Victory for the ACT Exam 16e TG Sample

526 • M ATH

“Meastimating” is a combination of “guesstimating” and measuring. The idea is to approximate ml a seta rs eusroe rmt es nt rtast be ga ys e—d noont tpheer fi encf ot r( mb eactai ou ns et ha a� ti gi su rper omvai dy endo itnbteh de r�ai gwunr ea. cRc eu mr aet eml yb)e br ut ht abte tt ht ei sr itsh aa n doing nothing at all.

“Meastimating” Items #35–36

STUDENT TEXT, p.192 35. In the �igure below, what is the area of square ABCD ?

EXPLANATIONS

35. (C) Mathematics/Geometry/Complex Figures and Rectangles and Squares CC: HSG-SRT.B.5 CCRS: ADV.G.3 Difficulty Level = 1; Teaching Time = 3–6 minutes; Purpose = Application Mark off the length of AE on a piece of paper—this length is . 2 1 4 . . Compare this length of AE to one side of the sloqnugaraes—the side is about 1.5 times as AE , or 2 units. Thus, the area of the square is approximately 2 4 2 = , so (aCn)s wa pepr ecahrosi cc eo sr roenc tb. oDtohusbi dl ee- sc hoef c(kC )t .h(eB ) is approximately 2(1.4) 2.8 = ; (D) is approximately 4(1.4) 5.6 = . Therefore, (AClt)eirsncaotrivreelcyt,. double-check (C) using tThhee phryoppoetret ni euss oe f i sa e4q5u° -a4l 5t o° - t9h0e° l terni ag nt hg l oe f. the given side multiplied by 2 0 , so the hypotenuse is 2 2 20 = ^ h , and the area of the square is 2 4 2 = . 36. (H) Mathematics/Geometry/Triangles/ 30° − 60° − 90° Triangles CC: HSG-SRT.B.5 CCRS: ADV.G.3 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Application On paper, mark the length of AB (e2q uuanli tpsa)r, tasn(d0 d. 5i ,v1i d, e1 . t5h, ias ni nd t2o) f. oUusre t h i s mofakeshift ruler to measure the length AC : between 1.5 and 2 units long, or about 1.7, (H). The length of AC can also be determined from the 30° − 60° − 90° triangle ratio of : : 2 1 2 3 1 . Since AB 20 = , AC 2 2 3 . = e o 1.7 . Ag ul teesrsn”astti rvaetl ey,gaypbpal ys etdh eo n“ etl hi me iinnaf ot er -ma na tdi -o n provided in the �igure. Since AC is shorter than AB but not less than or equal to half the length of AB , (F) and (G) can be eolfimguiensastiendg. Ncoorwre, cytolyu. have a 50/50 chance

The Cambridge Edge “aMc oe amsbt iimn aattiionng ”oifs “mg euaessus triimn ga. tTi nhge” iadneda i m s e to as a u p r p e r m o e x n im ts ate bi nafsoerdmoant i ot hnet h a t is provided in the �igure.

A B. . 2 2 2 0 C. 4 D. 4 2

36. In the triangle below, the measure of

BAC + is 30° and the length of AB is 2. Wthehilcehngotfhthoef following best approximates AC ?

F G . . 1 0 . . 0 8 H. 1.7 J. 1.9