Victory for the ACT Exam 16e TG Sample

516 • M ATH

STUDENT TEXT, p. 188 19. The �igure below shows two circles of datiapmoientter 2 that are tangent to each other P . The line segments form a rt he ce t pa no ignl et sasnhdo awrne . tWa nhgaetni ts ttoh et haer ec ai r colfetshaet shaded portion of the �igure? A. 4 2 − r B. 4 0 − r C. 8 2 - r D. 8 0 − r

EXPLANATIONS

19. (C) Mathematics/Geometry/Properties of Tangent Lines and Rectangles and Squares and Circles CC: HSG-MG.A.1 CCRS: EXP.G.2

Difficulty Level = 4; Teaching Time = 7–10 minutes; Purpose = Application Dtarnagwenacrya:dius to one of the points of Td ihaemwe it de rt ho of fo tnhee cri er cc ltea, n2g, l ae ni sd et qh ue al el nt og tt hh e odfiatmheetreercst,angle is equal to two circle 2(2) 4 = . Thus, the area of the shaded region of the rectangle is: area 2(area ) area circle shaded region rectangle 2(4) 2 r 2 r ^ h 8 2 (1) 8 2 r r 2 .

COMPLEX FIGURES

Mc oamnpy loe fx t�hi geu�ri ge us .rWe shi ennMwaot hr ke mi n ag twi c ist hi t ecmo ms pa rl eexc�oi gmupr oe ss ,e�di nodf amloi nr ee tohraannognl ee t�hi gaut rsee.rTv ehse st we aor e functions. STUDENT TEXT, p. 188 EXPLANATIONS 20. Ii nf saccriirbcel ed wi ni tahsaq ur aadr ei u, swohfa1t ifso ot ht ei sa r e a , i n square feet, of the square? F. 2 2 0 G H . . 1 20 J. 4 20 . (J) Mathematics/Geometry/Complex Figures and Circles and Rectangles and Squares CC: HSG-MG.A.1 CCRS: ADV.G.1 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Example The item is simpli�ied by drawing a �igure since none is provided:

From the �igure, it is clear that the do fi atmh ee tseqruoa fr et h. Se i cnicrec ltehies reaqdui ua ls toof tthhee s i d e cl ei rncgl tehi so f1 a, tshi ed ed ioafmt heet esrqius a2r.eTihs u2s, , atnhde s 2 4 area = = = 2 2 square .