Edexcel AS and A Level Modular Mathematics: Core Mathematics 1

By David Macpherson, Greg Altwood

Edexcel and a degree Modular arithmetic C1 gains:

•Student-friendly labored examples and options, major as much as a wealth of perform questions.
•Sample examination papers for thorough examination training.
•Regular assessment sections consolidate studying.
•Opportunities for stretch and problem awarded during the direction.
•‘Escalator section’ to step up from GCSE.

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Unϩ1 ϭ 1. 2Un (or Un ϭ (1. 2)nϪ1) mathematics sequences are: a a ϭ five, d ϭ 6 b a ϭ three, d ϭ three d a ϭ 10, d ϭ Ϫ5 a eighty one b 860 b 5050 32 a £13 780 c £42 198 a a ϭ 25, d ϭϪ3 b Ϫ3810 a 26 733 b fifty three 467 a five b forty five a Ϫ4k ϩ 15 b Ϫ8k2 ϩ 30k Ϫ 30 c Ϫᎏ14ᎏ, four b 1500 m a U2 ϭ 2k Ϫ four, U3 ϭ 2k2 Ϫ 4k Ϫ four b five, Ϫ3 a £2450 b £59 000 c d ϭ 30 a dϭ5 b fifty nine 11k Ϫ nine 18 b ᎏᎏ three c 1. five d 415 Chapter 7 solutions workout 7A 1 2 a i iv b 6 a i iv b eight workout 7G 7 6. 01 ii v nine eight. 01 6. five hϩ6 ii v iii 6. 1 eight. five 8ϩh iii eight. 1 1 2t Ϫ three 2 2␲ three Ϫ12tϪ2 four nine.

E. Unϩ1 ϭ Un ϩ 6 (or Un ϭ 6n Ϫ 1) b upload three to the former time period, i. e. Unϩ1 ϭ Un ϩ three (or Un ϭ 3n) c Multiply the former time period by means of three, i. e. Unϩ1 ϭ 3Un (or Un ϭ 3nϪ1) d Subtract five from the former time period, i. e. Unϩ1 ϭ Un Ϫ five (or Un ϭ 15 Ϫ 5n) e The sq. numbers (Un ϭ n2) f Multiply the former time period by means of 1. 2, i. e. Unϩ1 ϭ 1. 2Un (or Un ϭ (1. 2)nϪ1) mathematics sequences are: a a ϭ five, d ϭ 6 b a ϭ three, d ϭ three d a ϭ 10, d ϭ Ϫ5 a eighty one b 860 b 5050 32 a £13 780 c £42 198 a a ϭ 25, d ϭϪ3 b Ϫ3810 a 26 733 b fifty three 467 a five b forty five a Ϫ4k ϩ 15 b Ϫ8k2 ϩ 30k Ϫ 30 c Ϫᎏ14ᎏ, four b 1500 m a U2 ϭ 2k Ϫ four, U3 ϭ 2k2 Ϫ 4k Ϫ four b five, Ϫ3 a £2450 b £59 000 c d ϭ 30 a dϭ5 b fifty nine 11k Ϫ nine 18 b ᎏᎏ three c 1.

1 eight. five 8ϩh iii eight. 1 1 2t Ϫ three 2 2␲ three Ϫ12tϪ2 four nine. eight five 1 Ϫ 5rϪ2 6 Ϫ12 ϩ 8t 7 10 Ϫ 2x workout 7H a y ϩ 3x Ϫ 6 ϭ zero b 4y Ϫ 3x Ϫ four ϭ zero c 3y Ϫ 2x Ϫ 18 ϭ zero d e y ϭ 12x ϩ 14 f 2 a 7y ϩ x Ϫ forty eight ϭ zero b yϭx y ϭ 16x Ϫ 22 17y ϩ 2x Ϫ 212 ϭ zero three (129ᎏᎏ, 189ᎏᎏ) four y ϭ Ϫx, 4y ϩ x Ϫ nine ϭ zero; (Ϫ3, three) y ϭ Ϫ8x ϩ 10, 8y Ϫ x Ϫ a hundred forty five ϭ zero 1 workout 7B 1 7 x6 Ϫ four ᎏ1ᎏ three 7 Ϫ3xϪ4 x eight x7 2 2 ᎏ three Ϫ four ᎏ three five ᎏ1ᎏ four eight Ϫ4xϪ5 x 10 Ϫ5xϪ6 eleven Ϫ1ᎏ3ᎏ x thirteen Ϫ2xϪ3 sixteen 9x8 14 1 17 5x4 Ϫ four ᎏ three three four x3 6 ᎏ1ᎏ three nine Ϫ2xϪ3 2 x Ϫ ᎏ3 12 Ϫ1ᎏ2ᎏ x Ϫ three ᎏ 2 five workout 7I 15 3x2 18 3x2 1 four, 1134ᎏᎏ, 1722ᎏ57ᎏ 2 zero, Ϯ2͙2 ෆ three (Ϫ1, zero) and (12ᎏ3ᎏ, 91ᎏ2ᎏ37) workout 7C 1 a 4x Ϫ 6 b x ϩ 12 d 16x ϩ 7 e four Ϫ 10x 2 a 12 b 6 c 7 d 21ᎏ2ᎏ e Ϫ2 f three four, zero four (Ϫ1, Ϫ8) five 1, Ϫ1 6 6, Ϫ4 five (2, Ϫ13) and (Ϫ2, 15) nine 6 a 1 Ϫ ᎏᎏ2 b x four x ϭ Ϯ3 7 x ϭ four, y ϭ 20 eight workout 7D 1 four 2, 2ᎏ23ᎏ c 8x a 4x3 Ϫ xϪ2 b ϪxϪ3 c Ϫx three three ᎏᎏ 2 1 x Ϫ ᎏ2 ϩ 2x 1 1 dy ᎏ Ϫᎏ nine a ᎏᎏ ϭ 6x 2 Ϫ 32ᎏᎏ x 2 b dx 1 ᎏ Ϫ ϭ ᎏ12ᎏ x 2 (12 Ϫ 3x) Ϫ ᎏ2 ϭ 32ᎏᎏ x 1112ᎏᎏ 2 a nil b three a (212ᎏᎏ, Ϫ614ᎏᎏ) b (4, Ϫ4) and (2, zero) c (16, Ϫ31) d (12ᎏᎏ, four) (Ϫ12ᎏᎏ, Ϫ4) three Ϫ ᎏ2 three ᎏ 2 1 Ϫ ᎏ2 10 a x ϩ x Ϫ x 1 ᎏ 2 three ᎏᎏ 2 (4 Ϫ x) 1 Ϫ ᎏ2 1 ᎏᎏ 2 (4, sixteen) b 1ϩ x ϩ x Ϫ1 three Ϫ ᎏ2 c 4ᎏ11ᎏ6 workout 7E 1 1 a x Ϫ ᎏ2 b Ϫ6xϪ3 d four ᎏᎏ three f Ϫ ᎏ3 1 ᎏᎏ three x Ϫ 2x three 2 x 2 Ϫ4 1 ᎏᎏ 2 ϩ x Ϫ xϪ2 g Ϫ3xϪ2 5x ϩ 32ᎏᎏ x Ϫ 1 ᎏ 2 h three ϩ 6xϪ2 three x2 Ϫ 2 x ϩ 2 j l 24x Ϫ eight ϩ 2xϪ2 a 1 b 29ᎏᎏ c Ϫ4 workout 7F 1 24x ϩ three, 24 2 15 Ϫ 3xϪ2, 6xϪ3 three nine ᎏᎏ 2 four 30x ϩ 2, 30 five Ϫ3xϪ2 Ϫ 16xϪ3, 6xϪ3 ϩ 48xϪ4 1 x Ϫ ᎏ2 1 Ϫ ᎏ2 1 ᎏᎏ 2 three ᎏ 2 i e Ϫ6x 2 c ϪxϪ4 ϩ 6xϪ3, Ϫ94ᎏᎏ x three Ϫ ᎏ2 Ϫ 18xϪ4 okay 12x3 ϩ 18x2 d four eleven 6x2 ϩ 12ᎏᎏ x 1 Ϫ ᎏ2 Ϫ 2xϪ2 10 2300␲ 12 ᎏᎏ, ᎏᎏ three 27 14 a ϭ 1, b ϭ Ϫ4, c ϭ five 15 a 3x2 Ϫ 10x ϩ five b i 1 ᎏᎏ three ii y ϭ 2x Ϫ 7 sixteen y ϭ 9x Ϫ four and 9y ϩ x ϭ 128 17 a (45ᎏᎏ, Ϫ25ᎏᎏ) b 1 ᎏᎏ five iii 72ᎏᎏ͙5 ෆ Chapter eight solutions workout 8A workout 8D 1 ᎏᎏ 6 1 y ϭ x6 ϩ c 2 y ϭ 2 x5 ϩ c three yϭx ϩc four yϭx three five y ϭ 2x three ᎏᎏ five ϩc Ϫ2 Ϫ1 1 ϩc five ᎏ three 6 yϭ x ϩc three ᎏ 7 y ϭ 8ᎏ3ᎏ x 2 ϩ c eight y ϭ Ϫ2ᎏ7ᎏ x7 ϩ c nine y ϭ ᎏ12ᎏ x6 ϩ c 10 y ϭ ϪxϪ3 ϩ c 1 ᎏ eleven y ϭ 2x 2 ϩ c thirteen y ϭ 4x 1 Ϫ ᎏ2 12 y ϭ Ϫ10x 1 Ϫ ᎏ2 2 ϩc four ᎏ 14 y ϭ 9ᎏ2ᎏ x three ϩ c ϩc 15 y ϭ 3x12 ϩ c three sixteen y ϭ 2xϪ7 ϩ c 1 ᎏ three 17 y ϭ Ϫ9x ϩ c 18 y ϭ Ϫ5x ϩ c 19 y ϭ 3x ϩ c 20 y ϭ 1ᎏ3ᎏ0 x0.

Eighty two or x ϭ zero. 177 a a ϭ Ϫ4, b ϭ Ϫ45 b x ϭ four Ϯ 3͙5 ෆ a (x Ϫ 3)2 ϩ nine b P is (0, 18), Q is (3, nine) c x ϭ three ϩ four ͙2 ෆ okay ϭ 6, x ϭ Ϫ1 (same root) a a ϭ five, b ϭ eleven b discriminant < zero so no genuine roots c ok ϭ 25 d y 25 Ϫ5 zero 15 a a ϭ 1, b ϭ 2 b y 22 a unique genuine roots, determinant > zero, so k2 Ϫ 4k Ϫ 12 > zero b okay < Ϫ2 or okay > 6 23 zero < ok < ᎏ89ᎏ 24 a p2 Ϫ 8p Ϫ 20 > zero b p < Ϫ2 or p > 10 ෆ) (Ϫ3 Ϯ͙13 c x ϭ ᎏᎏ 2 25 a x(x Ϫ 2)(x ϩ 2) b y Ϫ2 zero y c Ϫ1 26 x 2 zero 1 three x a y x (3, 2) zero 2 four x three (2, zero) (4, zero) and (3, 2) sixteen 17 18 19 20 21 x zero c discriminant ϭ Ϫ8 ෆ okay < 2͙3 ෆ d Ϫ2͙3 y ϭ four, x ϭ Ϫ2 or y ϭ Ϫ2, x ϭ four a x2 ϩ four x Ϫ eight ϭ zero ෆ, y ϭ Ϫ6 Ϯ 2͙3 ෆ b x ϭ Ϫ2 Ϯ 2͙3 x ϭ 2, y ϭ Ϫ1 or x ϭ Ϫᎏ13ᎏ, y ϭ Ϫᎏ13ᎏ7 a x > ᎏ14ᎏ b x < ᎏ12ᎏ or x > three c ᎏ14ᎏ < x < ᎏ12ᎏ or x > three a 0 ᎏ53ᎏ a x ϭ ᎏ72ᎏ, y ϭ Ϫ2, x ϭ Ϫ3, y ϭ eleven b x < Ϫ3 or x > 3ᎏ12ᎏ b y zero 1 2 (1 12 , Ϫ2) (1, zero) (2, zero) and (112ᎏᎏ, Ϫ2) 27 a x Review workout 1 solutions 30 a y zero three x Ϫ2 (0, zero) and (3, zero) b 6 1 x four (1, zero) (4, zero) and (0, 6) c y three zero 2 eight x (2, zero) (8, zero) and (0.

E. Unϩ1 ϭ Un ϩ 6 (or Un ϭ 6n Ϫ 1) b upload three to the former time period, i. e. Unϩ1 ϭ Un ϩ three (or Un ϭ 3n) c Multiply the former time period by means of three, i. e. Unϩ1 ϭ 3Un (or Un ϭ 3nϪ1) d Subtract five from the former time period, i. e. Unϩ1 ϭ Un Ϫ five (or Un ϭ 15 Ϫ 5n) e The sq. numbers (Un ϭ n2) f Multiply the former time period by means of 1. 2, i. e. Unϩ1 ϭ 1. 2Un (or Un ϭ (1. 2)nϪ1) mathematics sequences are: a a ϭ five, d ϭ 6 b a ϭ three, d ϭ three d a ϭ 10, d ϭ Ϫ5 a eighty one b 860 b 5050 32 a £13 780 c £42 198 a a ϭ 25, d ϭϪ3 b Ϫ3810 a 26 733 b fifty three 467 a five b forty five a Ϫ4k ϩ 15 b Ϫ8k2 ϩ 30k Ϫ 30 c Ϫᎏ14ᎏ, four b 1500 m a U2 ϭ 2k Ϫ four, U3 ϭ 2k2 Ϫ 4k Ϫ four b five, Ϫ3 a £2450 b £59 000 c d ϭ 30 a dϭ5 b fifty nine 11k Ϫ nine 18 b ᎏᎏ three c 1.

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