Answer Keys for Calvert Math

Transcription

1 Answer Keys for Calvert Math Lessons CMAKF- Contents Math Textbook... Math Workbook... Math Manual...

2

3 Answer Keys Math Textbook Lessons Math Textbook Answer Key Lessons. Area and Circumference of Circles Exploration Exercise See student s work. base =. cm; height =. cm A = π r d = m r = / ft r =. cm C =. m, A =. m C =. in., A =. in. C =. mm, A =, mm C =. cm, A =. cm C = in., A =. in. C =. ft, A =. ft C =. ft, A = ft C =. mm, A =. mm C = cm, A =. cm. cm. in.. ft,. square miles square -inch cake Answers will vary. Sample answer: Given the circumference, you can divide it by and then multiply by both π and the radius to find the area.. Irregular Figures. in.. cm yd m. mm. m Find the area of the two large triangles that make up the figure. Area of irregular figure = Area of st + Area of nd = /()(.) + /()(.) = (.) + (.) =. +. =. m ft This problem cannot be solved as written. A =. ft, $. ft + = l = ft, w = ft miles miles miles Answers will vary. Sample answers: and. Mixed Review / / /. The Pythagorean Theorem cm ft. yd m yd cm c = c = b = a = b = a = square A = in., P = in. Answers will vary. Sample answer: No, because if a = m, b = m, and c = m, c a + b ; in order for a triangle to be a right triangle, c = a + b. xy =. ft, C =. ft, A =. ft. Problem-Solving Application: Using the Pythagorean Theorem b = ft b = in. a = m a =. m c = yd c = cm Solve. ft in.. ft side A = ft, side B =. ft, area = ft, perimeter =. ft. miles mi mi. ft rd Base nd Base. Squares and Square Roots /. / / /. /., -. m Home m ft ft st Base m CMAKF

4 Math Textbook Answer Key Lessons ft ft ; ; ; ; /; /; /; / golden ratio Test Prep d d ft Answers will vary. Sample answer: The four ratios from problem all equal., which is the golden ratio. Answers will vary. Chapter Review Language and Concepts e d b c a f Skills and. m. cm. cm. km A = m, P = m A =, in., P = in. A = mm, P = mm A =. in., P = in. A =. yd, P =. yd A =. cm, P =. cm m in. A =. cm, C =. cm A =. in., C =. in. A =. m, C =. m. /.. /. m ft. mm. km cm. ft. ft Chapter Test A = / mm, P = m A =. yd, P = yd A = cannot be determined, P = m A = in., P = in. A =. cm, P =. cm A = / ft, P = / ft A =. m, C =. m A =. cm, C =. cm A =. yd, C =. yd /. in. cm ft. m blocks. in. Answers will vary. Sample answer: Both measurements are equally precise because. cm = mm. Change of Pace The Golden Ratio a / =., less than the golden ratio b / =., greater than the golden ratio c / =., less than the golden ratio d / =., greater than the golden ratio e / =., equal to the golden ratio golden ratio Answers will vary. Sample answer: One of the ratios is equal to the golden ratio (/). Two of the ratios are less than the golden ratio (/, /), and two are greater than the golden ratio (/, /). Cumulative Test c c c c b c c b The correct answer (. in.) is not listed. b Chapter. Three-Dimensional Figures cone rectangular prism sphere cylinder sphere cylinder rectangular prism triangular prism faces, edges, vertices, rectangular pyramid faces, edges, vertices, triangular prism faces, edges, vertices, pentagonal prism hexagonal prism octagonal prism Answers will vary. Sample answer: False, because to be a prism, the solid must have two parallel congruent bases. Mind Builder: More About Solids Polyhedron Triangular prism rectangular prism Pentagonal prism Hexagonal prism octagonal prism Number of Faces (F ) Number of Vertices (V ) Number of Edges (E ), The sum of F and V is more than E., the sum of F and V is more than E. Answers will vary. Sample answer: F + V = E CMAKF

5 Math Textbook Answer Key Lessons. Surface Area of Prisms m in. in. cm mm m. yd / ft tubes x ft Constructed Response Taylor does not have enough paper to wrap the gift because the surface area of the box is in., and she only has in. of wrapping paper. Test Prep c a. Surface Area of Cylinders and Cones Exploration Exercise See student s work. The top and bottom are circles. The side is a rectangle. They are equal. Answers will vary.,. cm. cm. in.. mm. m. cm. m. ft cm Surface Area of a Cylinder S = πrh + πr². = (.)()h + (.)(²). =.h + Subtract from both sides.. =.h.. =.. h Divide both sides by.. Mixed Review m. in.. mm mm The Creative Cube Company faces = cubes, faces = cubes, face = cubes, no face = cubes Extension faces = cubes, faces = (n ) cubes, face = (n ) cubes, no face = (n ) (n ) cubes Cumulative Review,, / / / / / / / / n = t =. r =.. a =. b =. d = f =. b =. m b =. cm. % $. $ Change the given measurements from feet to yards by dividing by. ( yd = ft Change from a smaller unit to a larger unit by dividing.) feet/ = yd feet/ = yd Area = = yd Cost of carpet =.() = $. Volume of Prisms and Cylinders m m. ft. m. m, in. cm cm m in. in.,, cubes, cm Answers will vary. V = cm, S = cm = h Height of the cylinder = cm cm cm cm Constructed Response Answers will vary. Sample answer: The cylinders do not have the same surface area. Kelly s cylinder has a greater surface area. The surface area of Kelly s cylinder is. in. and the surface area of Pat s cylinder is. in. Kelly s cylinder has a greater surface area because the radius of her cylinder is larger than the radius of Pat s cylinder. cm cm To find the volume and surface area of the figure, divide the figure into two separate rectangular prisms. Add the two volumes to find the volume of the figure. Add the surface areas to find the surface area of the figure. CMAKF

6 Math Textbook Answer Key Lessons Larger rectangular prism Length = cm cm = cm Width = cm Height = cm Smaller rectangular prism Length = cm Width = cm Height = cm Volume of a rectangular prism = B h = (l w) h Volume of figure = volume of larger prism + volume of smaller prism V = ( )() + ( )() = + = cm Divide the irregular surfaces into two separate rectangles and remember to sum only the surfaces of the figure. This figure has surfaces: Front face = () + () = Back face = () + () = Large top face = () = Small top face = () = Large bottom face = () = Side faces = () = ( ) = () = () = Surface area of figure = = cm Another method for determining the surface area of the figure is by dividing the figure into two rectangular prisms, adding the surface areas of those two prisms and being careful not to include the areas that are no longer part of the surface of the figure. Surface area of a rectangular prism = sum of area of each face: S = (l w) + (l h) + (w h) Remember, however, that a piece of one of the side faces of the larger prism is no longer part of the surface of the figure. Front and back surface area = ()() + ()() = ( ) = cm Top and bottom surface area = ()() + ()() = ( ) = cm Left side surface area = ()() = cm Right side surface area = ()( ) = () = cm Surface area from larger prism part of figure = = cm Remember that one side of the smaller prism is no longer on the surface of the figure, so only add the area of one of the side faces of the prism. Surface area from smaller prism part of figure = ( ) + ( ) + ()() = + + = cm Surface area of the figure = cm + cm = cm. Volume of Pyramids and Cones ft cm ft ft m m cm in. cm in. ft in. in. cm Since a triangular prism is one-half of a rectangular prism, the volume of a triangular prism can be found by using the following formula: V = /B h = /(l w) h Length = cm Width = cm Height = cm V = /()()() = cm Mid-Chapter Review cm m S = in., V = in. S = m, V = m. Problem-Solving Application: Using Volume, cm. m Solve,. ft, in.. ft, lb,, yd / cups Answers will vary. Sample answer: The Great Pyramid was built in approximately B.C. Chapter Review Language and Concepts false, prism true true false, cylinders false, approximately false, rectangular prism true false, volume Skills and cylinder cone triangular prism m in. mm cm m in. in. in. in. cm in. m mm, ft in. Can B is the better buy with a volume of. in., which is greater than Can A s volume of. in.. in. m ft CMAKF

7 Math Textbook Answer Key Lessons Chapter Test rectangular prism cylinder rectangular pyramid m ft in. cm m m ft, in. in.. in. Volume of a cone = / B h = /(π r ) h r = /( in.) = in. h = in. V = /π() () = /(.)()() =. in. ratio of the surface areas = /, :, or to ; ratio of the volumes = /, :, or to Answers will vary. Sample answer: The formulas for the volume of a cone and pyramid are similar because the volume is equal to onethird of the base multiplied by the height. (V = / B h). Change of Pace Density. g/cm. g/cm g g ml. g/cm CMAKF

8 Math Workbook Answer Key Answer Keys Math Workbook Lessons Lessons Practice Area and Circumference of Circles A =. cm, C =. cm A =. m, C =. m A =. yd, C =. yd A =. in., C =. in. A = / in., C = / in. A =. mm, C =. mm A =. ft, C =. ft A =. m, C =. m A=. in. A =. in. Solution: (.) =. in. A =. cm Solution: (.) =. cm The area of a circle with radius cm is greater. This circle has an area of. cm. A circle of radius cm has an area of. cm. a. in. b. in. c. in. a. m b The area is. m, which is times the area of a circle with a radius of m. Practice Irregular Figures in. yd in. cm. m ft. in.. ft Solution: For the For the = = ft². ² =. =. ft² ft². ft² Area =. ft² = πr ² Mixed Practice x + -y + a + ab f + g -p -d + de + e Practice Squares and Square Roots units units units / / a ft b ft a. cm b cm Practice The Pythagorean Theorem. cm. ft cm. in. mm. ft..... g + h = i m + n = o s + t = u Mixed Practice - / /. Enrichment Pythagorean Triples yes yes no no yes yes yes no yes no yes no Practice Problem-Solving Application: Using the Pythagorean Theorem..... ft. ft. mi. =. m shorter Review Chapter Review nearest m nearest cm nearest km nearest. m nearest, cm nearest m.,. cm.,. km.,. mm km m mm, mm A =. cm, P = cm A = m, P = m A =. in., P =. in. A = m, P = m A = mm, P = mm A = / ft, P = / ft A =. m, C =. m A =. cm, C =. cm A =. cm, C =. cm /,.. in.. cm. ft ft in. km, mg Kelly, km kg Test Chapter Test Prep a a c c a; Answer should read yd, not yd. d b b in. m CMAKF

9 Math Workbook Answer Key Lessons Chapter Practice Three-Dimensional Figures sphere triangular prism rectangular prism rectangular prism sphere cone faces =, edges =, vertices = faces =, edges =, vertices = faces =, edges =, vertices = Sample answer: They are both made up of polygons and have line segments. A prism has bases that are parallel, and a pyramid has one base. Sample answer: The sphere contains no faces, edges, or vertices. A cube is a sixsided figure whose faces are all the same size. Practice Surface Area of Prisms rectangular prism, S = cm cube, S =, mm, mm. ft, cm, ft, in.. mm a in. b in. c The new surface area is four times as large as the old surface area. Practice Surface Area of Cylinders and Cones. m,. cm. in.. ft. mm. m, cm. ft. in. / ft or. ft. m Mixed Practice / or. x = total enrollment; /x = ; x = students x = original price; x = ; x = $ Practice Volume of Prisms and Cylinders in., ft, cm,. mm in., ft, cm, in. cm ft, cm in. a. in. b. in. Its volume is doubled. The cylindrical pool would have the greater volume. It has a volume of,. ft, while the rectangular pool has a volume of, ft. Mixed Practice p = - x = b = c = w = d = - Practice Volume of Pyramids and Cones ft in. ft ft, cm, m. mm, ft. in.. cm. m. ft Mixed Practice ways miles ounces $. Review Chapter Review cm mm, m in. cm m, ft yd in. mm, ft in. B, D, C, A Solution: Order the solids from greatest to least surface area. A. B. mm mm mm C. D. mm mm mm mm mm mm mm for A, C: S = (lw + lh + wh) A = ( ) = mm C = ( ) = mm for B, D: S = πr(r + h) B = π( + ) =. mm D = π( + ) =. mm Thus, the order is B, D, C, A. B, D, C, A ft ft in. ft Test Chapter Prep b c d c a a c b m in. Practice Problem-Solving Application: Using Volume, yd,, ft, cm ft, in. ft cm, lb CMAKF

10 Math Manual Answer Key Answer Keys Math Manual Lessons Lessons / LESSON LESSON cm LESSON cm LESSON Practice.sq. ft.. sq. ft. LESSON cm LESSON mm LESSON about cm CMAKF