AccelePrep for the ACT Test 2nd Edition Student Text

C HAPTER 4 | F AST T RACK TO M ATH M ECHANICS • 91

xy Ǥ ‡–‡”‹‡ –Š‡ ˜ƒŽ—‡ ‘ˆ 6 3 # 18

( , ) f x y is 6 x y ( , ) f 6 3 : ( , ) f 6 3

ȋ Ȍ ‹•…Ž‡ƒ”Ž› Žƒ”‰‡” –Šƒ ȋ ȌǤ ‹…‡ ȋ Ȍ ‹• †‘—„Ž‡ –Š‡ ˜ƒŽ—‡ ‘ˆ ȋ Ȍǡ ™Š‹…Š ‹• ‡‰ƒ–‹˜‡ǡ ȋ Ȍ ‹• ƒŽ•‘ Žƒ”‰‡” –Šƒ ȋ ȌǤ ȋ Ȍ ‹• Žƒ”‰‡” –Šƒ ȋ Ȍ „‡…ƒ—•‡ ™Š‡ ͳ ‹• •—„–”ƒ…–‡† ˆ”‘ ‡‹–Š‡” ƒ ’‘•‹–‹˜‡ ‘” ‡‰ƒ–‹˜‡ ˜ƒŽ—‡ǡ –Š‡ ”‡•—Ž– ‹• ƒŽ™ƒ›• Ž‡•• –Šƒ –Š‡ ‘”‹‰‹ƒŽ ˜ƒŽ—‡Ǥ ‘™‡˜‡”ǡ ‹ˆ ƒ ‡‰ƒ–‹˜‡ ˆ”ƒ…–‹‘ ‹• ”ƒ‹•‡† –‘ ƒ ‘†† ’‘™‡”ǡ –Š‡ –Š‡ ”‡•—Ž–‹‰ ˜ƒŽ—‡ǡ –Š‘—‰Š •ƒŽŽ‡” ‹ ƒ„•‘Ž—–‡ ˜ƒŽ—‡ǡ ‹• ‡‰ƒ–‹˜‡ ƒ† –Š‡”‡ˆ‘”‡ Žƒ”‰‡” –Šƒ –Š‡ ‘”‹‰‹ƒŽǤ ‘ǡ ȋ Ȍ ‹• Žƒ”‰‡” –Šƒ ȋ ȌǤ –ǯ• ’”‘„ƒ„Ž› ‡˜‡ ˆƒ•–‡” –‘ —•‡ –Š‡ Dz’Ž—‰Ǧƒ†Ǧ …Š—‰dz ƒ’’”‘ƒ…ŠǤ —„•–‹–—–‡ ƒ ‡‰ƒ–‹˜‡ ˆ”ƒ…–‹‘ƒŽ ˜ƒŽ—‡ ˆ‘” x , such as x 2 1 ǡ ƒ† ‡˜ƒŽ—ƒ–‡ –Š‡ answer choices: Ǥ Ȃͳ Ǥ x 2 1 & Ǥ & x 2 2 2 1 1 c m Ǥ x 2 1 2 1 2 1 8 1 3 & c c c m m m Ǥ & x 1 2 1 1 2 3 ‹…‡ ƒŽŽ ‘ˆ –Š‡ ƒ•™‡”…Š‘‹…‡• ›‹‡Ž† ‡‰ƒ–‹˜‡ ˜ƒŽ—‡•ǡ –Š‡ Žƒ”‰‡•– ˜ƒŽ—‡ ‹• –Š‡ ‘‡ –Šƒ– ‹•…Ž‘•‡•– to zero: 8 1 Ǥ Check your answer Ǥ ‹–Š‡” ‡–Š‘† •Š‘™• –Šƒ– x 3 ǡ ȋ Ȍǡ ‹• –Š‡ Žƒ”‰‡•– ‡š’”‡••‹‘ ˆ‘” ƒ ‡‰ƒ–‹˜‡ ˆ”ƒ…–‹‘ƒŽ ˜ƒŽ—‡ ˆ‘” x Ǥ 5. (A) Mathematics/Algebra and Functions/ Evaluating, Interpreting, and Creating Algebraic Functions/Function Notation Preview the question Ǥ Š‹• ‹• ƒ ‡†‹— †‹ˆϐ‹…—Ž–› ‹–‡Ǥ ‘—…ƒ —•‡ ›‘—”…ƒŽ…—Žƒ–‘” ‘ –Š‹• ‹–‡ǡ but the math is so simple it’s probably faster to †‘ –Š‡ ƒ”‹–Š‡–‹…„› Šƒ†Ǥ Strategize and solve Ǥ Š‡ ‹–‡ –‡•–• understanding of function math, so the best ƒ’’”‘ƒ…Š ‹• –‘ ’Ž—‰ ‹ –Š‡ ‰‹˜‡ ˜ƒŽ—‡• ˆ‘” x and y ƒ† ‡˜ƒŽ—ƒ–‡ –Š‡ ˆ—…–‹‘•Ǥ ‘” –Š”‘—‰Š –Š‡ ‹–‡ ƒ •–‡’ ƒ– ƒ –‹‡Ǥ ‡–‡”‹‡ –Š‡ ˜ƒŽ—‡ ‘ˆ b ˆ”‘ –Š‡ ‰‹˜‡ ˜ƒŽ—‡ ‘ˆ –Š‡ ˆ—…–‹‘ ˆ‘” x α ͳ and y α ʹǣ ( , ) f x y xy 1 2 1 2 1 2 # b b 4 & b 4 1 2 4 2 6 Ǥ Š‡ ˆ—…–‹‘

6 12 Ǥ #

6

6 3 Determine the ˜ƒŽ—‡ ‘ˆ ( , ) f 12 6 : 72 6 12 6 18 Ǥ Check your answer Ǥ Š‡ “—‡•–‹‘ ƒ•‡† ˆ‘” ( ( , ), ) f f 6 3 6 , and ( , ) f 6 3 12 , so the item stem asked for ( , ) f 12 6 ǡ ™Š‹…Š ‹• ͳͺǡ ȋ ȌǤ 6. (J) Mathematics/Algebra and Functions/ Manipulating Algebraic Expressions/Basic Algebraic Manipulations and Statistics and Probability/Data Representation/Tables Preview the question Ǥ Š‡ –ƒ„Ž‡ ‰‹˜‡• –Š‡ ™‡‹‰Š– …Žƒ••‹ϐ‹…ƒ–‹‘• ˆ‘” ϐ‹˜‡ ”ƒ‰‡• ƒ† –Š‡ ‹–‡ stem describes the equation for BMI and asks for the change in weight required to take a ’‡”•‘ ͳǤ͸ ‡–‡”• –ƒŽŽ ˆ”‘ ƒ Š‡ƒŽ–Š› –‘ ƒ ‘„‡•‡ Ǥ……‘”†‹‰ –‘ –Š‡ –ƒ„Ž‡ǡ ƒ ʹͶǤͻ ‹• Š‡ƒŽ–Š› ƒ† ƒ ͵ͲǤͲ ‹• ‘„‡•‡Ǥ Strategize and solve Ǥ Š‹• ’”‘„Ž‡ ‹• •–”ƒ‹‰Š–ˆ‘”™ƒ”†ǡ •‘ —•‡ –Š‡ ƒŽ‰‡„”ƒ •‘Ž—–‹‘Ǥ ”ƒ•Žƒ–‡ –Š‡ ‰‹˜‡ ‹ˆ‘”ƒ–‹‘ ‹–‘ ƒ equation for BMI, where w is the weight and h ‹• –Š‡ Š‡‹‰Š–ǡ ƒ† •‘Ž˜‡ ˆ‘” –Š‡ ™‡‹‰Š–ǣ & ( ( ( h w w h BMI meters) kilograms) BMI) 2 2 Ǥ Š‡ change in weight that accompanies a change in BMI of . . . 30 0 24 9 5 1 ǡ ˆ‘” ƒ ’‡”•‘ ͳǤ͸ meters tall, corresponds to a weight change of . . . 5 1 1 6 13 056 2 # ‹Ž‘‰”ƒ•Ǥ Check your answer Ǥ Š‘‹…‡ ȋ Ȍ ‹• –Š‡…Ž‘•‡•– –‘ ͳ͵ǤͲͷ͸Ǥ 7. (C) Mathematics/Algebra and Functions/ Evaluating, Interpreting, and Creating Algebraic Functions Preview the question. The item requires you –‘ –”ƒ•Žƒ–‡ –Š‡ ‰‹˜‡ ‹ˆ‘”ƒ–‹‘ ‹–‘ ƒ ‡š’”‡••‹‘ ™‹–Š —‹–• ‘ˆ ™‡‡•Ǥ 3 12 6 12 6 6 6