AccelePrep for the ACT Test 2nd Edition Student Text

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

‘–Š‡” ™‘”†•ǡ Dzͳͺ ‹• ʹͲΨ ‘ˆ ™Šƒ–ǫdz •‡ –Š‡ Dz‹•Ǧ‘˜‡”Ǧ‘ˆdz ‡“—ƒ–‹‘ǣ & & % of is x 100 18 100 20 x 20 18 100 90 # Ǥ —– †‘ǯ– „‡ †‹•–”ƒ…–‡† „›…Š‘‹…‡ ȋ Ȍǣ ›‘— ƒ”‡ •‘Ž˜‹‰ ˆ‘” Š‘™ ƒ› •–—†‡–• ƒ”‡ ϐ‹ˆ–ŠǦ‰”ƒ†‡”•ǡ •‘ –Š‡…‘””‡…– ƒ•™‡” ‹• 422 90 332 ǡ ™Š‹…Š ‹• ȋ ȌǤ 5. Ž–Š‘—‰Š –Š‡ ϐ‹‰—”‡ ‹• ‡…‡••ƒ”‹Ž› †”ƒ™ –‘ •…ƒŽ‡ǡ ›‘—…ƒ assume that points A , B , C , and D are on AD ‹ –Š‡ ‘”†‡” •Š‘™Ǥ Therefore, regardless of the accuracy of the drawing, it can be deduced mathematically that the length of AB CD —•– „‡ ʹͲǤ ˆ AD is ͵Ͳ —‹–• Ž‘‰ǡ ƒ† BC is 10 units long, the length of the other two segments together, AB CD ǡ —•– „‡ ͵Ͳ Ȃ ͳͲ α ʹͲǡ ƒ•™‡”…Š‘‹…‡ ȋ ȌǤ 6. Ž–Š‘—‰Š ȋ Ȍ ƒ† ȋ Ȍ ƒ’’‡ƒ” –”—‡ „ƒ•‡† ‘ –Š‡ ϐ‹‰—”‡ ƒ• ‹– ‹• †”ƒ™ǡ ‹– ‹• ‡…‡••ƒ”‹Ž› †”ƒ™ –‘ •…ƒŽ‡Ǥ ‘—…‘—Ž† †‹•–‘”– ‹– –‘ Ž‘‘ ƒ• follows: ŽŽ –Š‡ Ž‹‡• ƒ† ’‘‹–• ‹ –Š‹• ”‡Ǧ†”ƒ™ ϐ‹‰—”‡ ƒ”‡ ‹ –Š‡ •ƒ‡ ’‘•‹–‹‘ ”‡Žƒ–‹˜‡ –‘ ‡ƒ…Š ‘–Š‡” ƒ• –Š‡› ƒ”‡ ‹ –Š‡ ‘”‹‰‹ƒŽǤ ‘™‡˜‡”ǡ ‹ –Š‹• ϐ‹‰—”‡ǡ ‹– ƒ’’‡ƒ”• –Šƒ– –Š‡ ȋ Ȍ ƒ† ȋ Ȍ •–ƒ–‡‡–• ƒ”‡ ˆƒŽ•‡Ǥ † –Š‡ ϐ‹‰—”‡…‘—Ž† „‡ †”ƒ™ •—…Š –Šƒ– ȋ Ȍ ‹•…Ž‡ƒ”Ž› ˆƒŽ•‡Ǥ ‘ ƒ––‡” Š‘™ –Š‡ ϐ‹‰—”‡ ‹• †‹•–‘”–‡†ǡ –Š‡…‘„‹ƒ–‹‘ ‘ˆ x and y must equal z , so (J) ‹• ƒŽ™ƒ›• ˆƒŽ•‡Ǥ Š‡”‡ˆ‘”‡ǡ „› –Š‡ ’”‘…‡•• ‘ˆ ‡Ž‹‹ƒ–‹‘ǡ ȋ Ȍ —•– „‡ …‘””‡…–Ǥ †‡‡†ǡ PS is only a part of PR , so the length of PS must be less than the length of PR Ǥ 7. Draw a picture of a circle inscribed in a square with sides of 2 (the area is 4, so & s s 4 2 2 ȌǤ ‘–‡ ™Šƒ– ›‘— ƒ”‡ Ž‘‘‹‰ ˆ‘”ǣ –Š‡ ƒ”‡ƒ ‘ˆ –Š‡…‹”…Ž‡Ǥ ‘‡…– ™Šƒ– ›‘— †‘ǯ– ‘™ ™‹–Š ™Šƒ– ›‘— †‘ǣ –‘ ‰‡– –Š‡ area, you need the radius of the circle ( A r circle 2 S ȌǤ †† ƒŽŽ ‘ˆ –Š‹• –‘ ›‘—” ϐ‹‰—”‡ǣ 2

2

2

r

A Circle =?=π r 2

2

‘™ ‹–ǯ• ‡ƒ•› –‘ •‡‡ –Šƒ– –Š‡ •‹†‡ ‘ˆ –Š‡ •“—ƒ”‡ Šƒ• –Š‡ •ƒ‡ Ž‡‰–Š ƒ•