ALGEBRA Answers - Worksheet A - Physics & Maths Tutor
PMTC11Answers - Worksheet AALGEBRAa 7d 25g 2j 2346 54or 1 14c e 0.1f 0.3h 10i 3l 3 18k 12or 0.53 125852 or 2 12b 20c 27d 36e 4 2f 24 3g 16 4h 2 81 18ij k 6l 16 414 12a 9 2 3 2b 25 2 5 2d 49 2 7 2ea 4 3 2 3d 9 3 3 3eg 9 5 3 5 54c 4 2 2 2f 81 2 9 2b 4 7 2 7c 16 5 4 5 4 6 2 6f 64 2 8 2h 4 10 2 10i 25 3 5 3k 9 11 3 11l 49 3 7 3m 36 6 6 6n 400 2 20 2o 36 5 6 5p 4 15 2 15q 121 3 11 3ra 3 2 5 2 8 2b 4 3 3 3 3c 4 2 6 2 10 2d 6 10 4 10 2 10e 2 5 3 5 6 5 5 5f 2 6 5 6 8 6 6a 3 2 3b 4 c 2 16 7 4 7 100 2 10 2 2 d 4 8 3 3 6 10 9 37 a 7j5251613b 11a 10 3 5 2 5 3 13 5 5d 12 15 2 2 2 5 7 13 23 2 2 33e 27 24 3 16 43 24 3b 4 2 3 8 3 2 7 2 11e 5 2 10 10 4 1 10 16 13 4 133 2 3 3 5 3 3f 6 3 45 2 5 3 43 3c 28 12 7 9 37 12 7f (3 2 2 )(4 12 3 2 8 2 4 8 5 2 Solomon Press2)
PMTC18a 15 55 5b 23 33d 147 77 2 7e 3 23 33g j 911523 c 6f 53 52i 1l 1217h 122 6 22 36 6 66 1126k 8 52 9 22 3 762 22b 4 3 2 2 3 2 4 3 5 2 3 5 55 2 55 15 5 510 12(3 e 5)2316 7244910103 33103c 34 52 12 4 22 18f 22 2x 323x 6 3x 32x 2 3c 3 2x 4 2 21123 33 233 123125 x 2 2 5 (x 1)d5x 2 5 10(x 1)6x 4 4 25x 10 2 52)x 2 a 4 ( 3 )2 4 3 1b 22 3 2 3 2 3 2(2 3)1a 12 12 1 2 12 1 2 1b 43 1 4( 3 1) 3 13 13 1c d e 16 26 2 6 46 26 2 2( 3 1) 32 3 3(2 3) 4 32 3 2 312 5 2 5 4 52 5 2 5 4 2 32 1 12( 6 2) or 120 56 5216 2 426x 4 2 4(1 55126 1 3(2 3)5 2 Solomon Press255 162 36 23page 226 2 22 22x 4 2x 13 3315 73 6 33b x 4 3 2 3 2xa x2 4x 4x 3223 14 3 2 2312 3 22 12 2 22377 a 2 2 d 10Answers - Worksheet AALGEBRA133
PMTC122 12( 2 1) 2 12 12 1 2 2g 67 3 6( 7 3) 7 97 37 3 3(3 7)h 13 2 2 3 2 2 9 83 2 2 3 2 2 3 2 2i 14 2 3 4 2 3 4 2 3 4 2 3 16 12 12j 33 2 4 3(3 2 4) 18 163 2 4 3 2 4 f k l1314 65 3 6( 5 3) 5 35 35 35x 2 5x(3 5) 2 5x 2 53 5x 6 5 104l 63 2 3b c d 2 53 5 3 53 552325 18( 2 1)9a (2 3) or 1 12 3322 37 4 3 2 3(7 4 3) 49 487 4 3 7 4 33x l 15Answers - Worksheet AALGEBRA 63 2 3 3 2 33 2 3(3 2 4) or922 6 2(7 3 12) 3( 5 3)2 5(3 5)9 5 6(3 2 3)18 9 2 2 222 62( 2 6) 2 62 62 61 3 2 3 (1 3)(2 3) 4 32 3 2 3 14 (2 2 3) 12 ( 3 1) 2 3 2 3 3 3 11 1010 3 (1 10)( 10 3) 10 910 310 3 10 3 10 3 10 13 4 103 2 4 3 2 (3 2)(4 3 2) 12 9 2 4 2 6 16 18 24 3 2 4 3 2e 1 2 3 2 2 (1 2)(3 2 2) 9 83 2 2 3 2 2f 3 5 2 3 4 ( 3 5)(2 3 4) 6 4 3 10 3 20 12 16 42 3 4 2 3 412 (13 2 18) or 3 2 2 3 2 4 1 2 g 2 3 3 3 3 (2 3 3)(3 3) 6 3 6 9 3 3 9 363 3 3 3h 3 7 2 2 7 5 (3 7 2)(2 7 5) 42 15 7 4 7 10 28 2532 7 5 2 7 5 Solomon Press121(72 3 3)(3 3 5) 13 (32 11 7)1322 9page 3
PMTC11Answers - Worksheet BALGEBRAa 64b 216c 1d 625e 243f h 641i ( 43 )2 or 5 161k 0.000 01l 0.008b 27c 20g 827j ( 32 )4 8116169or 1 792a 283a 8p7b x10c 6n5d y12e 2bf p4q3g x3yh 6r2s3j 4a5b8k 125r3s6 100r2s2 l 54 rs4i4 2x3y7a 312 19b 1d 62 36eg 4 16 2j 3 125 5m 4181 13e 29f 214 15p3qc ( 12)6 641f 9 3h 3 27 3i k l ( 32 ) 3 ( 23 )3 n 8p 3 125 255d 24116q a ( 4)3 23 8493 1 649482723 14 32 71149136 16o 5 32 2or 1 12r ( 278 ) 13 3b ( 3 27)2 32 9c ( 4 16)3 23 8d ( 3 125)2 ( 5) 2 25e ( 9)5 35 243fg (i136 )3 (4 3)9k (m 613 16 3)94100o (3 ( 34 )3 38276427or 2 1027 102 51 or 0.264 2)1000 (104 ) 2 81 4q ( 16) (481 3)16 ( 3 18 )2 122 14h ( 3 18 )4 ( 12 )4 1611216 ( 23 )3 827425j ( 3 216)2 62 36l ( 3 27)4 ( 34 )4 64n ( 94 )or 0.16 ( 23 )3 278or 3 83 32 (4 3)981256 ( 23 )3 82725p ( 16) 32 (16 3)2564 ( 54 )3 125 ( 64)27 43 (327 4)64 ( 34 )4 r Solomon Press81256 23
PMTC16Answers - Worksheet BALGEBRA4 3 27a b 4 16 25 2 3 6 2 5 7e 32 3 8 9 ( 2) 11i5e y21 p4m b8165 ( 15 )2 14 129k 100 ( 10 2 8b 3 14311 8b 12g x5k yj 9x 571 b4n y2a x 62 3618 13 1 y 16 1311x2 38 2f141 y3 2x 141a x2eb x31 ( x3 ) 2 x 2 1210a 4x11a (23)2 26d x4 3x 34 8114313b 1612x 151c11x2 3451d 53 1 12731 21) 93x 319dx 22x4x 34133h x3 x2 x 6e25x 13f1c (2 1 ) 3 26 x2g ( x 2 )5 x 2b (2 2) 2 24 23127h x2 1 x2 x3 x613xa (32)x 32xb (34)x 1 34x 4c (33 ) 4 3 4d (3 1)x 3 xe (32)2x 1 34x 2f (3 3)x 2 3 3x 6a 2 2x 2yb 2 2 2x c (2x)2 y2d (23)x 23x (2x)3 y3e 23 24x 8y414y Solomon Pressx 32 13f (2 5) 3 215 29 14 a 4112 x2 x 2 x 2cor 4 12 651 34 ( 12 )x ( 3)3 27 131 ae (23 ) 5 2 5d (24 )12f 43p 14 ax (992 13 tlg x 3 4 81 3x ( 4)3 64x 22 41h a21x 3 16 4 9 12or 10 81 ( 5 243) 21164 x 151 56 32x2 818d 8x 12x ( 12 )2 el 802 ( 1 ) 364c9 3)4 3 278 1 3)4o 2x 3b x 53 12527 (3h c 3p 44 p 20 4 27 108112 27 7 20or 3 15 11 2 13f 6 12 64 ( 9)33d g ( 4 81)3 49b y 6a x2i 42 16 3 j 121 5 32 3 ( 8) 24715 9 ( 5 32)3 125f 3618c page 23xf (2 1)x 3 23 2 x 8y
PMTC114Answers - Worksheet BALGEBRAa 2x 2 6x 6b 5x 1 5 3x 1 3x 4c 3x 4 27 33x 4 3x 1e 32x 1 322x 1 2x 32f 16 42 43x 22 3x 2x 43g (32)x 2 32x 4 33 h (23)2x 1 26x 3 242x 4 36x 3 4x 72x 16i1(72)x 1 72x 2 7 22x 2 12x 34151x k (6 1)x 3 6 x 3 62 l x 3 2x 589(2 1)3x 1 21 3x 231 3x 3x 23b 53x (52)x 1 52x 2 c (32)2x 34x 3x 33x 2x 24x x 3x 2x 1d (42)x 42x 41 x2x 1 xx 13e (22)x 2 (23)x22x 4 23x2x 4 3xx 4f (33)2x (32)3 x36x 36 2x6x 6 2xx 34g 63x 1 (62)x 263x 1 62x 43x 1 2x 4x 5h (23)x (24)2x 123x 28x 43x 8x 4x 45j (3 1)x 3x 43 x 3x 4 x x 4x 2k (2 1)1 x (2 3)2x2x 1 2 6xx 1 6xx 17la x3 1b 2x2 6x3c 3 x2d 12x3 8xe 3x3 2xf 3 3x2g 5x 2 x 2i(53)x 5x 353x 5x 33x x 3x 32 x6 x4 3x2 311b 2t3 3ta x2 2 x3 3 2x 3c x 3x 2(2 2)x 1 (23)x2 2x 2 23x 2x 2 3xx 52h 3x2 x 1j 2x9 6x5 x5 3x k x3 1 2 2x 3 l 2x9 7x5 3x172j 33x 2 (32 ) 3 3 33x 2 23d (23)x 23x 23x 1x 13a 2x 3 (22)x 22xx 3 2xx 3i16page 355 x3 2 x 2 x 2d 113e p4 p43f 2w 2 12 wg x 2 ( x 1)x 11 x2 Solomon Press5 x3 x 2 x 2 x 2y5 6 y23yy4 2 y131h t 2 2t (t 2 2)t2 23 2t 2
PMTC11Answers - Worksheet CALGEBRA9 3 2 25 2a 2 10 2 3 3x2 12b 18 48x 12 2 39 2 16 3 x2 2x 12 2xx 0 x 2 3 3 2 4 3325x (52)x 54x 1452x 54x 13a b381 2x 4x 18 3333 23327 24 333 33381 2 3 3 3 3 3 5 3 3 3 125 3 x 123375 n 375510 315 10 310105 5 355545 7 4( 5 7) 5 75 75 7 710 31545 7 2 56 2 5 2 7755 35 32 2222b 48 5 4 352 53 5533 2 7 [ k 2 ] 45 215a i xy 2t 1 23t 24t 1ii 2y2 2 (23t)2 2 26t 26t 18 526204 32 5 353 2 5 2 5 2 7b 26t 1 24t 1 09a 15 23 15153x 2 2 4x 6x(3 2 4) 6 2x 6 26 2 3 2 4 3 2 43 2 4 3 2 4 (6 2)(3 2 4)18 1626t 1 24t 1 12(18 2 24 6 4 2 )6t 1 4t 1 12(30 22 2 )t 1 15 11 2a 6 y 1 36x 2 (62)x 26 y 1 62x 410y 1 2x 4y 2x 5b x 12 y x 4x 12ya 3 3 2 2 2 1 2 2b 12(2x 5) x x 52 5252 4 ( 4)5 25 32 Solomon Press22 1 2 12 1 2 ( 2 1) 2 22( 2 1)2 1
PMTAnswers - Worksheet CC1ALGEBRA11(24)x 1 (23)2x 124x 4 26x 34x 4 6x 3x 1212a2 4a 3 12 b 20 3a and b integers 4a 20a 5alsoa2 12 bb 3713a (2 2)t 3 2314a 2 5 ( 5 3)26 2t 2 10 6 53b 3 2 5 3 5 106 2t 3t 7 32b (3 1)y (33)y 115c 51 55 2 (1 5)( 5 2) 5 45 25 23 y 33y 3 (1 y 3y 3 y 7 3 53439a a (b 4 )3 b 412941612a (b ) b1343b b (a ) a1249page 21212(2 3 1)( 3 2) 12(6 4 3 12(4 3 3 ) or 2 49b (a ) a5 2 5 2 5a area 98295 )( 5 2)3 2)323b AC2 (2 3 1)2 ( 3 2)2 12 4 3 1 3 4 3 4 20 AC 20 c tan ( ACB) 24 5 2 53 13 2(2 3 1)( 3 2) 3 43 23 2 (2 3 1)( 3 2) (6 4 3 3 2) (8 5 3 ) 5 3 817a i2x 2 22 2x 4yx2 x2x18x 2ii 4 (2 ) 2 (2 ) y2b y2 4y 0y(y 4) 0y 0 or 42x 0 (no solutions) or 2x 4x 25 3 2(1 3 )2 p(1 3) q5 3 2 4 3 6 p p 3 qp, q rational 5 3 4 3 p 3p 1and0 2 6 p qq 9 Solomon Press
PMTC11Answers - Worksheet DALGEBRAa 3x2 8x 3b x3 5x2 2x 1c 3x3 6x2 2x 7d x5 x4 8x3 5x2 4x 8e 3x3 7x2 2 x3 2x2 x 6 2x3 9x2 x 8f x5 3x4 x2 3 x4 2x3 3x 2 x5 2x4 2x3 x2 3x 5g 2x7 9x5 x3 x 3x6 4x3 x 5 2x7 3x6 9x5 5x3 5h 2x4 8x2 6 x4 3x3 8 3x4 3x3 8x2 14i 21 12x 3x2 6x3 10 15x 5x3 x3 3x2 3x 11j 6x3 30x2 12 6x3 3x2 3x 33x2 3x 12k 8x4 16x2 32x 8 10 6x 2x3 8x4 2x3 16x2 26x 182l 7x6 21x3 7x2 28 8x6 4x5 12x 28 x6 4x5 21x3 7x2 12xa 3y3 2y2 y 6b 3t 4 3t 3 12t 6 t 3t3 2t 4 4t 2 8 5t4 6t 3 4t 2 11t 14c x3 6x2 8 5x2 x 1 2x3 3x2 x 7 x3 4x2 2x 16d 6 2m 14m2 6m5 6 6m2 12m4 5m5 15m3 5m2 10 2 2m 13m2 15m3 12m4 11m5e 13 23 23 34u 1615u u2 u4 1 215u2 1412u 13u2 14u3u3 u4a 2x 3x2 x3 4 8x2 4x3 4 2x 5x2 3x3b x5 7x3 5x2 9x 2x4 8x3 6 6 9x 5x2 15x3 2x4 x5c 10x 8x2 2x4 14 21x2 7x4 14 10x 13x2 5x4d 8x2 2x3 x4 15 12x2 3x3 15 4x2 x3 x4e 3x3 9x2 x4 4x3 5x3 10x 10x 9x2 4x3 x4f 6x2 x3 5x4 14x 7x4 4 12x 4x2 4 2x 2x2 x3 2x4a LHS (3x 1)(x2 2x 4) 3x(x2 2x 4) (x2 2x 4) 3x3 6x2 12x x2 2x 4 3x3 5x2 10x 4 RHSb LHS (1 2x x2)(1 2x x2) (1 2x x2) 2x(1 2x x2) x2(1 2x x2) 1 2x x2 2x 4x2 2x3 x2 2x3 x4 1 4x2 4x3 x4 RHSc LHS (3 x)3 (3 x)(9 6x x2)3(9 6x x2) x(9 6x x2)27 18x 3x2 9x 6x2 x327 27x 9x2 x3 RHS Solomon Press
PMTC15Answers - Worksheet DALGEBRAa x(x2 5x 6) (x2 5x 6) x3 5x2 6x x2 5x 6 x3 6x2 x 6b 2x(x2 3x 7) 5(x2 3x 7) 2x3 6x2 14x 5x2 15x 35 2x3 11x2 29x 35c 4(2 5x x2) 7x(2 5x x2) 8 20x 4x2 14x 35x2 7x3 7x3 39x2 6x 8d e x2(2x2 x 9) 3(2x2 x 9) 2x4 x3 9x2 6x2 3x 27 2x4 x3 15x2 3x 27f 4x(x4 3x2 5x 2) (x4 3x2 5x 2) 4x5 12x3 20x2 8x x4 3x2 5x 2 4x5 x4 12x3 23x2 3x 2(3x 2)(3x 2)2 (3x 2)(9x2 12x 4)3x(9x2 12x 4) 2(9x2 12x 4)27x3 36x2 12x 18x2 24x 827x3 54x2 36x 8g x2(x2 3x 1) 2x(x2 3x 1) 5(x2 3x 1) x4 3x3 x2 2x3 6x2 2x 5x2 15x 5 x4 5x3 12x2 17x 5h x2(2x2 x 4) x(2x2 x 4) 3(2x2 x 4) 2x4 x3 4x2 2x3 x2 4x 6x2 3x 12 2x4 x3 3x2 7x 12i 3x2(2x2 4x 8) 5x(2x2 4x 8) 2(2x2 4x 8) 6x4 12x3 24x2 10x3 20x2 40x 4x2 8x 16 6x4 22x3 32x 16j x2(x2 2x 6) 2x(x2 2x 6) 6(x2 2x 6) x4 2x3 6x2 2x3 4x2 12x 6x2 12x 36 x4 4x3 8x2 24x 36k x3(2x4 x2 3) 4x2(2x4 x2 3) (2x4 x2 3) 2x7 x5 3x3 8x6 4x4 12x2 2x4 x2 3 2x7 8x6 x5 6x4 3x3 13x2 3l6page 2 6(3 x2 x3 2x4) 2x(3 x2 x3 2x4) x3(3 x2 x3 2x4) 18 6x2 6x3 12x4 6x 2x3 2x4 4x5 3x3 x5 x6 2x7 2x7 x6 3x5 14x4 5x3 6x2 6x 18a (p2 1)(2p2 11p 12)p2(2p2 11p 12) (2p2 11p 12)2p4 11p3 12p2 2p2 11p 122p4 11p3 10p2 11p 12b t(t 2 3t 5) 2(t 2 3t 5) t(t 2 t 7) 4(t 2 t 7) t 3 3t2 5t 2t 2 6t 10 t 3 t2 7t 4t 2 4t 28 2t 3 10t2 22t 38c 2x2(x2 x 4) 6(x2 x 4) 3x(4x3 2x2 x 6) (4x3 2x2 x 6) 2x4 2x3 8x2 6x2 6x 24 12x4 6x3 3x2 18x 4x3 2x2 x 6 14x4 4x3 19x2 13x 18d u(u3 4u2 3) 2(u3 4u2 3) 2u3(u2 5u 3) u(u2 5u 3) (u2 5u 3) u4 4u3 3u 2u3 8u2 6 2u5 10u4 6u3 u3 5u2 3u u2 5u 3 2u5 9u4 3u3 12u2 5u 9 Solomon Press
PMTC11a (x 1)(x 3)b (x 2)(x 5)c (y 1)(y 2)d (x 3)2e (y 1)(y 2)f (a 4)(a 2)g (x 1)(x 1)h (p 2)(p 7)j (m 2)(m 8)k (t 6)(t 3)lm (r 4)(r 4)n (y 7)(y 9)o (a 11)2p (x 12)(x 6)q (x 2)(x 13)r (s 8)(s 15)s (p 17)(p 3)t (m 10)(m 9)a (2x 1)(x 1)b (3p 1)(p 2)c (2y 3)(y 1)d (2 m)(1 m)e (3r 1)(r 1)f (5 y)(1 4y)g (3a 1)(a 4)h (5x 2)(x 2)ij (3s 1)2k (2m 5)(2m 5)lm (4u 1)(u 4)n (3p 4)(2p 1)o (8x 3)(x 2)p (6r 5)(2r 3)a (x 1)(x 3) 0x 1 or 3b (x 4)(x 2) 0x 4 or 2c (x 5)(x 1) 0x 5 or 1d x2 7x 8 0(x 1)(x 8) 0x 1 or 8e (x 5)(x 5) 0x 5 or 5f x2 x 42 0(x 6)(x 7) 0x 6 or 7g x2 3x 0x(x 3) 0x 0 or 3h (x 9)(x 3) 0x 9 or 3i23Answers - Worksheet EALGEBRAi(x 3)(x 5)(2x 1)(2x 3)x2 4x 60 0j x2 5x 14 0(x 10)(x 6) 0(x 2)(x 7) 0x 10 or 6k (2x 1)(x 1) 0 lx 12 or 1x 2 or 7(y 5)(y 8)(2 3y)(1 2y)x2 x 6x 12x2 7x 12 0(x 3)(x 4) 0x 3 or 4m 3x2 11x 4 0 n 2x2 3x 5 0o 4x2 23x 6 0 p 6x2 19x 10 0(3x 1)(x 4) 0(2x 5)(x 1) 0(4x 1)(x 6) 0(3x 2)(2x 5) 0x 4 or 13x 1 or 52x 14 or 6x 23 or 52q (2x 1)2 0x 12r 3x2 13x 12 0 s 4x2 20x 25 5 x t 6x2 21x 14x 6(3x 4)(x 3) 04x2 21x 20 06x2 35x 6 0x 443or 3(4x 5)(x 4) 0(6x 1)(x 6) 0x 4 or 54x 16 or 6a 2(y2 5y 6) 2(y 3)(y 2)b x(x2 x 2) x(x 1)(x 2)c p(p2 4) p(p 2)(p 2)d 3m(m2 7m 6) 3m(m 1)(m 6)e (a2 1)(a2 3)f (t 2 5)(t 2 2)g 4(3 5x 2x2) 4(3 x)(1 2x)h 3(2r2 3r 14) 3(2r 7)(r 2)i 2x(3x2 13x 4) j y2(y2 3y 18) 2x(3x 1)(x 4) y2(y 6)(y 3)k (m2 1)(m2 1) l p(p4 4p2 4) (m2 1)(m 1)(m 1) p(p2 2)2 Solomon Press
PMTC15Answers - Worksheet EALGEBRAa x2 3x 2 0(x 1)(x 2) 0x 1 or 2c x2 9 0(x 3)(x 3) 0x 3 or 3b x2 5x 6 0(x 3)(x 2) 0x 3 or 2yyy(0, 6)(0, 2)( 3, 0)(3, 0)xOO (1, 0) (2, 0)x(0, 9)( 3, 0) ( 2, 0) O xd x2 2x 0x(x 2) 0x 0 or 2e x2 10x 25 0(x 5)2 0x 5yyf 2x2 14x 20 02(x 2)(x 5) 0x 2 or 5y(0, 25)(0, 0)O(0, 20)(2, 0) xOOg x2 5x 4 0x2 5x 4 0(x 1)(x 4) 0(5, 0)(5, 0)xh 2 x x2 0x2 x 2 0(x 1)(x 2) 0x(2, 0)i2x2 3x 1 0(2x 1)(x 1) 0x 12 or 1x 1 or 2x 1 or 4yyy(0, 2)O(1, 0)(4, 0)x(0, 1)( 1, 0)(0, 4)(2, 0)OxOk 3 8x 4x2 0(2x 1)(2x 3) 0x 12 or 32j 2x2 13x 6 0(2x 1)(x 6) 0x 6 or 12l(1, 0)( 12 , 0)x2 7x 4x2 04x2 7x 2 0(4x 1)(x 2) 0x 14 or 2yy(0, 6)( 6, 0)O( , 0)12y(0, 3)x(0, 2)O((1232, 0), 0) Solomon Pressx( 14 , 0)O(2, 0)xpage 2
PMTC1Answers - Worksheet EALGEBRAm 5x2 17x 6 0(5x 2)(x 3) 0x 25 or 3n 6x2 7x 2 06x2 7x 2 0(2x 1)(3x 2) 012x yor23y( 12 , 0)O6o 6x2 x 5 0(6x 5)(x 1) 0x 1 or 56y(0, 6)O(3, 0)( 25 , 0)a x2 5x 4 0(x 1)(x 4) 0x 1 or 4x(23, 0)x( 1, 0) O(0, 2)b x2 10 3xx2 3x 10 0(x 2)(x 5) 0e 5 4x x2 0x2 4x 5 0(x 1)(x 5) 0x 1 or 5f x 6 x(x 4)x 6 x2 4xx2 5x 6 0(x 2)(x 3) 0x 2 or 34x4 7x2 2 0j 2x(x 2) 3 x(4x2 1)(x2 2) 02x2 4x 3 xx2 2 (no sol’s) or 14 2x2 5x 3 0x 12( 56 , 0)x(0, 5)c x(2x2 x 3) 0 d 10x2 x4 9x(2x 3)(x 1) 0x4 10x2 9 0x 1, 0 or 32(x2 1)(x2 9) 0x 2 or 5ipage 3x2 1 or 9x 1 or 3g (x 5)(x 3) 3x2 8x 15 3x2 8x 12 0(x 6)(x 2) 0x 6 or 2h x4 4 3x2x4 3x2 4 0(x2 1)(x2 4) 0x2 1 (no sol’s) or 4x 2k x(2x 1) 2(x 3) l2x2 x 2x 62x2 x 6 07 3x(x 2) 2(x 2)7 3x2 6x 2x 43x2 8x 3 0(2x 1)(x 3) 0(2x 3)(x 2) 0(3x 1)(x 3) 0x 3 orx x 3 or12 Solomon Press32or 213
PMTC11Answers - Worksheet FALGEBRAa (x 1)2 1 4 (x 1)2 3b (x 1)2 1 4 (x 1)2 3e (x 2)2 4 8 (x 2)2 4f (x 4)2 16 5 g (x 6)2 36 30 h (x 5)2 25 25 (x 4)2 21 (x 6)2 6 (x 5)2i (x 3)2 9 9 (x 3) 18j (x 2)2 4 18 k (x (x 2) 1422m (x 9)2 81 100 n (x (x 9) 19 (x 2q (x (x 23 2)23 2)2 94 114c (x 2)2 4 1 (x 2)2 31 2)21 2)2 1434 (x 12 (x 5 r (x 112 )2 121 37 s (x 41 2)31 2)311 2)2 9434 3 l274 (x 7 2)27 2)2 1 2)41 2)4 (x 14 (x 1989 1 t (x 1 2)21 2)2 (x o (x 92 )2 814 20 p (x 9 2)2 (x 3 2)23 2)2d (x 3)2 9 (x 11454494574 2116516 14a 2[x2 2x] 3b 2[x2 4x] 7c 3[x2 2x] 3d 4[x2 6x] 11222 2[(x 1) 1] 3 2[(x 2) 4] 7 3[(x 1) 1] 3 4[(x 3)2 9] 11 2(x 1)2 1 2(x 2)2 15 3(x 1)2 4(x 3)2 25e [x2 2x] 5f [x2 10x] 1 g 2[x2 x] 1h 3[x2 3x] 5222 [(x 1) 1] 5 [(x 5) 25] 1 2[(x 12 ) 14 ] 1 3[(x 32 )2 94 ] 5 (x 1)2 4i 3[x2 8x] 48 3[(x 3(x 4) 3(x 4[(x 4(x 23x] 723 2) 169 ] 743 2) 3744 2(x j 3[x2 5x] 3[(x 4)2 16] 48m 4[x2 3 (x 5)2 265 2) 25425 2) 75421 2)2 3(x 32k 5[x2 8x] 70]n 2[x2 2x] 1l 5(x 4) 10 o 3[x2 23x] 4p 13 3[(x 13 )2 19 ] 4 13 2(x 1)2 1 3(x 13 133745x] 225 2252[(x 4 ) 162(x 54 )2 98 2[(x 1)2 1] 11 2)3 2[x2 5[(x 4)2 16] 7023 2)2] 23x] 142[(x 34 )2 169 ](x 34 )2 167[x2 14a (y 2)2 4 2 0 b (p 1)2 1 2 0 c (x 3)2 9 4 0 d (r 5)2 25 7 0(y 2)2 2(p 1)2 3(x 3)2 5(r 5)2 18p 1 3y 2 2x 3 5r 5 18 3 2y 2 2e (x 1)2 1 11p 1 3x 3 5f (a 6)2 36 18 0 g (m 3 2)23 2)2 94 1 0 h (t (x 1)2 12(a 6)2 54(m x 1 12 2 3a 6 54 3 6m 32 x 1 2 3a 6 3 6m 12(3 Solomon Pressr 5 3 2 7 2)27 2)254(t 52t 72t 125) 494134 9 0132(7 13 )
PMTC1Answers - Worksheet FALGEBRAi7 2)27 2)2(u (u 494 225415 2 44 j y2 2y (y 1)2 1 12u 72 152y 1 12u 11 or 4y 1 72 m m2 m 1(m 1 2)21 2)2(m 1454 12 m 12(1 x2 7x 1525)(x 7 2) 2(x 7 2)2x 0 12 2494494 0(x 3)2 9 (p 3)2 43(x 3)2 272p 3 23 23 3x 3 2723x 3 1 2)61 2)6(t 494 0(t 07292(p 3)2 9 233p 3 2x2 6x l23t 16t 16 p a2 131361336 (a 13(a 3292 32 667a 2 27 249) 1647 2) 17416136a 74( 1 13 )a 140 2 0174 (7 17 )a y (x 1)2 1 7y (x 1)2 6y 6 at x 1, minimumb y (x 1)2 1 3c y (x 3)2 9 12y (x 1) 4y (x 3)2 8y 4 at x 1, minimumy 8 at x 3, minimumd y (x 5)2 25 35e y [x2 4x] 4y [(x 2) 4] 4y (x y 10 at x 5, minimumy (x 2) 8y 8 at x 2, maximumy 2g y 2[x2 4x] 5y 2[(x 2)2 4] 53 2)23 2)2f y (x y (x 5) 1022h y 3[x2 2x]y 3[(x 1)2 1]i174y (x y 3 at x 2, minimumy 3 at x 1, maximumy y 4(x y 0 at x3 2)2 32y 4(x , minimuma y (x 2)2 4 3y (x 2)2 1minimum (2, 1)5 2)2 33l5345 2)2 minimum534y 2[x2 x] 17y 2[(x 12 )2 14 ] 17y 3521 2)2 352at x 12 , maximumb y (x 1)2 1 24y (x 1)2 25minimum ( 1, 25)c y (x 1)2 1 5y (x 1)2 4minimum (1, 4)yyy(0, 3)Ox2at x 52 , maximumy 2(x y 33 at x 52 , minimum 9 4174 32 ,y [x2 5x] 7y [(x 52 )2 254 ] 7y 3(x 1)2 3k y 4[x2 5x] 8y 4[(x 52 )2 254 ] 8 at x y 2(x 2)2 3j y 4[x2 3x] 9y 4[(x 32 )2 94 ] 9512n 4x2 28x 49 0 o t2 13 t m 12k p2 6p 233 0(y 1)2 u 412page 2(0, 5)(1, 4)O(2, 1)x( 1, 25)(0, 24) Solomon PressOx
PMTC1Answers - Worksheet FALGEBRAd y (x 4)2 16 30y (x 4)2 14minimum ( 4, 14)e y (x 1)2 1 1y (x 1)2minimum ( 1, 0)ypage 3f y [x2 2x] 8y [(x 1)2 1] 8y (x 1)2 9maximum (1, 9)yy(0, 30)(1, 9)(0, 8)( 4, 14)(0, 1)Ox( 1, 0)g y [x2 8x] 7Oxh y [x2 4x] 7iy [(x 4) 16] 7y [(x 2) 4] 7y (x 4)2 9y (x 2)2 3maximum (4, 9)maximum ( 2, 3)2O2yxy (x 5 2) 2542y (x 52 )2 94minimum ( 52 , 94y 4)y(4, 9)( 2, 3)OOx(0, 7)x(0, 7)j y (x y (x 3 2)23 2)2O 9434minimum ( 32 ,k y 4[x2 2x] 3 334)y 4(x 1)2 1y 2(x 2)2 7minimum ( 1, 1)maximum (2, 7)y(0, 3)O)(2, 7)x( 1, 1)Oxx] 1n y 4[x2 5x] 25y 2[(x 14 )2 161y 2(x 14 )2 98maximum ( 14 , 98 )y 4[(x 52 )2 254y 4(x 52 )2minimum ( 52 , 0)12] 1y)o y 3[x2 ] 25y 3[(x y 3(x x] 22 2) 9432 2) 233minimum ( 23 ,y(0, 1)43Oxa (x 2 2 )2 8 5 (x 2 2 )2 3b x 2 2O (23] 2)y(0, 25)(0, 2)(6x(0, 15)m y 2[x2 98x, 94 )y 2[x2 4x] 15yO( 14 ,52y 2[(x 2)2 4] 15(0, 3)34l(y 4[(x 1)2 1] 3y( 32 ,(0, 4)52, 0)7xOx2 2kx 3 0(x k)2 k2 3 0(x k)2 k2 3x k k2 3x k Solomon Pressk2 323,23)x
PMTC11ax2 bx c 0x2 ba(x b2a)2 (x b2a)2 x 2Answers - Worksheet GALGEBRAx b2aca 0b24a2b24a 2 ca 0 ca b 2 4ac4a 2b 2 4ac2ax b2aa x 4 16 42x b 2 4ac2a b b 2 4ac2ab t t 8 64 16 2 8 4 5 23t 4 2 5 18 324 242f m2 5m 5 0 18 10 32m 5 25 202a 9 5 3m 12a i4a 2 4 2 32x 2 e a b 2 4acy 1 1 20 2y 12 (1 y 20 400 364220 62r g x x 11 121 108212x 3 9 164x 3 54k p p n 6u2 4u 1 0( 7 37 )l 6 36 244u 6 2 34u 12( 3 3)t2 14t 14 0t 14 196 562t 14 6 72t 7 3 7o 3y2 18y 4 0p 4x2 8x 11 0 14 196 362u 4 16 2412y 18 324 486x 8 64 1768r 14 2 582u 4 2 1012y 18 2 936x 8 4 158u 1658( 2 10 )y 3 2x2 8x 3 0x 2 4 22r r 7 3h u ( 11 13 ) 7 49 12616 2 4 282r 1 2 2y 7 or 13x 12 or 2m r2 14r 9 0d r (5 3 5 )j 2x2 3x 2 021 )c y 8 64 244 (2 12 8 2 104 2 10 , 0) and (2 12121010 , 0) Solomon Press1393x 1 1215
PMTC1Answers - Worksheet GALGEBRA4a b2 4ac 0b b2 4ac 05abpage 2c b2 4ac 0cdxxxx6a b2 4ac 32b b2 4ac 11 real and distinct not reale b2 4ac 0 real and equali not reald b2 4ac 24 real and distinctf b2 4ac 13g b2 4ac 53h b2 4ac 7 real and distinct real and distinct not realb2 4ac 4j b2 4ac 11 real and distinct not realm b2 4ac 7c b2 4ac 4 not realn b2 4ac 139 real and distinct7equal roots b2 4ac 01 4p 0p 148repeated root b2 4ac 04q2 4q 04q(q 1) 0q 0 q 19x2 rx 2x 4 0 has equal roots b2 4ac 0(r 2)2 16 0r2 4r 12 0(r 2)(r 6) 0r 2 or 6k b2 4ac 0 real and equallo b2 4ac p b2 4ac 1375116 real and distinct Solomon Pressb2 4ac 3 not real not real
PMTC11Answers - Worksheet HALGEBRAa 2x(10 x 3x2) 2x(2 x)(5 3x)b 2x(2 x)(5 3x) 0x 2, 0 or 532a AB 2 (6 2)2 (k 1)2 64 k2 2k 1 k2 2k 65b k2 2k 65 102 100k2 2k 35 0(k 5)(k 7) 0k 5 or 73a x2 5 4x4a y 2[x2 x2 4x 5 0 (x 1)(x 5) 0 x 1 or 512b 3 5x 2x2 02x2 5x 3 0(2x 1)(x 3) 0, x 3 oror 42(0, 3)( 3, 0)x 5 2 50 484 5 2 984 5 2 7 24 3 2 or12yy 3 5x 2x5] 3 turning point is ( 54 , 498 )b 9 (5 x) 2x(5 x)2x2 9x 4 0(2x 1)(x 4) 0x 5x] 325 225 2[(x 4 ) 16 2(x 54 )2 4986( 12 , 0)Oa y 3[x2 3x] k 3[(x 3(x 3 2)2 274b y-coord of P k 2 274 174 k 11 curve is y 3x 9x 11 coordinates of Q are (0, 11)7y2 10y 16 0(y 2)(y 8) 0y 2x 2 or 8x 1 or 38equal roots b2 4ac 04 4k(3 2k) 02k2 3k 1 0(2k 1)(k 1) 0k 12 or 19a f(x) [x2 4x] 310a x (x 2) 7b turning point is (2, 7)2 5 25 12616(5 13 )b x(x 1) 3(x 2)x2 4x 6 0c (x 2)2 7 2x 4 16 242 2 10(x 2)2 5x 2 5 Solomon Press] k322 [(x 2)2 4] 394 k x-coordinate of P 123 2)2x 4 2 102
PMTC111Answers - Worksheet HALGEBRAa (x 2k)2 4k2 6 012a x2 6x 3 0(x 2k)2 4k2 6x x 2k 4k 2 6b k 3 x 6 36 613b y(2y2 y 15) 0y(2y 5)(y 3) 0y 3, 0 or 52y px 1 or p14a f(x) 2[x2 3x] 5 2[(x 32 )2 94 ] 5 2(x yy (x 1)(x p)( 1, 0) O(0, p)3 2)2 12 A 2, B 32 , C 12b minimum value of f(x) 12x[ q 0]y (x q)2O2(p, 0)y q2x q(0, q2)156 4 32 30a x 0 y 0 b x 0 y 0 y6 36 122 3 2 3x 2k 4k 2 6 6 page 2( q, 0)x1a x 3 ( x 3 )2 t 2116b let t x 3 2t 2 t 6 0(2t 3)(t 2) 0t 2 or 32but x t 3 x 8 ora (k 4)2 16 20 (k 4)2 4b x2 kx 2k 5 0discriminant b2 4ac k2 4(2k 5)278 k2 8k 20using a (k 4)2 4for all real k, (k 4)2 0 discriminant 0 real and distinct roots for all real k17a (x2 2x 3)(x2 3x 4) x2(x2 3x 4) 2x(x2 3x 4) 3(x2 3x 4) x4 3x3 4x2 2x3 6x2 8x 3x2 9x 12 x4 x3 13x2 x 12b (x2 2x 3)(x2 3x 4) 0(x 3)(x 1)(x 1)(x 4) 0x 3, 1, 1 or 4 Solomon Press
PMTC11Answers - Worksheet IALGEBRAa 3x 2x 1b x 6 12x 4c 2x 6 3 4xx 1x 4x 12 x 1, y 3 x 4, y 2 x 12 , y 5e 2x 4y 22 02x 3y 1 0subtracting7y 21 0y 3f 6x 6y 8 015x 6y 15 0adding21x 7 0x 13d subtractingy 4 0y 4 x 7, y 4 x 5, y 32a x 2 x2 4x2 x 6 0(x 2)(x 3) 0x 2 or 3 ( 2, 0) and (3, 5)3a subtractingx2 x 2 0(x 1)(x 2) 0x 1 or 2b 4x 11 x2 3x 1x2 x 12 0(x 3)(x 4) 0x 3 or 4b adding2x2 7x 3 0(2x 1)(x 3) 0x 12 or 3x 1, y 4 x orx 2, y 7orx 3, y 6 orx 3, y 4x 1, y 81213, y 53c 2x 1 2x2 3x 72x2 x 6 0(2x 3)(x 2) 0x 2 or 32 ( 3, 1) and (4, 27) d y 2x 10sub.x2 2x(2x 10) 15 0x2 4x 3 0(x 3)(x 1) 0x 3 or 1 x ( 2, 5) and ( 32 , 2)c y 2x 5subx2 (2x 5)2 25x2 4x 0, y 72x(x 4) 0x 0 or 4 x 0, y 5orx 4, y 3e y 1 xf y 1 xsub.sub.x2 2x(1 x) (1 x)2 73x2 x (1 x)2 0x2 42x2 x 1 0x 2(2x 1)(x 1) 0 x 2, y 3x 1 or 12orx 2, y 1g y 4 xh x 2ysub.sub.222x x(4 x) (4 x) 22 (2y)2 4y y2 0 orix 1, y 2x 12 , y 12y 3 32 xsub.x2 x(3 32 x) 4x2 2x 3 0(x 1)(x 3) 0x 1 or 33y2 4y 0y(3y 4) 0y 0 or 43x2 6x 8 0(x 2)(x 4) 0x 2 or 4 or or orx 1, y 5x 3, y 1x 0, y 0x 83 , y 43 Solomon Pressx 2, y 0x 4, y 3
PMTC1Answers - Worksheet IALGEBRAj y 2x 3k y 2x 7lsub.sub.2x2 (2x 3) (2x 3)2 8x2 x(2x 7) (2x 7)2 13x2 7x 10 0x2 7x 12 0(x 2)(x 5) 0(x 3)(x 4) 0x 2 or 5x 3 or 4 or orx 2, y 1x 5, y 7x 3, y 1x 4, y 14o x 3y 17sub.(3y 17)2 (3y 17) 2y2 52 02x2 5x 2 0(2x 1)(x 2) 0x 12 or 2y2 9y 20 0(y 4)(y 5) 0y 4 or 5 x 2, y 6 x x 5, y 4orx 2, y 4orx 2, y 1orx 2, y 51y12, y 54b y x 5a subtracting 2y 1 0c y 7 4xsub.sub. 1 2y2 y 0x(x 5) 63x2y2 y 1 0(2y 1)(y 1) 0y 1 or 12x2 5x 6 0(x 1)(x 6) 0x 1 or 63 2x(7 4x) 4x 08x2 10x 3 0(4x 3)(2x 1) 0 x 5, y 1 x 1, y 6x orx 4, y orx 6, y 1 x orx 125 x x2 3x 2x2 2x 3 0(x 1)(x 3) 0x 1 or 3P and Q are the points ( 1, 6) and (3, 2)PQ2 (3 1)2 (2 6)2PQ 7x 1, y 2x 52 , y 52y2 10y 24 0(y 6)(y 4) 0y 6 or 4 5y 5 3xsub.x2 5x (5 3x)2 02x2 7x 5 0(2x 5)(x 1) 0x 1 or 52 orm x 2y 10n y 32 x 2sub.sub.222x2 x 4( 32 x 2) 63(2y 10) y(2y 10) y 36page 26 2(7 4x) 4 03x 1 (32)2y(23)x 2 (22)1 y B integer B 5 A 2B 9(1)and 2B2 9B 5 0A 1, B 5 Solomon Pressor341234,y 5,y 4 x 1 4y 3x 6 2 2y6x 16 4y6x 16 x 1x 3x 3, y 1232 4 2AB A 3 2B 3 6 9 3 1A and B integers AB 6 1(2) A 2B 9sub. (1)B(2B 9) 6 1(2B 1)(B 5) 0B 12 or 512(2)
PMTC11a 2x 6x 3b 3x 21x 7e 5x 15fi23Answers - Worksheet JALGEBRA13x 1c 2x 8x 4d 3x 36x 12g 9x 54h 3x 4x 3x 3x 6x 14j 4x 10k 2 3xx 52x x 43l5 12xx 1023a y 7b 4p 2p 12c 6 2xx 3d 2a 4a 2e 15 3uu 5f 2b 9b 92g 3x 18x 6h y 13i 20 4pp 5j r 2 6r 8k 3 6t t 47 7tt 1l6 2x 24 4x6x 18x 3m 7y 21 6y 2 0y 23n 20 8x 21 6x 1 2xx 12o 12u 3 5u 15 97u 3u 73a (x 1)(x 3) 01 23 1 x 3e (x 1)(x 5) 01x2 2x 63 0(x 9)(x 7) 0 927 x 9 or x 7c (x 5)(x 3) 0 5 4 5 x 3f x2 4x 12 0(x 6)(x 2) 0g (x 7)(x 3) 02 x 6 or x 2j (x 6)(x 5) 0 6 5 x 6 or x 5 7d x2 2x 8 0(x 4)(x 2) 0 3 2 x 2 65 x 1 or x
Solomon Press C1 ALGEBRA Answers - Worksheet B 1 a 64 b 216 c 1 d 625 e 243 f 1 16 g 8 27 h 1 64 i 4 2 3 16 9 or 7 9 1 j 3 4 2 81 16 or 1 16 5 k 0.000 01 l 0.008 2 a 28 b 27 9c 20 14 d 24 e 2 f 2 3 a 8p7 b x10 c 6n5 d y12 3e 2b 3f p4q g x y h 6r2s3 i 2x3y7 j 4a5b8 k 1253s6 100r r2s2 l 15p3q
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Week 3: Spotlight 21 Week 4 : Worksheet 22 Week 4: Spotlight 23 Week 5 : Worksheet 24 Week 5: Spotlight 25 Week 6 : Worksheet 26 Week 6: Spotlight 27 Week 7 : Worksheet 28 Week 7: Spotlight 29 Week 8 : Worksheet 30 Week 8: Spotlight 31 Week 9 : Worksheet 32 Week 9: Spotlight 33 Week 10 : Worksheet 34 Week 10: Spotlight 35 Week 11 : Worksheet 36 .
