Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up to 180. Work out the ngles in lphetil order. Angles on stright line dd up to 180. Rememer Vertilly opposite ngles re equl. Alternte ngles re equl. Corresponding ngles re equl. d The ngles of tringle dd up to 180. e Isoseles tringles hve two equl sides nd two equl ngles. The four ngles of qudrilterl dd up to 360. Originl mteril Cmridge University Press 2009 1
Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet 2 A squre hs four right ngles, four equl sides nd two pirs of prllel sides. Nme the qudrilterl tht hs the following properties. You n use nme more thn one. Four right ngles nd two pirs of equl sides Four equl sides, ut no right ngles Opposite sides prllel, ut no right ngles d Just one pir of prllel sides e Just one line of symmetry f Rottionl symmetry of order 2 3 Drw line AB, 7.5 m long. Use pir of ompsses to onstrut the perpendiulr isetor of AB. Choose from: trpezium rhomus retngle kite prllelogrm rrowhed Leve ll your onstrution lines nd rs in the digrm. 4 Drw n ngle similr to this. Use pir of ompsses to onstrut the isetor of your ngle. 5 The digrm elow shows the right ngled tringle ABC. Construt the perpendiulr isetor of the side BC. Construt the perpendiulr isetor of the side AB. Turn the pge round so AB is horizontl. Put your ompss point where the two isetors meet. Put the penil point on B. Drw irle. Does it go through A nd C? If it does, well done! Your onstrutions must e very urte. Originl mteril Cmridge University Press 2009 2
Cmridge Essentils Mthemtis Core 8 GM2 Consolidtion Worksheet 1 GM2 Consolidtion Worksheet 1 1 Are tells you the mount of spe inside flt shpe. It is mesured in squre units. Are of retngle = length width Clulte the re of eh retngle. m 2, m 2 nd mm 2 re ll exmples of squre units. 5 m 1 m 2 m 30 m 7 m 15 mm Rememer to hek tht the length nd width re in the sme units. If not, onvert one of the lengths. 2 Are of tringle = (se height) 2 Clulte the re of eh tringle. 11 m 9 m 12 mm 20 mm 14 m 7 mm 3 Volume mesures the totl spe inside three-dimensionl (3-D) shpe. Volume is lwys mesured in ui units. A ui entimetre is ue tht is 1 m long, 1 m wide nd 1 m high. This ue hs volume of 1 m 3. Volume of uoid = length width height Clulte the volume of eh uoid. 1 m 1 m 1 m 2 m 3 m 5 m 2 m 6 m 10 m 4 mm 10 mm 4 mm Originl mteril Cmridge University Press 2009 1
Cmridge Essentils Mthemtis Core 8 GM2 Consolidtion Worksheet 1 4 An 8 m ue is not the sme s shpe tht hs volume of 8 m 3. 8 m An 8 m ue is ue with length, width nd height eh 8 m. Its volume is 8 m 8 m 8 m = 512 m 3. 8 m 8 m Look t this uoid. Its volume is 4 m 2 m 1 m = 8 m 3. 4 m 1 m 2 m Wht is the side length of ue with volume 8 m 3? Drw different uoid with volume 8 m 3. Mrk the length of eh edge. 5 Surfe re is the totl re of ll the fes of the shpe. A uoid hs six fes. Top nd ottom hve the sme re. Front nd k hve the sme re. The two sides hve the sme re. Find the surfe re of these uoids. A 2 m B 9 m Rememer to inlude the fes you nnot see. It helps to write the length of eh edge on the digrm. 4 m 6 m 3 m 2 m A net of 3-D shpe is 2-D shpe tht n e folded to mke the 3-D shpe. The surfe re is lso the re of the net. P Q Front This is net for uoid A. Top i Wht is the length QR? ii Wht is the length TU? V W Bk R S iii Work out the totl re of the net. Side Bottom Side iv Does your nswer mth prt? U T i Drw net of uoid B. Lel the fes nd show the edge lengths. ii Find the surfe re. Chek tht it mthes your nswer to prt. Originl mteril Cmridge University Press 2009 2
Cmridge Essentils Mthemtis Core 8 GM2 Consolidtion Worksheet 2 GM2 Consolidtion Worksheet 2 1 2-D drwings n e used to represent 3-D shpes. The 3-D shpes re drwn from different views. The pln is the view of the 3D shpe from ove. An elevtion is view from the side, front or k. Look t these solid shpes. For eh shpe, drw i the pln ii the front elevtion 2 When onverting from one unit to nother, kilo- lwys mens 1000 so 1 km = 1000 m nd 1 kg = 1000 g enti- lwys mens milli- lwys mens 1 100 1 1000 so 1 m = so 1 mm = 1 100 1 1000 m or 100 m = 1 m m or 1000 mm = 1m Chnge 6 mm to entimetres. Millimetres re smller thn entimetres, so divide y 10: 6 10 = 0.6 m. Chnge 9 m to entimetres. Metres re igger thn entimetres, so multiply y 100: 9 100 = 900 m. When hnging from smller unit to igger unit, divide. When hnging from igger unit to smller unit, multiply. Chnge eh quntity to the unit given in rkets. Show wht you did to get the nswer. 14 km (m) 36 mm (m) 425 m (m) d 3265 g (kg) e 1200 mg (g) f 42 kg (g) g 8260 ml (litres) h 466 kg (tonnes) Originl mteril Cmridge University Press 2009 1
Cmridge Essentils Mthemtis Core 8 GM3 Consolidtion Worksheet GM3 Consolidtion Worksheet 1 Congruent shpes re extly the sme shpe nd size. These tringles re ongruent. These re not ongruent. Whih two of these shpes re ongruent? 2 To reflet shpe in mirror line find the imge of eh vertex (orner) of the shpe in the mirror line. The imge of eh vertex will e the sme distne from the mirror line s the originl. The shpe nd its imge will e ongruent. Sometimes the shpe eing refleted is known s the ojet. Reflet the shpe in the mirror line x = 2. (The line x = 2 joins ll points with n x oordinte of 2.) Chek your imge using mirror pled on the line x = 2. Originl mteril Cmridge University Press 2009 1
Cmridge Essentils Mthemtis Core 8 GM3 Consolidtion Worksheet 3 When you rotte shpe it helps to use tring pper. Tre the shpe nd the entre of rottion. Pin the tring pper to the entre of rottion using penil point. Turn the tring pper round through the required ngle. Mrk the position of the orners of the imge on the squre grid. Join the orners with ruler nd penil to show the new shpe. Use tring pper to rotte the tringle in this digrm through 90 lokwise. Use the point (1, 2), mrked, s the entre of rottion. 4 When you trnslte shpe find the imge of eh vertex of the shpe. Use the vetor to ount long, then up or down to find the imge. The vetor is written long up/down. A minus sign efore the top numer mens you move left. A minus sign efore the ottom numer mens you move down. Trnslte the L-shpe in this digrm 8 using the vetor. 6 Along 8 to the left, then up 6. Originl mteril Cmridge University Press 2009 2
Cmridge Essentils Mthemtis Core 8 GM3 Consolidtion Worksheet 5 An enlrgement of sle ftor 3 gives n imge with sides 3 times s long s the originl shpe. Eh vertex of the imge will e 3 times s fr from the entre of enlrgement s the originl vertex nd in the sme diretion. You n do this more esily on squred pper y ounting squres. Enlrge this shpe y sle ftor of 2. Use the point P s the entre of enlrgement. Rememer to go twie s fr from P to the imge vertex. Count twie the distne long nd twie the distne down. Originl mteril Cmridge University Press 2009 3
Cmridge Essentils Mthemtis Core 8 GM4 Consolidtion Worksheet GM4 Consolidtion Worksheet 1 Look t the digrms. Stte whih tringles re equilterl right-ngled isoseles S Explin how you know. 2 A lous is set of points tht oey set of onditions. It n e line or n re. Complete the following sttements. The first letter of eh missing word hs een shown. The lous of ll points 4 m from point X would e with rdius of 4 m. The lous of ll the points tht re equidistnt from two lines OA nd OB is the of the etween the two lines. To find the lous of ll the points whih re the sme distne from two points X nd Y, onstrut the p of the line joining X nd Y. 3 Desrie the shded region in eh digrm. Explin the differene etween the two digrms. Originl mteril Cmridge University Press 2009 1
Cmridge Essentils Mthemtis Core 8 GM4 Consolidtion Worksheet 4 An ngle mesures n mount of turn. Angles n e mesured using protrtor. A ering is n ngle mesured from North in lokwise diretion. It desries the diretion of one point reltive to nother. Rememer North is lwys up the pge. Berings hve 3 digits so ering of 20 is written s 020. The ering of Q from P is x. The ering of P from Q is y. For eh digrm elow, write down the three-figure ering of Q from P. d 5 In sle drwing, the rel length is either deresed or inresed in ertin rtio. A rtio of 1:200 mens 1 m s sle drwing represents 200 m (2m) of rel length. The sle ftor is 200. To hnge from the sled length to the rel length you multiply y the sle ftor. To hnge from the rel length to the sled length you divide y the sle ftor. A pln is drwn to sle of 1:30. Clulte the tul length in metres. i Sled length 10 m ii Sled length 3.8 m Chek tht A pln is drwn to sle of 1:250. The sled length is 12 mm. your nswers re in the Wht is the tul length in metres? orret units. The sle used on pln is 1:500. The rel length is 100 m. Wht will the sled length e in entimetres? 1000 mm = 1 m Originl mteril Cmridge University Press 2009 2