Victory for the ACT Student Text 15e

M ATH S TRATEGY S UMMARY • 279

STRATEGY SUMMARY

MATH STRATEGIES

When approaching a Mathematics item, there are several things to which you should pay careful attention: Figures are usually, but not always, drawn to scale. When all other options for answering the ‹–‡ ˆƒ‹Žǡ –”› –Š‡ •–”ƒ–‡‰› ‘ˆ ƒ••—‹‰ –Š‡ ϐ‹‰—”‡ is †”ƒ™ –‘ •…ƒŽ‡Ǥ Š‡ǡ —•‡ –Š‡ ϐ‹‰—”‡ –‘ Š‡Ž’ ›‘— answer the item. Most answer choices are arranged in order of ascending or descending value and many incorrect answer choices correspond to conceptual errors. Typically, “signal” words are capitalized (e.g., thought-reversers, such as “NOT,” “CANNOT,” and Dz dzȌǢ Š‘™‡˜‡”ǡ –Š‡› ƒ› •‘‡–‹‡• „‡ —†‡”Ž‹‡† ‘” ‹–ƒŽ‹…‹œ‡† ȋ‡Ǥ‰Ǥǡ •’‡…‹ϐ‹‡† —‹–•ȌǤ Š‹Ž‡ –Š‡ •’‡…‹ϐ‹…ˆ‘”ƒ––‹‰ ‘ˆ –Š‡•‡ ™‘”†• ƒ› ˜ƒ”›ǡ –Š‡›…ƒ „‡…”‹–‹…ƒŽ –‘…‘””‡…–Ž› —†‡”•–ƒ†‹‰ the item. Pay careful attention to thought-reversers, as they reverse the apparent meaning of an item. ‹ˆϐ‹…—Ž– ƒ–Š‡ƒ–‹…• ‹–‡• –‡† –‘ „‡…Ž—•–‡”‡† ‡ƒ” –Š‡ ‡† ‘ˆ –Š‡ •‡…–‹‘Ǥ Š‡ •‘Ž˜‹‰ ‹–‡• –Šƒ– ƒ”‡ Š‹‰Š ‘ –Š‡ Žƒ††‡” ‘ˆ †‹ˆϐ‹…—Ž–›ǡ „‡ ™ƒ”› ‘ˆ •‹’Ž‹•–‹…ƒ•™‡”• ƒ† –Š‡ Dz ƒ‘– „‡ †‡–‡”‹‡†ǥdz ”‡•’‘•‡Ǥ ‡‡„‡” –‘ ’ƒ…‡ ›‘—”•‡ŽˆȄ†‹ˆϐ‹…—Ž–ǡ –‹‡Ǧ…‘•—‹‰ ‹–‡• Šƒ˜‡ –Š‡ same value as the easy items. ‡ƒ† –Š‡ ‹–‡ •–‡ ϐ‹”•–Ǥ Ž› –Š‡ •Š‘—Ž† ›‘— ”‡ƒ† –Š‡ †‡–ƒ‹Ž• ‘ˆ –Š‡ ‹–‡ǡ ‡‡’‹‰ –Š‹• ‹–‡ stem in mind. ‘—„Ž‡Ǧ…Š‡… –Š‡ •‘Ž—–‹‘ „›…‘ϐ‹”‹‰ –Šƒ– ‹– ƒ•™‡”• –Š‡ ’ƒ”–‹…—Žƒ” “—‡•–‹‘ –Šƒ– ‹• „‡‹‰ ƒ•‡†Ǥ Š‡ ƒ’’Ž‹…ƒ„Ž‡ǡ –Š‹•…‘ϐ‹”ƒ–‹‘ ‹…Ž—†‡• ˜‡”‹ˆ›‹‰ –Šƒ– –Š‡ •‘Ž—–‹‘ ‹• ‰‹˜‡ ‹ –Š‡ —‹–• •’‡…‹ϐ‹‡† „› –Š‡ ‹–‡ •–‡Ǥ ˆ ›‘— ƒ”‡ —ƒ„Ž‡ –‘ ‡‹–Š‡” ϐ‹† ƒ ‡Ž‡‰ƒ– ȋ“—‹…Ȍ •‘Ž—–‹‘ ‘” •‘Ž˜‡ –Š‡ ‹–‡ †‹”‡…–Ž› „ƒ•‡† ‘ •—„Œ‡…– ‘™Ž‡†‰‡ǡ –Š‡ ˆ‘ŽŽ‘™‹‰ ƒŽ–‡”ƒ–‹˜‡ •‘Ž—–‹‘• •–”ƒ–‡‰‹‡•…ƒ „‡ ‡š–”‡‡Ž› Š‡Ž’ˆ—Žǣ “Test-the-Test” Strategy Š‡…‘””‡…– ƒ•™‡” –‘ ƒ› ‹–‡ ‹• ƒŽ™ƒ›• ‘‡ ‘ˆ ϐ‹˜‡ ‰‹˜‡…Š‘‹…‡•Ǥ ‘‡–‹‡•ǡ –Š‡ ‡ƒ•‹‡•– ƒ† “—‹…‡•– ™ƒ› –‘ •‘Ž˜‡ ƒ ‹–‡ ‹• –‘ –‡•– ‡ƒ…Š ‘ˆ –Š‡ ƒ•™‡”…Š‘‹…‡•Ǥ Š‡ Dz–‡•–Ǧ–Š‡Ǧ–‡•–dz •–”ƒ–‡‰› …ƒ ‡ƒ ’Ž—‰‰‹‰ ƒ•™‡”…Š‘‹…‡• „ƒ… ‹–‘ –Š‡ ‹–‡ ȋ•–ƒ”–‹‰ ™‹–Š –Š‡ ‹††Ž‡ ƒ•™‡”…Š‘‹…‡Ȍ –‘ –‡•– –Š‡ ˜ƒŽ‹†‹–› ‘ˆ ƒ ‡š’”‡••‹‘ǡ ‘” ‹–…ƒ ‡ƒ…Š‡…‹‰ ‡ƒ…Š ƒ•™‡”…Š‘‹…‡ ƒ‰ƒ‹•– ƒ› stated conditions. The “test-the-test” strategy is typically useful for items with numerical solutions or variables and values that meet stated conditions. “Plug-and-Chug” Strategy This strategy is similar to the “test-the-test” strategy in that the item stem and answer choices (rather than direct mathematical solution strategies) are used to isolate the correct answer. The difference is that rather than testing the validity of each answer choice against the item stem conditions, the item stem and/or answer choices are evaluated by plugging in chosen numbers: “plug-and-chug.” This strategy is especially helpful when solving Algebra items.

Figures

Answer Choices

“Signal” Words

/DGGHU RI 'LIÀFXOW\

Item Stems

Solutions