Exploring Maths Workbook 3B (2 nd Edition) Answers Last update 2/1/2006. (b) (i) common h (ii) AED. Exercise 8A (P. 1) 1.
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1 Exercise 8A (P. ). ABC RQP (SSS) ABC PQR (RHS). (a) (i) given (i) common h (ii) AED (iii) h sum of (iv) 80 (v) 80 (vi) 80 (vii) AAA (ii) alt. hs, AB // CD cm (iii) alt. hs, AB // CD (iv) ASA (i) given (ii) given (iii) common side (iv) SAS. (a) (i) common side (ii) given (iii) DC (iv) ADC (v) SSS (vi) DAC (i) common side (ii) given (iii) (v) CAD (iv) EDC CDA (vi) ASA Exercise 8B (P. 5). (a) ABC ~ RPQ (AAA) ABC ~ PQR ( sides prop.) ABC ~ QPR (ratio of sides, inc. h). (a) (i) corr. hs, DE // BC (ii) corr. hs, DE // BC (iii) common h (iv) AAA Exercise 8C (P. 9). (a) ADC given (e) ACB (f) AB. (a) alt. hs, AB // DE h sum of 0 0 (e) CED (f) sides opp. eq. hs. (a) given 90 given BC (e) BCE (f) CE 4. (a) base hs, isos. ext. h of a a (e) BAD (f) 6. 6 sides opp. eq. hs 7. (a) (i) (ii) Exercise 8D (P. ). AE: a median; BD: an angle bisector; EF: a perpendicular bisector. (a) AD AD (i) vert. opp. hs (ii) given CF, AD, BE (any two) (iii) alt. hs equal (iv) alt. hs, AB // DE AD. (a) given 80 ANC (v) AAA. (a) (i) (ii) 6 (iii) 8 BC (v) BE 0 0 (iv) (vi) sides prop. common side ANC (e) RHS (f) corr. sides, 4. (a) ext. h of ACB base hs, isos. h sum of (e) 75 (f) given
2 Exercise 8E (P. 7). (a) 5 m 6 m. (a) Yes Yes 5.6 m 55. m No No 4. (a) = 0 x, y =.9 cm Supplementary Exercise 8 (P. 9) cm. C. B. C 4. A 5. A 6. C 7. B 8. D 9. A 0. B Exercise 9C (P. ). (a) Square; = 45 Rectangle; = 8 x, y = 45 x, y = 5 Rhombus; x = 90, = 4 Rectangle; = 55. (a) x = 4, y = a = 6. 5, b = a =, b = y, z = 68 x, y, z = 5. (a) 4 cm = (a) 0 75 Exercise 9A (P. 5). (a) Rectangle Rhombus Parallelogram (e) Trapezium. (a) (e). (a) x = 60 = 50 y, z = 5 l = w = 45, = 4 5. x = 60, y = 0 y = 45, z = 4 x, (a) 50 0 Exercise 9D (P. 7). (a) property of //gram property of //gram SSS. (a) opp. sides equal 90 property of rhombus. (a) AC Exercise 9B (P. 8). (a) = 4 x, y = 0 x = 8, y = = 6 = x, y 5. x = 5, y = 4. (a) (e) (f) QC corr. hs, QR // AB base hs, isos. (e) sides opp. equal hs (f) sides equal and //
3 Exercise 9E (P. 4). (a) x = 40, y = = 4 θ = 70 x, x =. x =, y =. (a). (a) x = 0. 8, y = 0. 8 x = 4, y = 8 = 6 x, y = 0 x =, y =. 5 Supplementary Exercise 9 (P. 45) Exercise 0B (P. 54). (a) B A. A. A 4. (a) (a) (i),, 4 (ii),, 5 Exercise 0C (P. 57). (a) B 5. D 6. C 7. A 9. Block : 4; Block : ; Block : 4 Block 4: 4; Block 5:. Maximum: 8; minimum: 4. x = 5, y = 9. = 50 x, y = = 50 DAP, ADC = 0 Exercise 0D (P. 6). (a) GF ED FE BYA (e) AB, AD, FE, FG (any two). (a) BDEG, BCHG BDEG, CDEH. D. C. B Point D Point G (e) DC 4. C 5. B 6. C 7. B 8. C 9. D 0. C. D. D. (a) Point O Point O OA VAO (e) OE 4. (a) AFGD, ABCD EFCD, ABCD Exercise 0A (P. 5). (a) III II II. (a) 6 4. (a) (i) (ii) (i) 5 (ii) 5 (i) (ii) 0 4. (a) (e) 6 5. (a) ABEF, BCDE BF, BD 6. (a) (i) 4 cm (ii) cm (i) (ii) (i) BG ABG (or DCH ) ABF (or DCE ) (ii) DH 7. (a) (i) Point A (ii) Point C (i) DB (ii) AF (i) (ii) ADE (or BCF ) AED (or BFC )
4 Exercise 0E (P. 68). (a) (i) 4 (ii) 4 (iii) 6 (i) 7 (ii) 0 (iii) 5 (i) 6 (ii) 8 (iii). (a) (a) (i) Square (ii) 6 (iii) 8 (iii) Exercise A (P. 79). 8 cm. 50 m. 8 cm cm cm 6. (a). cm 76 cm 7. (a) 9 cm 0 cm.5 cm (i) Equilateral triangle 8. (a) 4 cm 40 cm 60 cm (ii) 8 (iii) 6 (iii) (i) Regular pentagon (ii) (iii) 0 (iii) 0 4. (a) Regular tetrahedron Regular dodecahedron Regular icosahedron Regular octahedron 5. (a) No No Supplementary Exercise 0 (P. 7). (a) ABHE, ADHG, AFHC. A. B, C, D, F 7. (a) ADE or BCF DB AF BAD. D. A. B 4. D 5. D 6. A 7. B 8. A 9. C 0. B. D. D. A 4. D 5. A Exercise B (P. 8). (a) Volume = 09 cm, curved surface area = 48 cm Volume = 7 m, curved surface area = 0 m Volume = 49 cm, curved surface area = 8 cm Volume = 5 m, curved surface area = 6 m. (a) 9 cm 4π cm. (a) 90π cm 00π cm 4. 8 cm 5. (a) 4.9 m.9 m 6. 0 cm 7. (a) 8 cm 5 cm 0π cm Exercise C (P. 86). (a) 6π cm 6π cm. (a) 8 cm 54 cm. 44π cm 4. 9 cm 5. 4π cm 6. (a) 60π cm 6. cm π cm B 4
5 Exercise D (P. 89). (a). (a). (a) Quadratic Linear Cubic 4. (a) Linear Cubic Quadratic 5. (a) (ii), (iii), (v) (i), (iv), (vi) Exercise A (P. 0). (a) (a) B 4. isosceles Exercise E (P. 9). (a) 0. 6 : 5. 9 : : 7 5. : 8 6. (a) 75 cm 94 cm 7. (a) : : 6 : 6 8 : 7 Supplementary Exercise (P. 95) cm s. (a) 7 cm cm 4. (a) 47.6 cm 0.6% 5. (a) 67.0 cm 0 cm 6. (a) Enough 707 cm 7. (a) Quadratic Linear Cubic. D. C. A 4. C 5. D 6. B 7. B 8. C 9. A 0. B. C. C 7. (a) (8, 0) 0 Exercise B (P. 06). (a) F T T. (a) F 0 (e) T (e). (a) (a) 6. (a) AB Exercise C (P. 09). (a) // //. (a) F F T. (a) 4. BAC 5. (a) AB: ; BC: ; CD: ; DA: Yes 6. (a) 7. (a) BC: ; AD: 0 5
6 Exercise D (P. ). (a) (5, 6) (, ) (0, 5) Supplementary Exercise (P. 0). Perimeter =.7, area = 5. 45,. (a) 5. (a) (7, 0) ( 4, 4) (5, ). (a) : : 4. X: (0, 4.5); Y: (4, 6); Z: (8, 7.5) 5. (a) (4, ) 6. (a) :, 0 Exercise E (P. 6) 4. K:,, D: (, ) 5. (a) (0, 5.5) (4, 0) 5 6. (a) M:,, N:, : 5; 0, 5 6. C. D. B 4. A 5. C 6. C 7. A 8. C 9. B 0. B. C. C. D 4. D. (a) ( a 0) + ( a 0) a Exercise A (P. 7). (a) : 50 m ( a 0) + (0 a) 00 m 9 m a. (a) (a, 0) (a, b) ( a 0) + ( b 0) (e) : (f) 55 m. (a) (a) : 5 (e) (f) a + b ( a a) + (0 b) a + b 4. (a).7.85 m 5. (a) : 4 : 5 : 7 : 9 4. (a) C: (a, a); D: (0, a); E:, a F:, (a) (c, 0) 0 a ; 6. (a).0 (i) 6.7 (ii) 0.9 m 6 7. (a) AH: ; BH: 5 5 AH: 6. ; BH: 4.57 AH 6
7 Exercise B (P. ) m. (a) 50 5 m 4. (a) 4 m m 6. 7 m Revision Test (P. 47). 50. x = 5, = 4. 5 y, z = 05. (a) Point A AE DBE F = 7, V = 0, E = 5 6. (a) 7π cm cm 7. (a) 4 cm 6 : 9 64 : 7 Exercise C (P. 5). (a) (i) N 5 E (ii) 05 (i) S 78 E (ii) 0 (i) S (ii) 0 (i) N 4 (ii) 7. (a) 47 7 S 5 E N 5. 6 m 4. (a) 7 km S.0 5. (a) N 46 E 7 km Supplementary Exercise (P. 40). (a) 849 m :. 46. m. (a) 8.0 m 40 km/h 4. (a) 500 m N. 5. (a) 657 m 0. C. A. B 4. B 5. C 6. A 7. C 8. D 9. C 0. D. B. B. D 8. (a) No 9. P: (, 4); B: (7, 6) 0. (, 0). (a) 0 m km (a) 5.8π cm cm 5. (a) 6 (, 0) 0 6. (a) 66 m N m Revision Test (P. 57). D. A. C 4. B 5. B 6. D 7. A 8. A 9. C 0. C. B. A. B 4. D 5. C 6. B 7. C 8. A 9. D 0. C. D. D. B 4. D 5. D 6. C 7. B 8. B 9. B 0. B. B. C. A 4. A 5. C 6. B 7. D 8. B 9. B 40. C 7
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