10. (i) 8x + 10y, (ii) 31c + 9b, (iii) 27 1


11. 10x + 17y 12. 14m + 68n + 23 13. Length 6d; width 7c


Practice questions 8.2 1. (i) x3


, (ii) ab2 (v) −15m6 , (iii) a6 , (vi) 8a2 , (iv) 6p3 b4


2. (i) 10a, (ii) 14x, (iii) 21a, (iv) 28n, (v) 18y, (vi) 24m


3. (i) 12ab, (ii) 10bc, (iii) 4wx, (iv) −24dt, (v) −14sy, (vi) −7gk , (ii) 27h2


4. (i) 12g2 6. (i) 12a2


_ 3m3


, (iii) −12t2


5. (i) 2w, (ii) 3d, (iii) −5x, (iv) −1 (v) −1


(v) −30eh, (vi) −27np , (vi) −1


10. (i) 8a2, (ii) 27.6a2b3, (iii) 1 11. 42xy


7. (i) −20x3 8. (i) 8x4 9. (i) 12a2


(iv) −4mn2


, (ii) −5x4 , (ii) 48a2


b2


_ 6 y2


(iv) −15m3n2, (v) −20a2b3, (vi) −1 y, (ii) −10p3


b, (ii) −12p3


(iv) −4mn2 y2


, (iii) 16s3 q3 y4 , , (iii) −a3


_ 2 a2


, (iii) −x3 b4


,


, (iii) 120a2 b


b2 y3


_ 3 x3


, y


_ 5m3


, , (iv) –35d2 , ,


_ 6 d


4. 10xy 5. 6x 6. 6xy, 18xy2


, 108x2


y3


7. 113 rows 8. (i) 224ab, (ii) 896b


Unit 9 Solving linear equations


Practice questions 9.1 1. (i) a,c; 5, (ii) t,b; 5, (iii) f,m,d; none, (iv) x,y; –7, (v) k,g; 2, (vi) t,p; –4, (vii) θ,e; –24, (viii) r,x; –7, (ix) β,y; –12, (x) d,n; –6


2. (i) Total value = 4 + 6a (ii) Total value = 2 + 9v (iii) Total value = 7 − 3t (iv) Total value = −10 + 2d (v) Total value = −50 − 8n (vi) Total value = −21 + 4s (vii) Total value = 117 − 34r (viii) Total value = 1 024 − 64t (ix) Total value = −99 + 24k (x) Total value = 0 − 59x


3. (i) 7; 24; y, (ii) –4; 13; s, (iii) 31; –76; n, (iv) –17; –3; q, (v) 10; 2; x


Practice questions 8.3 1. (i) 2a, (ii) −2e, (iii) 3y, (iv) −2n, (v) −3c, (vi) 2m


2. (i) 3m, (ii) −4p, (iii) 5d, (iv) −3b (vi) 9d


3. (i) 2, (ii) 2, (iii) –5, (iv) –3, (v) –4, (vi) –2


_ 2


4. (i) −3y, (ii) 4w, (iii) 2x, (iv) −3b, (v) −2, (vi) −2


5. (i) 3y, (ii) −9g (vi) −2


6. (i) −16a, (ii) 32, (iii) −3c2 (v) −3b, (vi) 2


_ 3b


7. 8x 8. 6y 9. x2 10. 6b 11. 70xy 12. 10x 13. (i) 2x, (ii) 5a, (iii) −2p2 (v) 3a2


b4 , (vi) 4x2 y Revision questions


8A Core skills 1. (i) 7x + 6, (ii) 4x + 7, (iii) 10x + 3, (iv) 9a2


(vii) 4a + 8b, (viii) 5x2


2. (i) 5x2 10y2


3. (i) 16s2 n2


(iv) −28p3 (vii) 30a4


5. (i) 1 , (v) 6de3 , (iii) 40x4 ,


+ 2, (v) 7a + 8, (vi) 3a + 4b, + 10


− 3y, (ii) 23ab − bc, (iii) −9x2 + 2y, (iv) 18ab + 15bc , (ii) −15m3 n2


by, (viii) 20m3 (v) −1


_ 3w, (ii) −2


_ 4 xy, (vi) −2


_ 21 x2


, (vi) −24a3 n3


4. (i) 4x, (ii) 7x, (iii) 2d, (iv) 2x2


_ 5 m3


_ 11 m2


b2 ,


(vi) 2x, (vii) −5, (viii) 2x, (ix) −8b, (x) 24 , (iii) −3 n


, (v) 7x4 , (iv) 3


8B Taking it further 1. (i) 16yx, (ii) 80x2


,


_ c3


d


_ 13 ad,


y, (iii) 30m2


2. (i) 12a, (ii) 12m + 8m2 3. 12x


572 Linking Thinking 1 n2 , (iii) 28xy +


_ 2 , (iii) −2d, (iv) −w


_ 4 , (v) −3,


d, (iv) −3xy2 ,


_ 2 , (v) −t_


3 ,


4. (i) Height = 2 + 1(number of months)


(ii) Number of cakes = 5 + 3(number of hours)


(iii) Number of pages = 50 + 8(number of hours)


(iv) Number of blocks = 100 − 8(layer number)


5. (i) €12∙80 (ii) €52 (iii) €91∙20 (iv) €375∙30


6. (i) Fare = 4 + 1·10 (number of kilometres travelled)


(ii) €14 (iii) You could travel 21 kilometres


7. (ii) Stage 2: 2, 8, 10; Stage 3: 2, 12, 14; Stage 4: 2, 16, 18; Stage 5: 2, 20, 22; Stage 6: 2, 24, 26


(iii) Variables = number of blue blocks, total number of blocks


, (iv) 5x2 ,


(iv) Total number of blocks = 2 + 4 (stage number)


(v) T = 2 + 4s, where T = total number of blocks and s = stage number


(vii) (a) 402 (b) 2 red blocks (c) 400 blue blocks


8. (ii) Stage 2: 1, 8, 9; Stage 3: 1, 12, 13; Stage 4: 1, 16, 17; Stage 5: 1, 20, 21; Stage 6: 1, 24, 25


(iii) Variables are T and s (iv) Total number of dots = 1 + 4(stage number)


(v) T = 1 + 4s where T= total number of dots and s = stage number (or any valid variation of this)


(vi) (a) Total = 229 dots (b) Green dots = 1 (c) Black dots = 228


(vii) 19th stage


Practice questions 9.2 1. (i) 3, (ii) 12, (iii) 13, (iv) 53, (v) 20, (vi) 8,


(vii) 3, (viii)14.5, (ix) 3.5, (x) 1 1 (xii) –4


_ 3, (xi) –6,


2. (i) 23, (ii) 20, (iii) 33, (iv) 26 3. (i) 4, (ii) –25, (iii) 12, (iv) 3 4. (i) 11, (ii) 18, (iii) 13, (iv) 16, (v) 12, (vi) 21 5. (i) 5, (ii) 4, (iii) 6, (iv) 4, (v) 6, (vi) 2, (vii) 11, (viii) 10


6. (i) 11, (ii) 7, (iii) 1, (iv) 9 7. (i) α = 4 (ii) x = 4 (iii) w = 10 (iv) k = 5 (v) z = 10 (vi) β = 8 (vii) h = 11


Practice questions 9.3


1. (i) 2, (ii) –2, (iii) 6, (iv) 8, (v) –2, (vi) –1, (vii) 5 (viii) 12


2. (i) 4, (ii) –4, (iii) 2, (iv) 3, (v) –3, (vi) 15, (vii) –1 (viii) 13


3. (i) 2, (ii) 4, (iii) 2, (iv) −2, (v) −1, (vi) 4, (vii) 3, (viii) 10


4. (i) 1, (ii) 2, (iii) 5, (iv) 1, (v) –14, (vi) 1, (vii) 14, (viii) –17


5. (i) 35, (ii) 16, (iii) 77, (iv) 126, (v) 183, (vi) –81, (vii) 357, (viii) –13, (ix) 4, (x) 4


6. (i) 5, (ii) 8, (iii) 10, (iv) 6, (v) 16, (vi) 31, (vii) 143, (viii) 150, (ix) –386, (x) 351


Practice questions 9.4


1. €6 2. Pedro is 16 years old, José is 20 years old 3. Jan potted 26 plants 4. Henry solved 16 problems and Frank solved 64 problems


5. Bicycle costs €1 200 and car costs €14 400


6. Width = 18 cm, length = 36 cm 7. Present ages: Simon = 14 and his mother = 42


8. (i) Games won = 21, (ii) Games lost = 25 9. Length of field = 60 m 10.Width = 15 m, length = 45 m 11. Person with fewest votes = 6 689, person with most votes = 7 000


12. (i) 8x + 4 (ii) 9 metres


13. (i) x + 3x + (3x + 30) = 180 (ii) Smallest angle x = 30 ° (iii) Largest angle = 90°


Practice questions 9.5 1. (i)


4(2), 8; 4(4), 16; 4(6), 24; 4(8), 32; 4(10), 40


(ii) 2(7) + 3, 17; 2(9) + 3, 21; 2(11) + 3, 25; 2(13) + 3, 29; 2(15) + 3, 33


(iii) 5(4) – 8, 12; 5(8) – 8, 32; 5(12) – 8, 52; 5(16) – 8, 72; 5(20) – 8, 112


(iv) 14 – 6(1), 8; 14 – 6(2), 2; 14 – 6(3), –4; 14 – 6(4), –10; 14 – 6(5), –16


(v) 1 (vi) 1 + 6, 21; 1 9; 1


__ 2(10) + 6, 11; 1


__ 3(27) – 2, 7; 1


__ 2(40) + 6, 26; 1


2. (i) x + 7, (ii) 2x, (iii) 2x + 2, (iv) 3x − 20, (v) 1


__ 3(36) – 2, 10; 1


__ 3(39) – 2, 11


_ 2 x + 10, (vi) −2x − 4


__ 2(20) + 6, 16; 1


__ 3(30) – 2, 8; 1


__ 2(30)


__ 2(50) + 6, 31


__ 3(33) – 2,


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