Mathematics (9-1) - iGCSE 2018-20 Year 09 Unit 02 Answers 2 - Prior knowledge check 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 2 - Prior knowledge check 1. a. 6 b. 5 c. 6 2. a. 12 b. -2 c. -11 e. 16f. 81 3. a. b. c. d. 10 4. a. 2x b. y2
c. 2w d. t e. 5 f. 2z 5. a. p4 b. c2d2 c. 14m2 d. -18f2 e. 36x3 f. y 6. a. 32b. 20 c. 37 d. 1 Page Page 627 627 d. 22 d. 8 2 - Prior knowledge check 2.1 2.1 Algebraic Algebraic Indices Indices 7. 8. 9. 10. 11. 12. 13. 14. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences
Expanding Equations Formulae Sequences Sequences Expanding 16 a. 7x +21 b. 2x 6 +21 d. 18x 9y + 9 a. 2(4x -1) b. 5(4y + 3) d. n(1 + 2n) a. -2 b. 4 c. 5 5 3x + 90 = 180; x = 30 a. x y + 5 b. x a. 22 b. 17 15. a. 9, 16, 23, 30 Page Page 627 627 c. 3y2 c. c(c - 2) d. 8 b. 14,8,2,-4 2 - Prior knowledge check 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6
Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 627 627 16. a. add 9; 29, 38 b. multiply by 3; -27, -81 c. subtract 4; -6, -10 d. divide by 10; 0.002, 0.0002 17. a. a and c b. b and d c. a d. b, c and d 18. a. 4, 11, 18, 25 b. 3, 6, 12, 24 19. a. i. 3 ii. 6 iii. 10 iv. 15 b. Students' own answers c. 5050 d. i. 9 ii. 36 iii. 100 iv. 225 e. n2(n +1)2 2.1 Algebraic Indices 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5
Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 1. a. 27 b. 23 c. 212 b. 53 b. x7 e. m2 b. 8c6 c. 33 c. a11 Page Page 627 627 d. 2- 1 2. a. 105 3. a. x7 d. y9 4. a. 6a8 7v5 e. 15s5t5 5. a. x2 c. 40n7 b. 30p6q6 b. x3 c. p3 d. d.
2.1 Algebraic Indices 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 6. a. 2g2 b. 3f4 c. 3x2 d. 3w2 7. a. x6 b. x18 c. t9 d. j18 8. a. 8r6 b. 9f8 c. 9. Clockwise for multiply; 3x4y3, 18x7y5, 72x8y5, 12x5y3. Didive: 4x,
6x3y2 10.a. 8x6y9 b. 36x10y4 2.1 Algebraic Indices 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 11. a. x3 x3 = x3-3 = x0 x 3 x3 = = 1 Therefor x0 = 1 b. x3 x4 = x3-4 = x-1 x3 x4 = = Therefor x-1 = c. x3 x5 = x3-5 = x-2 x3 x 5 = = Therefor x-2 = Page Page 628 628 2.1 Algebraic Indices
2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 12.a. 13.a. 12c3d 14.a. w 15.a. 1 c. 16.a. x2 c. 2x4 b. b. x2 c. 1 b. 3 c. 1 b. d. b. 3x d. 4x2y3
Page Page 628 628 d. d. 2.1 Algebraic Indices 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 17. a. x1/3 x x1/3 x x1/3 = x1/3 +1/3 +1/3 = x1 = x x x =x Therefor x1/3 = 18. a. c. b. 4c3
d. 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 1. a. 4x + 8 b. 3q - 15 c. 14m +7 d. -2y 12 2. a. 9a + 5 b. x + 4 c. 5s 3. a. 2 b. 9 c. 3 4. a. 2(x + 5) b. 2x, 10 c. The answers to part b add up to
give the answer to part a. 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 6. a. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 6. b. 2.2
2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 6. c. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6
2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 628 628 7. a. i. 5xy + 20x ii. 3xy + 6y b. 8xy + 20x + 6y 8. a. 8e + 18 b. 8y +14 c. 4x + 27 d. 9m + 27 e. 5a + 8b f. 13x + 8y 9. a. x2 2x b. 11y - 12 c. 10t 6 d. 2p2 + pq + q2 e. w + 3w2 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628
628 11.a. 2(x + 6) b. 2x(2 + 3y) c. b(3a - 5) d. 7x(y + z) 2 e. ab(1 - c) f. t (t + 2) g. 3pq(2p - 3) h. 3xz(x + 4) i. 5jk(4k 3j) j. 2pq(6r - 5s) 12.a. 4(s + 2t) b. = 4(s + 2t)[(s + 2t) - 2] = 4(s + 2t)(s + 2t -2) 2.2 Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628
628 13. a. 7(p + 1)(2p + 5) b. 5(c + 1)(c - 1) c. 4(y + 4)(3y + 10) d. (a + b)(a + b 2) e. 5(f + 5)(1 + 2f) f. 5(a + b)(a + b - 2) 14. One of the numbers is even so can be written as 2m. One of the other numbers is a multiple of three so can be written as 3n. If the other number is p their product is 2m x 3n x p = 6mnp so is divisible by 6. 2.3 Equations 2.1 2.1 Algebraic Algebraic Indices Indices 1. 2. 3. 4. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences
Expanding Page Page 628 628 a. x = 7 b. x = 1 c. x = 2 a. 6 b. 24 c. 12 33 - 2 x 3 = 27 - 6 = 21 a. 8x + 6 b. 21x 4 c. -8x + 17 5. a. 3x + 1 3x = 5x - 9 3x 1 = 2x 9 b. x = 5 6. a. 5 b. 4 c. 10 d. 2 2.3 Equations 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences
Expanding Equations Formulae Sequences Sequences Expanding 8. a. 3x + 16 b. x = 3 9. a. 1 b. -1 10.a. x = b. x = d. x = e. x = 11. a. 2x b. c. 9z 12.a. x 4 = 5 x 4 b. 3 Page Page 628 628 c. x = f. x = d. 6w 2.3 Equations 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More
Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 628 628 13.a. x (x - 4) = 3 x (x - 4) 10 = 3x - 12 b. 14.a. b. 15.a. b = 9 b. n = 1 c. c = d. x = e. x = 2.3 Equations 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences
Sequences Expanding 16. 30 17. a. b. c. + = 7 d. 180 miles. 0 Page Page 628 628 2.4 Formulae 2.1 2.1 Algebraic Algebraic Indices Indices 1. 2. 3. 4. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 628 628 a. 4 b. 13 c. 32 d. 17 a. 7.5 x 107 b. 300,000,000 1.22 a. Formula b. Equation c. Expression d. Identity e. Expression f. Formula g. Expression h. Equation i. Identity j. Equation 5. a. 2000 b. -2 6. a. 350 b. 8 7. a. 130 minutes b. T = 30 + 40m 2.4 Formulae 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences
Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 8. a. A = b. i. 9 ii. 10 9. 12,521,56 10. a. 320m b. 22.4ms-1 11. a. a = b. n = c. G = d. Q = 7(R - C) e. V = 3T + W f. a = (s - ut) 12. a. 82.40F b. C = c. 400C 2.4 Formulae 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations
Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 13. a. T = b. 192 seconds 14. a. a = b. 6 15. a. 4654 m b. 179,107 m Page Page 629 629 2.5 Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 629 629 1. a. 6 b. 16 c. 26 2. 4, 25 3. a. 2, 4, 6, 8, 10 b. 4, 7, 10, 13, 16 c. -4, -8, -12, -16, -20 d. 1, -1, -3, -5, -7 4. a. 10, 13, 16, 37, 307 b. 98, 96, 94, 80, -100 c. 6, 6, 6, 6, 6, 5. a. 0.02 and 0.67 b. and c. -5 and-8 d. 1 and 2.569 2.5 Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 629 629 6. a. 3, 2, 3, -4, -2 b. In front of n c. i. 5 ii. -3 d. i. 3. 8, 13 ii. 1, -2, 5 7. a. 2n + 1 b. 4n + 10 2.5 Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 8. a. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629
nth term = 3n + 2. The solution to the equation 3n + 2 = 596 is n = 198; which is a whole number. Therefore 596 is a term in the arithmetic sequence, b. The solution to the equation 7n - 3 = 139 is n = which is not an whole number. Therefore 139 is not a term in the arithmetic sequence. 2.5 Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 9. a. 6n 3 b. No Ben is not right. The solution to the
equation 6n - 3 = 150 is n = 25.5 which is not a whole number. Therefore 150 is not a term in the arithmetic sequence. 10. a. 125.375 b. From part a it is the 126th term; this is 8 x 126 - 3 = 1005 11. a. 4007 b. 49 12. a. i. 99.6kg ii. 99.2kg iii. 98.8kg b. 28 weeks 2.5 Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 13. 28 weeks
14. a. 10, 17, 24, 31 b. 7 c. 3 15. a. i. 9, 21, 33, 45, 57 ii. 41, 81, 121, 161, 201 b. Sequence Input difference Output difference i. ii. 3 10 12 40 The differences are scaled by 4 which is the multiplier in the function machine. 16. a. 4 b. 8 c. 2 d. q = 4 17. p = 7, q = 6 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 629 629 1. a. 1248 b 153 2. a. 48,96. Multiply by 2. b. 27, . Divide by 3 c. 18. Multiply by -3. 3. a. 5, 8, 13 b. 5, 9, 14 c. -1, 0, -1 4. a. 1, , , b. 2, 4, 8, 16 c. 0.3, 0.09, 0.027, 0.0081 5. a. , 2, 2, 4, 4 b. 3, , 36, 72 6. 8 months 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 629 629 7. a. 8,400 b. i. 8,820 ii. 9,261 8. Option 1 gives 10,400 and Option 2 gives 14,486.54. Option 2 gives more money. 9. a. 1, 4, 9, 16, 25, 36 b. i. n2 + 1 ii. n2 - 1 iii. (n + 1)2 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 10.
11. a. 126 b. 46 c. 10 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 12. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices
2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 13. a. 2n2 + 1 b. 3n2 5 14. a. 1, 5, 10, 10, 5, 1 b. Row, n Sum 0 1 1 2 2 4 Page Page 629 629 c. n2 + 4 3 4 5 8 16 32
c. 2n 15. a. 2. Halve the second difference to find the coefficient of n2. Therefore a = 1. b. 3, 5, 7 c. 2n - 1 d. n2 + 2n -1 2.6 Non-Linear Sequences 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 16. a. n2 + 3n or n(n + 3) b. (n-1)2 c. 2n2 + n + 2 d. 3n2 - n + 1 17. u5 x u8 = 105 x 108 = 105+8 = 1013 = u13
18. a. 2, 4, 8, 16 b. Multiply by 2 c. um x un = 2m x 2n = 2m+n = um+n 2.7 More Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 629 629 1. a. 2, 3 b. -4, -1 2. a. 4x2 b. 25y2 3. a. (x + 2)(x + 1) b. x2 + x + 2x + 2; x2 + 3x + 2 4. a. x2 + 16x + 60 b. x2 + 3x 18 c. x2 + 6x - 40 d. x2 - 7x + 12 5. a. (x + 2)(x + 3) = x2 + 5x + 6
b. (x - 3)(x + 8) = x2 + 5x - 24 6. i. x2 + 4x + 4 b. x2 - 6x + 9 c. x2 + 10x + 25 d. x2 - 8x + 16 2.7 More Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630 630 7. a. (51 + 49)(51 - 49) = 2 x 100 = 200 b. i. 400 ii. 0.12 8. a. x2 16 b. x2 - 4 9. a. (x - 5)(x + 5) b. (y - 7)(y + 7) c. (t - 9)(t + 9) 10. a. (x +1)(x + 7)
b. (x + 3)(x + 4) c. (x + 3)(x + 5) d. (x + 3)(x - 1) e. (x - 3)(x + 1) f. (x - 2)(x - 4) g. (x - 7)(x + 1) h. (x - 3)(x - 4) i. (x - 2)2 j. (x - 12)(x 2) k. (x - 8)(x + 2) I. (x + 1)2 2.7 More Expanding and Factorising 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630 630 11. a. (x + 5)(x + 2) = x2 + 7x + 10 b. 7x + 10 c. x = 3
12. x = 1.5 13. a. 4x2 - 9 = (2x)2 32 = (2x - 3)(2x + 3) b. 16y2 - 1 = (4y)2 = (4y - 1)(4y + 1) 14. a. (3m - 5)(3m + 5) b. (5c - 9)(5c + 9) c. (x 7y)(x + 7y) 15. a. (x + 5)(x + 6) b. 9u2 - 24uv + 16v2 2 Problem Solving 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 1. a. 3500 m 2. a. 64 3. a. 115 4. a. 462 5. a. 273 Page Page 630 630
b. 7xyz + b. b. xy - mn b. x(x - 1) b. 2n - 1 2 Check Up 2.1 2.1 Algebraic Algebraic Indices Indices 1. 2. 3. 4. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630 630 a. 20p4 b. 5a2 c. b-6
5q a. 2y(x - 3) b. 3a(b - 2a) a. x2 2x - 24 b. x2+10x + 25 5. a. b. 4 c. 3c d. 4p-5 6. 2s2 + 5rs - 3r2 7. a. (x - 9)(x + 9) b. (x - 2)(x 7) 2 Check Up 2.1 2.1 Algebraic Algebraic Indices Indices 8. 9. 10. 11. 12. 13. 14. 15. 16. 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
a. Formula b. Identity c. Expression d. Equatic x= x = -17 40 1.13 + 4 x 1.1 = 5.731 < 6 and 1.23 + 4 x 1.2 = 6.528 > 6 C = 25 + 36n a. y = b. b = x = 10 18, 29 Page Page 630 630 2 Check Up 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 630 630 17. a. 9n 7 b. The equation 9n - 7 = 167 has solution which is not a whole number. Therefore 167 is not a term in the sequence. c. 173 18. 3n2 + 7 20. a. Clockwise from top left: x2 + x - 6, 3x2 7x + 2, 6x2 + 10x - 4, 2x2 + 10x +12. b. 12x2 + 14x + 4. Any order would give the same result, multiplication is not commutative, c. 2(2x +1)(3x + 2) 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630
630 Simplifying, expanding and factorising 1. a. t5 b. t7 c. t4 d. t2 e. t-7 f. t2 2. a. 18p5 b. 72z5 c. 14b8 d. 8r3 e. 6x2 f. 10s-6 3. a. t4 b. t3 c. t0 = 1 4. a. 5p4 b. 3a5 c. 3y-3 d. 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences
Sequences Expanding Page Page 630 630 5. a. (x2)2 = x2 x x2 = x4 b. (x2)3 = x2 x x2 x x2 = x6 c. (x2)4 = x2 x x2 x x2 x x2 = x8 d. When you find the power of a power you 6. 7. 8. 9. multiply the powers together. a. a2 b. r-2 c. 8g a. 6x + 3y b. 6x 8y c. 12x 5y a. 11c + d b. 12m + 10n a. ab(3b 2) b. 2x(4y + 3) 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 10.a. 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More
Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding x x +4 x x2 4x Page Page 630 630 +5 5x +20 b. (x + 4)(x + 5) = x2 + 5x + 4x + 20 = x2 + 9x + 20 11.a. x2 12x + 36 b. x2 - 16 x x -6 x x2 -6x -6 -6x +36 x x -4 x x2 -4x +4 +4x -16 2 Strengthen 2.1 2.1
Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 12. a. 3x2 + 26x + 16 x+ 3 3x +2 x +8 xc. X +4 3x2 +24x +2x +16 -7 3x2 3x + 5x - 28 3x2 +12x
-7x -28 Page Page 630 630 b. 10x2 + 11x x 5x +3 2x 10x2 +6x +1 +5x +3 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding
Page Page 630 630 13. (x - 3)2 = x2 6 + 9 (x + 1)(x + 5) = x2 + 6x + 5 2 (x - 3)(x + 3) = x - 9 (x + 2)(x - 3) = x2 - x - 6 (x + 3)(x + 2) = x2 + 5x + 6 14. a. 3 and 4, 2 and 6 b. 2 and 6 c. (x + 2)(x + 6) 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630 630
15. a. (x + 12)(x + 1) b. (x + 3)(x + 4) 16. a. 2 and -5, 1 and -10, -1 and 10 b. i. (x -10)(x + 1) ii. (x +10)(x - 1) iii. (x + 5)(x -2) iv. (x - 5)(x + 2) 17. a. -24 and -1, -4 and -6, -2 and -12 b. i. (x - 1)(x - 24) ii. (x - 2)(x - 12) 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 630 630 Equations and Formulae 1. a. Expression b. Identity c. Formula d. Equation
2. a. 9 b. 36 3. 23 4. -5 5. x = or (y + 4) or y + 2 6. Q = aP - ab or a(P - b) 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 7. a. b = b. s = 8. x = 4 9. a. i. 14x 28 b. x = 10. a. 2x 2 b. x = 11. a. x 4x 12. a. x = 20 b. x = Page Page 631
631 ii. 6x + 10 b. 2x c. 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 13. a. x = 18 b. x = c. Find the LCM of the denominators. 14. a. x = 60 b. x = 1 Sequences 15. a. 13, 21 b. 50, 81
68 16. a. 5, 7, 9 b. 48, 46, 44 c. 2, 5, 10 d. 10, 40, 90 17. a. 3 b. 36 c. The general term is 3n c. 42, 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 4. a. 10n b. 7n c. 12n 5. a. 6
b. The general term is n + 12 6. a. n + 2 b. n + 12 c. n 4 7. a. 4n b. 3 c. 4n + 3 8. a. i. 20, 36 ii. 9, 11 iii. 16, 19 iv. 5, 0 b. i. 6n ii. 2n - 1 iii. -5n + 2 Strengthen 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 9. a. 14, 18, 22, 26, 30
b. The numbers in the sequence are even but 351 is odd. c. 23rd 10. a. 20th b. 112 c. 152 11. a. 53, 14, 18, 4, 4 b. 2n2 + 3 12. a. 4n2 + 5 2 Extend 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 1. a. i. 6, 7, 8 ii. 20,10, 5 iii. 3, -1, -5 iv. -3, 9, -27 b. i and iii are arithmetic; ii and iv
are geometric 2. a. 0.473 b. 11.5 c. 13 d. 15.7 3. a. In-store; 12800,10240; Online; 3240, 4860 b. 2017 4. 838.76 2 Extend 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding 6. a. 950 c. 700 7. a. a = b. P = c. a = 8. a. 2c4d4 c. 16m-1n3
d. y = b. 12x2y d. 2p-1q4 b. h = Page Page 631 631 2 Extend 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 9. x2 + 20x + 19 10. a. p2 + 5p - 36 b. w = -2 c. (x + 3)(x - 3)
d. 3x4y 11. a. It is not lower as the temperature in Mr. Smith house is 250C. b. F = 2 Extend 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 12. a. The odd numbers are one greater than the even numbers which are multiples of 2. b. (2m + 1)(2n + 1) = 4mn + 2m + 2n + 1 = 2(2mn + m + n) + 1 which is odd. 13. a. (x - 4)(x - 8) b. (x - 6)2 c. (x - 2)(x + 1) d. ( - )( + )
14. a. x = - b. 26 c. - d. -1 2 Extend 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 15. If the consecutive numbers are n and n + 1 then the difference between their squares is (n + 1)2 - n2 = n2 + 2n + 1 - n2 = 2n + 1, which is an odd number, 16. a. -2n2 + 3
2 2 b. n + 2n - 1 or -(n - 1) 2 Unit Test 2.1 2.1 Algebraic Algebraic Indices Indices 2.2 2.2 Expanding Expanding & & Factorising Factorising 2.3 2.4 2.5 2.3 -2.4 -2.5 Linear Linear 2.6 2.6 Non-Linear Non-Linear 2.7 2.7 More More Equations Formulae Sequences Sequences Expanding Equations Formulae Sequences Sequences Expanding Page Page 631 631 Sample student answer a. You can label the dimensions you know. b. From the formulae sheet. c. It separates the sphere from the cone. d. So it doesn't get confused with the radius of the sphere.
