AccelePrep for the ACT Test 2nd Edition Student Text

108 • S URGE TO S UCCESS ! M ATH T EST P REP

Now test those same values in the choices. The correct choice will return the value 12: 2(1) 2 (Wrong) 12(1)(1) 12 (Correct?) 2(1) 6(1) 8 (Wrong) 6(1) 6(1) 12 (Correct?) 8(1) 9(1) 17 (Wrong) ‡ǯ˜‡ ‡Ž‹‹ƒ–‡† –Š”‡‡…Š‘‹…‡• –Šƒ– ƒ”‡ †‡ϐ‹‹–‡Ž› ™”‘‰ǡ „—– „‘–Š (B) and (D) returned the value 12. Do we have two right answers? No. Since (1)( n ) n , two choices returned the same value—a coincidence. —•– —•‡ –™‘ ‘”‡ ˜ƒŽ—‡•ǡ •ƒ› a 1 and b 0: 4 3 4 0 6 1 0 2 1 3 0 2 0 ^ ^ ^ ^ ^ ^ h h h hh h B. 12(1)(0) 0 (Wrong) D. 6(1) 6(0) 6 (Correct) 6. You can use the rules for working with exponents to simplify the expression: x y x y x y x y x y x y 3 9 3 9 9 9 1 6 9 2 2 3 6 2 6(2) 9(2) 2(6) 3(6) 12 18 12 18 _ _ ^ ^ _ _ i i h h i i . Or you can Plug-and-Chug. Let’s say x = 1 and y = 1. On that assumption, since 1 to any power is just 1, the complicated expression in the question stem becomes 9 9 1 . If you substitute 1 for both x and y in the choices, the correct choice will return the value 1: F. 1 (Correct?) G. 3 (Wrong) H. 1 (Correct?) Ǥ ͵ ȋ ”‘‰Ȍ K. 9 (Wrong) We have two seemingly right choices. Why? Because 1 1 1 1 ^ h , duplicates are possible. So we just pick another pair of values: x = 1 and y = 2. On those assumptions, the complicated expression in the question stem becomes 1 (use your calculator), and of (F) and (H), only (F) returns the value 1. 7. At take-off, the plane is already 750 feet above sea level. Climbing at 1,000 feet per minute, it will attain an additional altitude of 1,000 m feet. So after m minutes, the plane has attained an altitude of 1,000 m + 750, (D). Want to avoid all that? Then Plug-and-Chug. Pick a numerical value for m . Say m = 1, which is to say 1 minute after take-off. At that point, the plane will be 1,000 feet higher than the airport, and since the airport is 750 feet above sea level, the plane will be a total of 1,000 + 750 = 1,750 feet above sea level. Substitute 1 for m in the answer choices. The correct choice will return the value 1,750: D. A = 1,000 m + 750 = 1,000(1) + 750 = 1,750