AccelePrep for the ACT Test 2nd Edition Student Text

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

Strategize and solve. The algebra approach may be faster, depending on your algebra •‹ŽŽ•Ǥ ‘—ǯŽŽ Šƒ˜‡ –‘ †‡…‹†‡ ™Š‹…Š •–”ƒ–‡‰› ™‘”• „‡•– ˆ‘” ›‘—Ǥ Š‡ ƒŽ‰‡„”ƒ •‘Ž—–‹‘ uses ratios and cancellation of units: weeks # 6 week pads ‘—…ƒ ƒŽ•‘ ƒ””‹˜‡ ƒ– –Š‹• ƒ•™‡” „› ”‡ƒ•‘‹‰ –Š”‘—‰Š –Š‡ •–‡’•ǣ ͳȌ ‡ƒ…Š ™‡‡ǡ –Š‡ ϐ‹” ‡‡†• x legal pads for each of p paralegals, or xp pads; 2) each of c packs contains 6 pads, so there are 6 c ’ƒ…•Ǣ ͵Ȍ –Š‡ ͸ c packs will last 6 xp c ™‡‡•Ǥ Š‹Ž‡ –Š‡ –‡•–Ǧ–Š‡Ǧ–‡•– ‡–Š‘† ‹• Ž‹‡Ž› •Ž‘™‡” –Šƒ –Š‡ ƒŽ‰‡„”ƒ •‘Ž—–‹‘ǡ ‹–ǯ• ƒ ˜‹ƒ„Ž‡ ƒ’’”‘ƒ…Š ‹ˆ ›‘—ǯ”‡ •–—…Ǥ ‡’Žƒ…‡ –Š‡ ˜ƒ”‹ƒ„Ž‡• ™‹–Š ‡ƒ•› —„‡”•Ǥ ˆ –Š‡ ϐ‹” ‡‡†• ʹ Ž‡‰ƒŽ ’ƒ†• ’‡” ’ƒ”ƒŽ‡‰ƒŽǡ ƒ† ‹ˆ –Š‡”‡ ƒ”‡ ͵ ’ƒ”ƒŽ‡‰ƒŽ•ǡ –Š‡ ϐ‹” ‡‡†• ͸ ’ƒ†• ‡ƒ…Š ™‡‡Ǥ ˆ –Š‡› Šƒ˜‡ Ͷ ’ƒ…•ǡ –Šƒ–ǯ• ʹͶ ’ƒ†•Ǥ Š‡ ’ƒ†• ™‹ŽŽ Žƒ•– Ͷ ™‡‡•Ǥ Š‡… –Š‡ ƒ•™‡”…Š‘‹…‡• –‘ ϐ‹† –Š‡ ‘‡ –Šƒ– ‡“—ƒŽ• 4 for 2 x , 3 p , and 4 c Ǥ Ž•‘ǡ —•‡ ›‘—” number sense so you don’t perform needless …ƒŽ…—Žƒ–‹‘•Ǥ ȋ Ȍ „‡…‘‡• p xc 6 6 3 2 4 # # , which is Ž‡•• –Šƒ ͳǤ ȋ Ȍ „‡…‘‡• c xp 6 6 4 2 3 # # , which is ƒŽ•‘ Ž‡•• –Šƒ ͳǤ ‡•– ȋ Ȍǣ xp c 6 2 3 6 4 6 24 4 # # , so –Š‡ ƒ•™‡” ‹• ȋ ȌǤ Check your answer Ǥ ‘—„Ž‡Ǧ…Š‡… –Š‡ —‹–• ‹ –Š‡ ƒŽ‰‡„”ƒ ƒ’’”‘ƒ…ŠǤ Š‡ ϐ‹ƒŽ ‡š’”‡••‹‘ 6 xp c has —‹–• ‘ˆ ™‡‡•ǡ •‘ ȋ Ȍ ‹• –Š‡…‘””‡…–…Š‘‹…‡Ǥ 8. (J) Mathematics/Geometry/Rectangles and Squares Preview the question. The problem asks for the ƒ”‡ƒ ‘ˆ ƒ •“—ƒ”‡ǡ ‘ —‹–• ƒ”‡ ‰‹˜‡ǡ ƒ† –Š‡ ϐ‹‰—”‡ ‹• ‘– ‡…‡••ƒ”‹Ž› †”ƒ™ –‘ •…ƒŽ‡Ǥ Š‡ ƒ•™‡”…Š‘‹…‡• ƒ”‡ ™‡ŽŽ †‡ϐ‹‡†Ǥ Strategize and solve. If the area of the smaller rectangle is 12, the missing side length of the •ƒŽŽ‡” ”‡…–ƒ‰Ž‡ —•– „‡ ͵Ǥ †…‘’ƒ”‹‰ –Š‡ c # . x p xp c 6 paralegal pads paralegals pack packs #

–™‘ •‹†‡• ‘ˆ –Š‡ •ƒŽŽ‡” ”‡…–ƒ‰Ž‡ǡ –Š‡ ϐ‹‰—”‡ ƒ’’‡ƒ”• –‘ „‡ †”ƒ™ –‘ •…ƒŽ‡Ǥ ‹’ –Š‡ ‰‡‘‡–”› •‘Ž—–‹‘ ƒ† •‘Ž˜‡ –Š‡ ‹–‡ —•‹‰ ‡•–‹ƒ–‹‘Ȅ ‹–ǯ• –Š‡ ˆƒ•–‡•– •‘Ž—–‹‘ ‰‹˜‡ –Š‡ †‹ˆˆ‡”‡…‡• „‡–™‡‡ –Š‡ ƒ•™‡”…Š‘‹…‡•Ǥ ‘’ƒ”‹‰ –Š‡ ‰‹˜‡ Ž‡‰–Š ‘ˆ Ͷ ™‹–Š QR , QR must be close to 5 —‹–•Ǥ Šƒ– ™‘—Ž† ƒ‡ –Š‡ ƒ”‡ƒ ‘ˆ PQRS ʹͷǤ Ž–‡”ƒ–‹˜‡Ž›ǡ —•‡ –Š‡ ’”‘’‡”–‹‡• ‘ˆ –”‹ƒ‰Ž‡•Ǥ Š‡ side QR of the square is the same as the diagonal ‘ˆ –Š‡ •ƒŽŽ‡” ”‡…–ƒ‰Ž‡Ǥ Š‡ ƒ”‡ƒ ‘ˆ –Š‡ •ƒŽŽ‡” rectangle is 12, the width of the rectangle is ͵ǡ ƒ† ‡ƒ…Š ‘ˆ –Š‡ •ƒŽŽ‡” –”‹ƒ‰Ž‡• ƒ”‡ ͵ǦͶǦͷ –”‹ƒ‰Ž‡•Ǥ Š‡ Ž‡‰–Š ‘ˆ QR , a side of the square, is 5, and the area of the square is 5 25 2 Ǥ Check your answer. ˜‡ ‹ –Š‡ ‡•–‹ƒ–‹‘ approach, a quick glance at the answer choices ‹• ‡‘—‰Š –‘ †‡–‡”‹‡ –Šƒ– –Š‡ ƒ•™‡” —•– „‡ ȋ ȌǤ Preview the question. Š‹• ‹• ƒ †‹ˆϐ‹…—Ž– ‹–‡ due to the tested concept: transformations ƒ† –Š‡‹” ‡ˆˆ‡…–• ‘ ‰”ƒ’Š• ‘ˆ ˆ—…–‹‘•Ǥ ‡ˆ‘”‡ ’‡”ˆ‘”‹‰ ƒ –”ƒ•ˆ‘”ƒ–‹‘ǡ ›‘— —•– ϐ‹”•– determine the equation of the line plotted in the ϐ‹‰—”‡Ǥ Strategize and solve. Calculate the slope of –Š‡ Ž‹‡ ˆ”‘ –Š‡ –™‘ ’‘‹–• ‰‹˜‡ ‹ –Š‡ ϐ‹‰—”‡ǣ ( ) 4 4 2 2 2 1 Ǥ ‹…‡ –Š‡ y- intercept, b , is 0, the original equation of the line is 2 y mx b x Ǥ ‡’Žƒ…‡ x with 1 x in the original equation: the transformed line equation is ( ) y f x x x 1 2 1 2 2 1 Ǥ ‘Ž˜‡ ˆ‘” 4 x and 4 x : ( ) y 4 2 4 2 1 2 3 , and ( ) y 4 2 4 2 1 2 5 Ǥ Check your answer. The graph in (D) is the only one to include points ,4 2 3 d n and ,4 2 5 d n , so ȋ Ȍ ‹• –Š‡…‘””‡…–…Š‘‹…‡Ǥ

9. (D) Mathematics/Algebra and Functions/ Coordinate Geometry/Transformations and Their Effects on Graphs of Functions