AccelePrep for the ACT Test 2nd Edition Student Text

C HAPTER 4 | F AST T RACK TO M ATH M ECHANICS • 83

Š‡ ƒ•™‡”…Š‘‹…‡•…ƒ ƒŽ•‘ Š‡Ž’ ‹ˆ ›‘— ƒ”‡ •–—… ‘ ƒ •‘Ž—–‹‘Ǥ ‡ ‘ˆ –Š‡…Š‘‹…‡• ‹• –Š‡…‘””‡…– ƒ•™‡”Ǥ •–‹ƒ–‹‘ ƒ† ‰—‡••‹‰ „ƒ•‡† ‘ –Š‡ ‹ˆ‘”ƒ–‹‘ ’”‘˜‹†‡† ‹ ϐ‹‰—”‡•…ƒ „‡ ƒ ‰”‡ƒ– ƒŽ–‡”ƒ–‹˜‡ •–”ƒ–‡‰›ǡ ‡•’‡…‹ƒŽŽ› ™Š‡ ‘‡ ‘ˆ –Š‡…Š‘‹…‡• „ƒ…• —’ ›‘—” ‹–—‹–‹‘Ǥ Š‡ ’‘••‹„Ž‡ǡ —•‡ –Š‡ ƒ•™‡”…Š‘‹…‡• –‘ ›‘—” ƒ†˜ƒ–ƒ‰‡ǡ ƒ• –Š‡ ‡š– ‡šƒ’Ž‡ ‹ŽŽ—•–”ƒ–‡•Ǥ 3 Ǥ  –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ PQRS is a rectangle, T is the midpoint of PQ, and TS # and TR $ are arcs of circles with centers P and Q ǡ ”‡•’‡…–‹˜‡Ž›Ǥ ˆ 1 PT TQ , what is the area of the shaded area? P T Q

Example:

STRATEGY ALERT ‡…”‡ƒ–‹˜‡ ™‹–Š Š‘™ ›‘— —•‡ –Š‡ ϐ‹‰—”‡• –‘ ‡•–‹ƒ–‡Ǥ ‘” example, if you’re estimating how long one line segment is compared to another, instead ‘ˆ Dz‡›‡„ƒŽŽ‹‰dz ‹–ǡ —•‡ –Š‡ edge of your test booklet or scratch paper to mark the length of one line and directly compare that to the other for ƒ ‘”‡ ƒ……—”ƒ–‡ ‡•–‹ƒ–‹‘Ǥ

Ǥ 2 Ǥ 4 r Ǥ 2 2 r Ǥ 1 4 r Ǥ 4 r S 4 S

R

Answer choices function as a feedback loop on the accuracy of your …ƒŽ…—Žƒ–‹‘•Ǥ ‘ǯ– ™ƒ•–‡ –‹‡ †‘—„Ž‡Ǧ…Š‡…‹‰ ›‘—”…ƒŽ…—Žƒ–‹‘• Ǥ ˆ ›‘— ϐ‹‹•Š ›‘—”…ƒŽ…—Žƒ–‹‘• ƒ† ƒ ƒ•™‡”…Š‘‹…‡ ƒ–…Š‡• ›‘—” ”‡•—Ž–•ǡ †‘ …Š‡… ›‘—” ƒ”‹–Š‡–‹…Ǥ Š‡ ’‘••‹„‹Ž‹–› –Šƒ– ›‘— †‹† –Š‡ ƒ”‹–Š‡–‹…ǡ made a mistake, and still got a number that matches an answer choice is –‘‘ ”‡‘–‡ –‘…‘•‹†‡”Ǥ  –Š‡ ‘–Š‡” Šƒ†ǡ ‹ˆ ›‘— †‘ǯ– ϐ‹† ƒ…Š‘‹…‡ –Šƒ– matches your calculation, then you’d better check both your set-up and ›‘—” ƒ”‹–Š‡–‹…–‘ ϐ‹† –Š‡ ‡””‘”Ǥ Ž‰‡„”ƒ ‹• —•—ƒŽŽ› Šƒ”†‡” –Šƒ ƒ”‹–Š‡–‹…„‡…ƒ—•‡ ‹– †‡ƒŽ• ™‹–Š ˜ƒ”‹ƒ„Ž‡• ™Š‹Ž‡ ƒ”‹–Š‡–‹…†‡ƒŽ• ™‹–Š —„‡”•Ǥ ‘—…ƒ –—” ƒ ’”‘„Ž‡ ™‹–Š ˜ƒ”‹ƒ„Ž‡• ‹–‘ ƒ ƒ”‹–Š‡–‹…’”‘„Ž‡ ƒ† ƒ‡ ‹– ‡ƒ•‹‡”Ǥ 4. Šƒ– ‹• –Š‡ –‘–ƒŽ ˜ƒŽ—‡ǡ ‹…‡–•ǡ ‘ˆ x dimes and x + 6 nickels? Ǥ ʹ x + 6 Ǥ ͷ x + 10 Ǥ ͳͳ x + 15 Ǥ ͳͷ x + 6 Ǥ ͳͷ x Ϊ ͵Ͳ Examples:

PLUG-AND-CHUG

STRATEGY ALERT Always read a problem carefully before plugging ‹ ˜ƒŽ—‡•Ǥ ‘” ‡šƒ’Ž‡ǡ ‹ˆ ƒ ’”‘„Ž‡ ‹˜‘Ž˜‡• ƒ ‡“—ƒ–‹‘ that only holds true when x ‹• ’‘•‹–‹˜‡ǡ –Š‡…Š‘‘•‡ ƒ ’‘•‹–‹˜‡ ˜ƒŽ—‡ ˆ‘” x Ǥ