5. (i)


|∠C| = 114° vertically opposite angles


|∠D| = 66° alternate angles |∠F| = 114° vertically opposite angles


|∠G| = 66° vertically opposite angles


(ii)


|∠I| = 63° vertically opposite angles


|∠J| = 63° vertically opposite |∠H| = 63° corresponding angles


(iii) |∠O| = 47° straight angle |∠P| = 47° straight angle


|∠K| = 117° straight angle |∠L| = 117° straight angle |∠M| = 117° vertically opposite |∠N| = 117° vertically opposite


|∠Q| = 47° vertically opposite angles


|∠U| = 133° vertically opposite angles


|∠R| = 133° straight angle |∠S| = 47° straight angle |∠T| = 133° corresponding angles


6. (i) Sometimes true, (ii) Sometimes true, (iii) Always true, (iv) Sometimes true, (v) Never true


11B Taking it further 1. (i)


(ii) |∠B| = 105° straight and alternate angles


|∠A| = 75° corresponding angles


(iii) |∠C| = 105° vertically opposite and corresponding angles


(iv) |∠D| = 105° corresponding angles


(v)


(vi) |∠F| = 105° straight angle or corresponding angles


2. (i) 3. (i)


(ii) |∠B| = 124° straight angle (iii) |∠C| = 124° vertically opposite angles


(iv) |∠D| = 56° vertically opposite angles


(v)


(vi) |∠F| = 124° vertically opposite angles


|∠E| = 124° alternate angles


(vii) |∠G| = 56° vertically opposite angles


4. (i)


|∠A| = 66° straight and corresponding angles


(ii) |∠B| = 114° corresponding angles


(iii) |∠C| = 114° vertically opposite angles


(iv) |∠D| = 66° vertically opposite angles


(v) 5. (i)


|∠E| = 114° vertically opposite angles or corresponding angles


(ii) |∠O| = 102° straight angle (iii) |∠P| = 102° alternate angles


|∠M| = 78° alternate angles


(ii) |∠X| = 77° alternate angles (iii) |∠Y| = 103° alternate angles |∠A| = 56° corresponding angles


|∠J| = 75° alternate angles |∠A| = 103° straight angle


|∠E| = 75° corresponding angles


(vii) |∠G| = 105° corresponding angles (viii) |∠H| = 75° corresponding angles (ix) |∠I| = 75° corresponding angles (x)


4. (a)


|∠A| = 66° corresponding angles |∠B| = 114° straight angle


Unit 12 Linking Thinking revision material


Questions 1. (a)


(i) 2, 1, 3, 6, 9; whole, positive numbers


(ii) 2, 0, 1, 3, –5, 6, –7, 9; whole numbers, both negative and positive


(iii) 2, 1


numbers that can be written as fractions


__ 2 , 0, 1, 3, 2


__ 7, –5, 6, –7, 9;


(b) (i) {1, 2, 3, 6} (ii) Any of {1, 2}, {1, 3}, {1, 6}, {2, 3}, {2, 6}, {3, 6}


(iii) 2 (c) (i) 0, (ii) 1 (d) (i) (1 + 2) + 3 = 1 + (2 + 3)


_ 2, (iii) 2


_ 7


(ii) 2 × 3 = 3 × 2 (iii) 2 × (1 + 6)


2. (a) 3. (a) = (2 × 1) + (2 × 6)


(i) 12 minutes (ii) 194 mins/3 hours 14 mins


(b) (i) 5·15%, (ii) 15·46%, (iii) 74·22% (c) €350, €210, €140


(i) Jakob: –4; Larissa: –3; Jakob is the winner.


(ii) Linear: same first difference (c)


(b) The Eiffel Tower: (i) 243 m (ii) 182·25 m (iii) 5 bounces The Statue of Liberty: (i) 69·75 m (ii) 52·3125 m (iii) 5 bounces The Burj Khalifa: (i) 621 m (ii) 465·75 m (iii) 5 bounces (a) 3


(i)


(ii) (a) 7 (iii) (a) 1 (iv) (a) 12


__ 14 = 1


__ 14 (b) 0·21 (c) 21·43%


__ 2 (b) 0·5 (c) 50%


__ 14 (b) 0·07 (c) 7·14%


__ 14 = 6


__ 7 (b) 0·86 (c) 85·71%


(i) A = 270˚, B = 90˚, C = 150˚, D = 210˚, E= 60˚, F = 300˚, G = 90˚, H = 270˚


(ii) A = reflex; B = right-angled; C = obtuse; D = reflex; E = acute; F = reflex; G = right-angled; H = reflex


(b) (i) A = {2, 4, 6, 8, 10, 12}; B = {1, 3, 5, 7, 9, 11}


(iii) (a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}; (b) { }; (c) 6


5. (b) Stones A. 8 bags of small Stones A €1 118 and 10 bags of Stones B cost €1 285 (i) 202·5 m2


(c) 6. (a) (b) (i) (c) , (ii) 69%


(i) 3 : 2, (ii) 10 litres 6 litres


(ii) White: 3·6 litres; black: 2·4 litres


(i) Variable = number of hours worked; constants = €100 and €50


(ii) Cost = €50(number of hours) + €100


(iii) 150; 200; 250; 300; 350; 400; 450; 500


(v) 50 (vi) €375 (vii) 3·5 hours


2. (i) (ii) (ii)


7. (a)


(i) D, (ii) B, (iii) E and C, (iv) A and C, (v) C: it is cheaper and weighs more


(b) (i) 405 calories and 540 calories (ii) 649 calories; 24%


(c)


(i) €1·92 (ii) 390 g of oats, 42 g of nuts, 168 g of the mix


(d) (i) 600 g (ii) 4 : 1 (iii) 480 g


8. (a) (i) 72 cm, (ii) 20, (iii) 120 bricks


(b) €91·94 (c) 90 (d) 105 kg


Section B


Unit 13 Money matters 1 Practice questions 13.1 1. (i)


(a) Monthly = €3 041·67 (b) Fortnightly = €1 403·85 (c) Weekly = €701·92 (d) Hourly = €17·55


(a) Monthly = €4 058·33 (b) Fortnightly = €1 873·07 (c) Weekly = €936·54 (d) Hourly = €23·41


(iii) (a) Monthly = €1 645·83 (b) Fortnightly = €759·62 (c) Weekly = €379·81 (d) Hourly = €9·50


(iv) (a) Monthly = €5 499·58 (b) Fortnightly = €2 538·27 (c) Weekly = €1 269·13 (d) Hourly = €31·73


(v)


(a) Monthly = €8 750·00 (b) Fortnightly = €4 038·46 (c) Weekly = €2 019·23 (d) Hourly = €50·48


(a) Fortnightly = €1 615·38 (b) Weekly = €807.69 (c) Hourly = €20·19


(a) Fortnightly = €2 065·38 (b) Weekly = €1 032·69 (c) Hourly = €25·82


(iii) (a) Fortnightly = €2 774·77 (b) Weekly = €1 387·38 (c) Hourly = €34·68


(iv) (a) Fortnightly = €2 515·38 (b) Weekly = €1 257·69 (c) Hourly = €31·44


(v)


(a) Fortnightly = €1 231·15 (b) Weekly = €615·58 (c) Hourly = €15·39


3. (i) Jane has a higher weekly wage (ii) She earns €30·60 more per week than Simon


4. Jill worked 32 hours 5. (i) 12 hours (ii) €8·75 per hour


6. (i) Yes, Bobby has been underpaid [show supporting work for justification]


(ii) €399·50


7. €276·00 8. €3 856·00 9. €10 670·00


Answer key 575


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