, does not contain the term 6,561a4. Therefore, 9a4 + 12a2b2 + 4b4 ≠ (9a + 4b)4.  \nQUESTION 5.  \n_  \nChoice C is correct. Since √2k2 + 17 − x = 0, and x = 7, one can substitute 7 for x, which gives √_2k2 + 17 − 7 = 0. Adding 7 to each side of √_2k2 + 17 − ","cbCaioRlWISaiVb7","https://ap.wps.com/l/cbCaioRlWISaiVb7","pdf",322441,"English","# Section 3: Math Test — No Calculator\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n## Question 6\n## Question 7","[{\"question\":\"How are Question 1 and Question 2 solutions constructed in these explanations?\",\"answer\":\"Question 1 solves a linear equation to find x, then substitutes into the target expression to get the correct numeric result. Question 2 uses elimination-like steps to solve a system and then states the solution pair (x, y).\"},{\"question\":\"What algebra skills are emphasized in the explanation for Question 4?\",\"answer\":\"Question 4 emphasizes recognizing polynomial forms and rewriting expressions using perfect-square identities, then verifying equivalence by checking whether specific terms (like a^4 coefficients) appear in the expanded result.\"},{\"question\":\"Why do the explanations for radical equations mention extraneous roots?\",\"answer\":\"When both sides are squared to remove a square root, extra solutions may be introduced. The explanations confirm the final answer by substituting it back into the original equation to ensure it satisfies the initial radical form.\"}]","SAT Practice Test 2 - Math Test (No Calculator) Answer Explanations | PDF"]