AccelePrep for the ACT Test 2nd Edition Student Text

C HAPTER 4 | F AST T RACK TO M ATH M ECHANICS • 81

–Š‡ †‹ƒ‡–‡” ‘ˆ –Š‡…‹”…Ž‡ǡ ™Š‹…Š ‹• –™‹…‡ –Š‡ ”ƒ†‹—•Ǥ Š‡ †‹ƒ‡–‡” ‘ˆ the circle is 2, the radius is 1, and the area of the circle is ( ) 1 2 r r ǡ ȋ ȌǤ 8. —’’‘•‡ ›‘—…ƒǯ– ”‡‡„‡” –Š‡ ”—Ž‡• ˆ‘” ™‘”‹‰ ™‹–Š ‡š’‘‡–• ƒ† •…‹‡–‹ϐ‹…‘–ƒ–‹‘Ǥ •‡ ›‘—”…ƒŽ…—Žƒ–‘”Ǩ – ‹‰Š– ‡˜‡ „‡ “—‹…‡” ‘˜‡”ƒŽŽ –‘ •–ƒ”– ™‹–Š ›‘—”…ƒŽ…—Žƒ–‘” ‹ –Š‡ ϐ‹”•– ’Žƒ…‡Ǥ  –Š‹•…ƒ•‡ǡ ƒˆ–‡” entering < > < > 12 EE 10 3 EE 5 ' (or depending on your calculator; be sure ahead of the exam to know how your particular …ƒŽ…—Žƒ–‘” ™‘”•Ȍǡ –Š‡ †‹•’Žƒ› ™‹ŽŽ ”‡ƒ† ͶͲͲǡͲͲͲ ‹ˆ ‹ ‘”ƒŽ ‘†‡ ‘” Ͷ ͷ ‹ˆ ‹…‹‡–‹ϐ‹…‘†‡ǡ ™Š‹…Š ‹• ‡“—ƒŽ –‘ Ͷ ˆ‘ŽŽ‘™‡† „› ͷ œ‡”‘•ǡ ‘” 4 10 5 # ǡ ƒ•™‡”…Š‘‹…‡ ȋ ȌǤ 9. ‘—…‘—Ž† •‘Ž˜‡ –Š‹• ’”‘„Ž‡ „› ”‡…‘‰‹œ‹‰ –Šƒ– –Š‡ ‰‹˜‡ ‡š’”‡••‹‘ is the difference of two squares: a b a b a b 2 2 ^ ^h h Ǥ Š‡”‡ˆ‘”‡ǡ 2 2 x x x x c cm m x x 2 3 4 3 3 5 2 2 c m ǡ ȋ ȌǤ ” —•‡ –Š‡ ‡–Š‘† –‘ ‰‡– –‘ –Š‡ Žƒ•– •–‡’Ǥ If you don’t see the algebra solution, use your calculator: . x x 3 3 1 73 2 & ! ! . and . 3 2 1 15 ! ! . , so 1.15 . 1.15 . ( ) ( ) 2 3 2 3 1 73 1 73

STRATEGY ALERT Use your calculator if ›‘—…ƒǯ– ϐ‹† ƒ †‹”‡…– solution or if it offers a time ƒ†˜ƒ–ƒ‰‡ǡ „—– †‘ǯ– ƒ••—‡ ƒ—–‘ƒ–‹…ƒŽŽ› –Šƒ– ‡˜‡”› ’”‘„Ž‡ ”‡“—‹”‡• ‹–Ǥ

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STEP 2—STRATEGIZE AND SOLVE

Š‡ •‡…‘† •–‡’ ‘ˆ –Š‡ ƒ‡ Žƒ ‹• –‘ ’‹… ƒ •–”ƒ–‡‰› ƒ† •‘Ž˜‡ –Š‡ ’”‘„Ž‡Ǥ Š‡ •–”ƒ–‡‰› ›‘—…Š‘‘•‡ †‡’‡†• ‘ –™‘ ˆƒ…–‘”•ǣ Š‘™ „‡•– –‘ •‘Ž˜‡ –Š‡ ‹–‡ correctly and quickly Ǥ Š‡ •–”ƒ–‡‰‹‡• ‹ –Š‹• •‡…–‹‘ ƒ”‡ †‡•‹‰‡† ™‹–Š –Š‹• ‹ ‹†Ǥ Š‡ ƒ–Š‡ƒ–‹…ƒŽ •‘Ž—–‹‘ ‹•ǯ– ƒŽ™ƒ›• –Š‡ ˆƒ•–‡•–ǡ ‘” •‘‡–‹‡• ‹– „‘‰• ›‘— †‘™ ‹ ˜ƒ”‹ƒ„Ž‡•ǡ ƒ‹‰ ƒ ’”‘„Ž‡ ‡˜‡ Šƒ”†‡”Ǥ ‡ǯ˜‡ ƒŽ”‡ƒ†›…‘˜‡”‡† •‡˜‡”ƒŽ –‡…Š‹“—‡• ‹ –‡’ ͳ –Šƒ– ƒŽ™ƒ›• ƒ’’Ž›ǡ •—…Š ƒ• ”‡ƒ†‹‰…ƒ”‡ˆ—ŽŽ›ǡ ‘”‰ƒ‹œ‹‰ –Š‡ ‰‹˜‡ ‹ˆ‘”ƒ–‹‘ǡ –”—•–‹‰ ϐ‹‰—”‡•ǡ †”ƒ™‹‰ ϐ‹‰—”‡• ™Š‡ ‡‡†‡†ǡ ƒ† —•‹‰ ›‘—”…ƒŽ…—Žƒ–‘”Ǥ ‘™ǡ ™‡ǯŽŽ…‘˜‡” –Š”‡‡ ƒ††‹–‹‘ƒŽ •–”ƒ–‡‰‹‡• –Šƒ– ƒ”‡ ‡•’‡…‹ƒŽŽ› —•‡ˆ—Ž ‹ˆ ›‘—…ƒǯ– ϐ‹† –Š‡ ƒ–Š‡ƒ–‹…ƒŽ •‘Ž—–‹‘ –‘ ƒ ‹–‡Ǥ ˜‡ ‹ˆ ›‘— ‘™ Š‘™ –‘ •‘Ž˜‡ ƒ ’”‘„Ž‡ǡ –Š‡•‡ •–”ƒ–‡‰‹‡•…ƒ ‘ˆ–‡ „‡ —•‡† –‘ •‘Ž˜‡ ƒ ‹–‡ ‡˜‡ ˆƒ•–‡”Ǥ Answer choices are chosen and distributed according to certain test •’‡…‹ϐ‹…ƒ–‹‘•Ǥ •‡ –Š‹• ˆ‡ƒ–—”‡ –‘ ‰‡– Ž‡˜‡”ƒ‰‡ ‘ –Š‡ –‡•–Ǥ ‹”•–ǡ ‡Ž‹‹ƒ–‡ …Š‘‹…‡• –Šƒ–…ƒǯ– ’‘••‹„Ž› „‡ ƒ ƒ•™‡” –‘ –Š‡ “—‡•–‹‘ „‡‹‰ ƒ•‡†Ǥ † USE THE ANSWER CHOICES STRATEGY ALERT ƒ‡ •—”‡ ›‘— Šƒ˜‡ –Š‡ …‘””‡…– ‹†•‡– ™Š‡ •‘Ž˜‹‰ ƒ–Š ’”‘„Ž‡•Ǥ Š‡ Math Test is not a traditional, in-class math test that requires you to show your ™‘”Ǥ  –Š‡ –‡•– ›‘— are rewarded for a correct answer regardless of how you …Š‘•‡ ‹–Ǥ