Victory for the ACT Student Text 15e

212 • M ATH

MATRICES AND VECTORS

What is the matrix product ? a 1 2 1 1 0 < 7 F A F. a a a a 2 2 0 0 = G G. a a a a 3 2 3 2 0 0 = G SSSSSSSS V H. a a 3 0 R T X WWWWWWWW J. a a 3 0 6 @ Ǥ Š‡ ƒ–”‹š ’”‘†—…– ‹• —†‡ϐ‹‡†Ǥ

If , 3 2 1 1 what is the vector form of a b c 2 − + ? a −= 2 0 , and , c , , b

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Throwback to Math Class To add or subtract two vectors , add or subtract the corresponding components. To multiply a vector by a scalar , simply multiply the similar components, that ‹•ǡ –Š‡ ˜‡…–‘”ǯ• magnitude by the •…ƒŽƒ”ǯ• ƒ‰‹–—†‡Ǥ

A. ,5 2 B. ,4 1 C. ,3 4 D. ,4 3 E. ,3 4 Vector u point ( , )2 3 Given that G. i j − + H. i j 2 J. i j K. i j 2

has initial point ( , )3 2 . Vector v ( ) u v w 4 2 − + + = and has initial and terminal point ( , )1 4 . 0 , what is the form of w in unit vector notation? F. i j terminal point ( , )4 2

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The Cambridge Edge Š‡ —Ž–‹’Ž›‹‰ ƒ–”‹…‡•ǡ †‘ǯ– †‘ ‘”‡ ™‘” –Šƒ ‹• ‡…‡••ƒ”› –‘ ƒ•™‡” –Š‡ ‹–‡Ǥ Ž‹‹ƒ–‡ ƒ›…Š‘‹…‡• –Šƒ– †‘ǯ–…‘–ƒ‹ –Š‡ correct number of rows and columns. Then, determine only as many elements in the product matrix necessary to choose between the remaining choices. RATES AND PROPORTIONS

…Ž‘™ ‹• ϐ‹ŽŽ‹‰ Š‡Ž‹— „ƒŽŽ‘‘• ˆ”‘ tanks that contains 80 cubic feet of helium each. At most, how many 11-inch helium „ƒŽŽ‘‘•…ƒ „‡ ϐ‹ŽŽ‡† ˆ”‘ ʹ –ƒ•ǫ (1 balloon = 480 cubic inches) A. 40 B. 288 C. 480 D. 576 E. 3,456

28. Doreen can wash her car in 15 minutes, while her younger brother Dave takes twice as long to do the same job. If they work together, how many minutes will the job take them? F. 5 G. 7 2 1 H. 10 J. 22 2 1 K. 30

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Test Specs You will be expected to know basic conversions like 12 3 1 feet yard , and minutes 60 1 hour . If a problem requires any conversion factors beyond the basics, the conversion factor will be included in the item stem. 1 inches foot ,