2 Calculate the size of each angle marked by a letter in these triangles.
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1 Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked y letter in these qudrilterls. 4 Clculte the size of ech ngle mrked y letter. Originl mteril Cmridge University Press
2 Cmridge Essentils Mthemtics Support 8 GM1.1 5 Joe mesures the ngles in tringle. The sketch shows his results. How cn you tell tht Joe hs mde mistke? 6 Clculte the size of ech lettered ngle. Explin your methods clerly. c d Originl mteril Cmridge University Press
3 Cmridge Essentils Mthemtics Support 8 GM1.2 GM1.2 1 Look t the digrm. Write down line tht is prllel to AF. Write down line tht is perpendiculr to FC. 2 ACDE is rectngle. Mrk E on the grid. Write the coordintes of E. ABCF is squre. Mrk F on the grid. Write the coordintes of F. c ABDG is prllelogrm. Mrk G on the grid. Write the coordintes of G. Originl mteril Cmridge University Press
4 Cmridge Essentils Mthemtics Support 8 GM1.2 3 The digrm shows two prllel lines intersected y nother stright line. Which ngle is corresponding to? Which ngle is lternte to? c Which ngle is verticlly opposite m? 4 Look t the digrm in question 3. Which ngle rule links ngles c nd d? Which ngle rule links ngles nd l? c Which ngle rule links d nd l? 5 Clculte the size of ech lettered ngle. Give resons for your nswers. c d Originl mteril Cmridge University Press
5 Cmridge Essentils Mthemtics Support 8 GM1.3 GM1.3 1 Find the cute ngles shown on these protrctor scles. c d 2 Find the otuse ngles shown on these protrctor scles. c d 3 Find the reflex ngles shown on these protrctor scles. 4 Use protrctor to drw these ngles. Lel ech ngle clerly c 148 d 306 Originl mteril Cmridge University Press
6 Cmridge Essentils Mthemtics Support 8 GM1.3 5 Look t tringle ABC. Mesure the size of these sides (to the nerest millimetre) nd ngles (to the nerest degree). AB BC c AC d BAC e ABC f ACB 6 Look t the sketch of tringle PQR. Use the informtion in this sketch to construct tringle PQR. i Find the length of QR. ii Mesure PQR. Don t forget to lel your tringle with the informtion from the sketch. 7 Look t the sketch of tringle JKL. Use the informtion in this sketch to construct tringle JKL. i Find the length of JK. ii Find the length of KL. Rememer to leve in your construction lines. Originl mteril Cmridge University Press
7 Cmridge Essentils Mthemtics Support 8 GM2.1 GM2.1 1 The shded shpes re on centimetre squre grid. Find the perimeter of ech shpe. i ii iii Wht do you notice out the perimeters of the shpes in prts ii nd iii? 2 Find the perimeter of these rectngles. c 3 The shded shpes re on centimetre squre grid. Find the re of ech shpe. c 4 Find the re of ech rectngle in question 2. Rememer to use the correct units in your nswers. 5 A squre hs re 100 m 2. Wht is the length of ech side of the squre? Clculte the perimeter of the squre. Originl mteril Cmridge University Press
8 Cmridge Essentils Mthemtics Support 8 GM2.1 6 Clculte the re of ech tringle. c 7 Clculte the height h of ech tringle. h h Are = 40cm 2 Are = 15cm 2 8 Clculte the re of ech prllelogrm. c 9 Work out the re of ech shpe. Split the first two shpes into rectngles. You will hve to work out some of the side lengths. c 10 Work out the shded res of these digrms. Originl mteril Cmridge University Press
9 Cmridge Essentils Mthemtics Support 8 GM2.2 GM2.2 1 Use centimetre cues to mke the 3-D shpes shown in these digrms. c How mny centimetre cues did you need for ech shpe? 2 These shpes re mde from centimetre cues. How mny centimetre cues re in ech shpe? c 3 Wht is the volume of ech shpe in question 2? 4 Rjiv wnts to mke cuoid tht is 3 cm long, 3 cm wide nd 2 cm high. How cn Rjiv work out how mny centimetre cues he needs to mke the cuoid? Wht is the volume of the cuoid? 5 Alexei hs twenty centimetre cues nd wnts to mke cuoid using ll the cues. Wht could the length, width nd height of the cuoid e? 6 Find the volume of ech cuoid. c 7 Work out the volume of this shpe y splitting it into cuoids. Originl mteril Cmridge University Press
10 Cmridge Essentils Mthemtics Support 8 GM2.3 GM2.3 1 This digrm shows the net of cuoid. The ts for sticking it together re not prt of the net, nd re not shown. c d e How mny fces does the solid hve? If fce 6 is the se, which fce will e the top? Which fces will e the front nd the ck? Which fces will e the two sides? Copy the digrm onto centimetre squre pper nd cut it out. See if your nswers to prts, c nd d re correct. 2 A cue hs side length 4 cm. How mny fces does cue hve? Wht is the re of ech fce of this cue? c Hrry sys tht the surfce re of the cue is 96 cm 2. Is he correct? Explin your nswer. 3 Work out the re of one fce nd then clculte the surfce re of ech cue. c 4 A cuoid is 3 cm long, 5 cm wide nd 2 cm high. On centimetre squred pper, copy nd complete the net for this cuoid. Use your net to find the surfce re of the cuoid. Originl mteril Cmridge University Press
11 Cmridge Essentils Mthemtics Support 8 GM2.3 5 Clculte the surfce re of ech cuoid. 6 Look t the nets elow. Mtch ech net to its 3-D shpe from the list. i ii cuoid cue cylinder squre-sed pyrmid tetrhedron tringulr prism iii iv v Drw the net of the 3-D shpe tht hs not een used. 7 This is digrm of tringulr prism. Drw net for this tringulr prism on centimetre squre pper. Use your net to find the surfce re of the tringulr prism. 3 cm 10 cm 5 cm 4 cm Originl mteril Cmridge University Press
12 Cmridge Essentils Mthemtics Support 8 GM2.4 GM2.4 1 Mtch ech 3-D shpe (lettered A to K) to its pln (numered 1 to 7). Some plns mtch more thn one shpe. J K 2 For ech 3-D shpe, three views re shown. Write whether ech view is the pln, front elevtion or side elevtion. i ii iii i ii iii Originl mteril Cmridge University Press
13 Cmridge Essentils Mthemtics Support 8 GM2.4 3 Drw the pln, front elevtion nd side elevtion of ech shpe. Use centimetre squre pper. c 4 Sketch the pln, front elevtion nd side elevtion of ech shpe. Originl mteril Cmridge University Press
14 Cmridge Essentils Mthemtics Support 8 GM3.1 GM3.1 1 The digrm shows rectngle tht hs een split into two congruent shpes y shding hlf the squres. Drw more of these rectngles elow. How mny different wys cn you find to split the rectngle into two congruent shpes y shding hlf the squres? 2 Look t the shpes elow. List four of pirs of shpes tht re congruent. 3 How mny lines of symmetry does ech picture hve? c d e f g h Originl mteril Cmridge University Press
15 Cmridge Essentils Mthemtics Support 8 GM3.1 4 Mrk ll the lines of symmetry on ech of these shpes. c 5 Colour 2 more squres on this grid so tht it hs exctly one line of symmetry. Now colour 4 more squres on this copy of the grid so tht it hs exctly two lines of symmetry. 6 Which of the shpes in question 3 hve rottionl symmetry? For ech shpe with rottionl symmetry, stte the order of rottionl symmetry. 7 Colour whole squres on the grids elow to drw shpes which hve line symmetry nd rottionl symmetry line symmetry ut no rottionl symmetry c rottionl symmetry ut no line symmetry Originl mteril Cmridge University Press
16 Cmridge Essentils Mthemtics Support 8 GM3.2 GM3.2 1 Reflect ech shpe in the dshed mirror lines. c d e 2 The fce rottes clockwise through one right ngle ech time. Drw the lst fce. Originl mteril Cmridge University Press
17 Cmridge Essentils Mthemtics Support 8 GM3.2 3 Rotte tringle M 180 clockwise with centre A. Lel your imge X. Rotte tringle M 90 nticlockwise with centre B. Lel your imge Y. 4 Drw the imge of the shpe fter trnsltion 2 units to the left nd 4 units up. Lel your imge X. 5 Reflect tringle A in the x-xis. Lel your imge X. Rotte tringle A 90 nticlockwise out the point (0, 0). Lel your imge Y. c Trnslte tringle A using the column 7 vector 6. Lel your imge Z. Originl mteril Cmridge University Press
18 Cmridge Essentils Mthemtics Support 8 GM3.3 GM3.3 1 Copy ech shpe onto centimetre squre pper. Enlrge ech shpe y scle fctor 2. c d e f 2 Copy ech shpe onto centimetre squre pper. Enlrge ech shpe y scle fctor 3. c 3 In ech digrm shpe B is n enlrgement of shpe A. Wht is the scle fctor of ech enlrgement? Originl mteril Cmridge University Press
19 Cmridge Essentils Mthemtics Support 8 GM3.3 4 Look t the tringles elow. Find the scle fctor of ech of these enlrgements. A to D B to F c G to E d A to C e F to E f A to G 5 Look t the sketch elow. It is not drwn to scle. Arrow X hs een trnsformed to rrow Y y n enlrgement of scle fctor 2. Write down the three missing lengths, nd c. Originl mteril Cmridge University Press
20 Cmridge Essentils Mthemtics Support 8 GM4.1 GM4.1 1 A mp uses the scle 1 cm to 5 km. Wht re the ctul distnces for these mesurements? i 3 cm ii 9 cm iii 20 cm iv 12 cm v 0.5 cm vi 3.5 cm Wht re the mesurements for these ctul distnces? i 10 km ii 20 km iii 25 km iv 1 km v 12.5 km vi 2.5 km 2 A scle drwing uses the scle 1 cm to 4 m. Wht re the ctul distnces for these mesurements? i 3 cm ii 5 cm iii 9 cm iv 11 cm v 7 cm vi 1.5 cm Wht re the mesurements for these ctul distnces? i 32 m ii 16 m iii 48 m iv 64 m v 6 m vi 10 m 3 A mp of Europe shows the distnce etween Pris nd Mdrid s 10 cm. The scle of the mp is 1 cm to 75 km. Work out the distnce in kilometres etween Pris nd Mdrid. The sme mp shows the distnce etween London nd Rome s 14 cm. i Write down the clcultion you would use to work out the ctul distnce in kilometres etween London nd Rome. ii Work out the distnce in kilometres etween London nd Rome. 4 Write ech scle s rtio in its simplest form. 1 cm : 1 m 1 cm : 3 m c 5 cm : 3 m d 8 cm : 1 km e 2 cm : 5 km f 4 cm : 1 km Originl mteril Cmridge University Press
21 Cmridge Essentils Mthemtics Support 8 GM4.1 5 A scle drwing of new kitchen uses the scle 10 cm to 3 m. Explin why this scle is 1 : 30. The length of the kitchen on the scle drwing is 15 cm. Explin why the rel length of the kitchen is 4.5 m. c The drwing shows the width of gp under worktop s 1.8 cm. Will dishwsher of ctul width 60 cm fit into the gp? Explin how you decided. 6 The digrm shows Misie s home, her school nd the lirry. Misie decides to drw scle digrm to show the informtion. She uses scle of 1 cm : 150 m. c Wht is the scle distnce from her home to the school? Wht is the scle distnce from the school to the lirry? Drw scle digrm to show the informtion. Use scle of 1 cm : 150 m. d Mesure the distnce of Misie s home from the lirry on your scle digrm. e Wht is the ctul distnce of Misie s home from the lirry? f How much shorter is it for Misie to wlk directly to the lirry, compred with wlking to the school first nd then the lirry? Originl mteril Cmridge University Press
22 Cmridge Essentils Mthemtics Support 8 GM4.2 GM4.2 1 The digrm shows rectngle WXYZ. WX = 12 cm nd XY = 9 cm. W X A P E Q F B 6 cm D C Z V Y How fr is the line PQ from the line WX? Ntlie sys tht V is the only point tht is the sme distnce from oth Y nd Z. Is this true? Explin your nswer. c Mtch the points A, B, C, D, E nd F to the rules elow. Rule 1: The point must e exctly 3 cm from the line WX. Rule 2: The point must e exctly 6 cm from Z. Rule 3: The point must e no more thn 6 cm from Y. Rule 4: The point must e less thn 6 cm from Z. Rule 5: The point must e more thn 6 cm from the line ZY. Rule 6: The point must e less thn 6 cm from YZ ut more thn 6 cm from Z nd more thn 6 cm from Y. Originl mteril Cmridge University Press
23 1 Cmridge Essentils Mthemtics Support 8 GM4.2 2 The digrm shows rectngulr A X ply re ABCD. P How fr is point X from A? Explin how you know. 30 m Q S Complete these rules for the possile positions of points 20 m R on the digrm. D 60 m 40 m i Point P is the position of climing frme. P must e less thn m from point. ii Point Q is the position of the swings. Q must e exctly m from line nd more thn m from line. iii Point R is the position of slide. R must e less thn m from line CD nd more thn 40 m from line. c Meliss s mother is stnding t the point mrked S. Descrie rule tht point S hs to follow. B C 3 On squred pper, drw rectngle ABCD so tht AB = 8 cm nd AD = 5 cm. P is point inside the rectngle ABCD. Point P hs to e exctly 3 cm from A. Drw the locus of point P ccurtely. c Q is nother point inside the rectngle ABCD. Q hs to e less thn 4 cm from D. Drw nd shde the locus of point Q ccurtely. d Point X is exctly 3 cm from D nd 4 cm from A. Lel point X on your digrm. e Drw tringle AXD. f Wht type of tringle is AXD? (Hint: Mesure the ngle AXD.) 4 This is sketch of tringle XYZ. Use ruler nd pir of compsses to construct tringle XYZ. Wht nme is given to this type of tringle? c Wht type of ngle is ngle XZY? d Mesure the ngle XZY. 5 This is Jne s sketch of tringle she wnts to drw. Explin why she will not e le to construct tringle ABC. Z 4 cm 7 cm X 10 cm Y C 6 cm 5 cm B A 12 cm Originl mteril Cmridge University Press
24 Cmridge Essentils Mthemtics Support 8 GM4.3 GM4.3 1 Explin why the three-figure ering for Est is Philipp sys, The ering of North West is 045, ecuse the ngle etween North West nd North is 45. Is Philipp correct? Explin how you decided. 3 For ech digrm, write the three-figure ering of point Q from point P. c 4 For ech digrm in question 3, write the three-figure ering of point P from point Q. 5 Look t the digrm. Descrie the ering tht is c 280 d 100 e 250 Originl mteril Cmridge University Press
25 Cmridge Essentils Mthemtics Support 8 GM4.3 6 On 5 mm squred pper, plot points A nd B so tht B is 5 squres elow nd 10 squres to the right of A. Add North line t A. Mesure the length AB. Give your nswer to the nerest millimetre. c Mesure the ering of B from A. 7 On 5 mm squred pper, plot points A nd B so tht B is 8 squres ove nd 5 squres to the left of A. Add North lines t A nd B. Mesure the line AB. Give your nswer to the nerest millimetre. c Mesure the ering of B from A. d Mesure the ering of A from B Point A is 7 cm due North of point B. Point C is on ering of 125 from A nd on ering of 038 from B. Drw n ccurte digrm using protrctor nd ruler nd work out the position of point C. It might help you to drw sketch first. c d e Mesure the distnce of C from A to the nerest millimetre. Mesure the distnce of C from B to the nerest millimetre. Without mesuring, work out the size of ngle CAB. Wht is the size of ngle ACB? Explin how you got your nswer. Originl mteril Cmridge University Press
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