AnSWErS to tHE StudEnt'S Book ExErCiSES - Hodder Plus Home

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4 a) (i) Angle QPX 5 angle XRS(Alternate angles.)Angle PQX 5 angle RSX(Alternate angles.)PQ 5 SR (Given.)So triangle PQX is congruent to triangleRSX (ASA).(ii) Angle QRX 5 angle SPX(Alternate angles.)Angle RQX 5 angle PSX(Alternate angles.)QR 5 SP (Given.)So triangle RQX is congruent to triangleSPX (ASA).b) SX 5 XQ -(Since triangles PQX and RSX are congruent.)PX 5 XR(Since triangles RQX and SPX are congruent.)So X is the midpoint of SQ and PR.SR 5 RQ (PQRS is a rhombus.)Angle RSX 5 angle RQX(Triangle QSR is isosceles.)XR is common to both triangle SXR andtriangle QXR.So triangle SXR is congruent to triangleQXR (SAS).So angle SXR 5 angle QXR.Angle SXR 5 angle QXR 5 90°(Since SQ is a straight line.)5 A and B6 AP 5 PB 5 BQ 5 QC 5 CR 5 RD 5 DS 5 AS(Because P, Q, R and S are the midpoints of thesides of the square ABCD)So all the triangles are isosceles and congruentand all the marked angles are 45°.SAPBQD R CSo the interior angles of the quadrilateral PQRSare 90°(Angles on a straight line.)All the sides, PS, SR, RQ and QP, are equal.So PQRS is a square.7 Angle DCB 5 angle DCA(CD bisects angle ACB.)Angle DCA 5 angle CAE(Alternate angles.)Angle DCB 5 angle AEC(Corresponding angles.)So angle AEC 5 angle CAESo triangle ACE is isosceles and AC 5 CE.8 Angle ACB 5 angle ABC 5 70°(Base angles of an isosceles triangle are equal.)Angle ACD 5 40°(Alternate angles.)So angle BCD 5 110°So angle DBC 5 angle BDC 5 35°(Base angles of an isosceles triangle are equal.)9 Angle BCD 5 122°(Alternate angles.)Angle DCE 5 58°(Angles on a straight line add up to 180°.)Angle BCY 5 58°(Vertically opposite angles are equal.)Angle ABC 5 58°(Angles on a straight line add up to 180°.)Angle BAD 5 89°(Angle sum of triangle BAE.)10 Angle BDC 5 80°(Base angles of an isosceles triangle are equal.)So angle DBC 5 20°(Angles in a triangle add up to 180°.)So angle ABC 5 40°(BD bisects angle ABC.)So angle BAC 5 60°(Angle sum of triangle BAC.)11 Angle BRQ 5 125°(Angles in a quadrilateral add up to 360°.)Angle BRP 5 55°(Angles on straight line add up to 180°.)So a 5 145°(Exterior angle of triangle is equal to the sum ofthe opposite, interior angles.)Mixed exercise 37 (page 505)1 x 5 22° (Alternate angles.)y 5 26° (Base angles of an isosceles triangle(PRS) are equal and Angles in atriangle add up to 180°.)z 5 48° (Alternate angles.)2 x 5 70° (Angles in a triangle add up to 180°.)y 5 60° (Alternate angles.)z 5 130° (Vertically opposite angles.)3 Angle DCB 5 80°(Angles in a quadrilateral add up to 360°.)So angle ACB 5 angle ACD 5 40°(Given that CA bisects angle DCB.)Angle DAC 5 10°(Angles in a triangle add up to 180°.)So angle CAB 5 70°(80° – 10°.)Since CAB 5 ABC, triangle CAB is isosceles.4 a 5 87° (Allied angles.)b 5 74° (Alternate angles.)5 x 5 100°(Angles in a quadrilateral add up to 360°.)234Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education
6 A7DCEBAD 5 AB, DE 5 DB and AE is common totriangles ADE and ABE.So triangles ADE and ABE are congruent (SSS).So angle DEA 5 angle BEAAngle DEA 5 angle BEA 5 90°.(Since DB is a straight line.)CD 5 CB, DE 5 EB and CE is common totriangles CDE and CBE.So triangles CDE and CBE are congruent (SSS).So angle CED 5 angle CEBAngle CED 5 angle CEB 5 90°(Since DB is a straight line.)This proves that the diagonals of a kite cross atright angles.ACEBCE 5 ED, angle CEA 5 angle DEA and EA iscommon to triangles AEC and AED.So triangles AEC and AED are congruent(SAS).So AC 5 DACE 5 ED, angle CEB 5 angle DEB and EB iscommon to triangles CEB and DEB.So triangles CEB and DEB are congruent (SAS).So CB 5 BDAE 5 EB, angle AED 5 angle BED and ED iscommon to triangles AED and BED.So triangles AED and BED are congruent(SAS).So DA 5 BDSo AC 5 CB 5 BD 5 DAChapter 38Exercise 38.1 (page 513)1 a 5 20° b 5 40° c 5 60°2 d 5 104° e 5 85°3 f 5 110° g 5 35°D4 h 5 66°5 i 5 50° j 5 56° k 5 34°6 m 5 49° n 5 41°7 p 5 45° q 5 60°8 r 5 20 cm9 s 5 40° t 5 80° u 5 50°10 v 5 95° w 5 126°11 x 5 42°12 y 5 30°13 z 5 57°14 a 5 44° b 5 46°15 c 5 30°16 d 5 90° e 5 40° f 5 32°17 g 5 120°18 h 5 10 cm19 i 5 98° j 5 120°20 k 5 18°Exercise 38.2 (page 517)1 a 5 142°2 b 5 70° c 5 50°3 d 5 50° e 5 50°4 f 5 90° g 5 35° h 5 55° i 5 35°5 j 5 36° k 5 108°6 m 5 74° n 5 32°7 p 5 70° q 5 40°8 r 5 45°9 s 5 61° t 5 61° u 5 58°10 v 5 85° w 5 71°Mixed exercise 38 (page 519)1 a 5 102° b 5 39°2 c 5 13°3 d 5 81° e 5 90°4 f 5 25° g 5 75°5 h 5 62° i 5 28° j 5 29°6 k 5 5.7 cm m 5 38.9°7 n 5 83° p 5 52°8 q 5 122° r 5 244°9 s 5 55° t 5 35° u 5 35°10 v 5 64° w 5 52°Chapter 39Exercise 39.1 (page 521)1Frequency2015105015 20 25 30 35 40 45 50Age (years)Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 235
Page 1 and 2: AnSWErS to tHE StudEnt’SBook ExEr
Page 3 and 4: Chapter 3Exercise 3.1 (page 47)1 a)
Page 5 and 6: Chapter 5Exercise 5.1 (page 73)1 5
Page 7 and 8: 4 a) 0.722 b) 1.26 c) 20.6495 a) 33
Page 9 and 10: Chapter 11Exercise 11.1 (page 144)x
Page 11 and 12: 2345y 3y4321R3 2 1 0 1 2 3 41y 2x
Page 13 and 14: 4 a) x 22 21 0 1 2 3 4 5x 2 4 1 0 1
Page 15 and 16: 10 a)x 22 21 0 1 2 3 4x 2 4 1 0 1 4
Page 17 and 18: 3 The velocity increases from 0 m/s
Page 19 and 20: 7 a)y302826242220181614121086420y
Page 21 and 22: 5 a) y 5 ___ 24xb) 486 a) d 5 ____
Page 23 and 24: Chapter 21Exercise 21.1 (page 283)1
Page 25 and 26: (x 2 np)2k) q 5 _________ l) x 5 6
Page 27 and 28: Mixed exercise 25 (page 328)1 a)c)2
Page 29 and 30: Exercise 27.5 (page 362)1 a) (5, 3,
Page 31 and 32: 6 a) A reflection in the line y 5 0
Page 33 and 34: 3 Scale 1 cm 5 10 mHedge2 Scale 1 c
Page 35 and 36: 7 163.4 cm (1 d.p.)8 14.8 cm (1 d.p
Page 37 and 38: Chapter 32All answers are given cor
Page 39 and 40: 6yd) (i)y1y cos 3 θ20130° 60° 9
Page 41: 2 a) (1, 8)b) 233 y1210CD8 A B64D C
Page 45 and 46: 4 a)Mark50403020100400 500 600Circu
Page 47 and 48: Exercise 42.2 (page 568)1 a)First d
Page 49 and 50: 7 a)First discSecond discOutcomePro
Page 51 and 52: 2 a) You are aged 19 up until your
Page 53: 15 23 (because 0 is in the sequence

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