6. (i) €243.30 (ii) €185.80 (iii) Total USC = €13.78 (iv) €650.42
7. (i) €2 200 (ii) €607.50 (iii) €555.25 (iv) €72.12 (v) €1 533.88
Unit 18 Geometry in proportion
Practice questions 18.1 2. (i) 2.1 cm (ii) 0.9 cm
8. A = € 4 890, B = €1 250.75, C = €1 287.25, D = €3 602.75
9. €3 500 10.(i) €35 119.50 (ii) €50 258.63
Revision questions
17A Core skills 1. Any valid mathematical explanation 2. €14 271.70 3. €644.65 4. 10 612 people 5. Option A = €12 400, option B = €12 682.42, option C = €12 909.20; option C gives the most interest
6. 10 480 bacteria 7. €802 000 8. €14 646.28 9. (i) €8 596.80 (ii) 30%
10.Any valid mathematical explanation 11.(i) €143 (ii) €85.25 (iii) €564.75
12.(i) €1 990 (ii)
t = €1 700
(iii) €290 (iv) No (v) Reduce her spending on socialising and lunches, etc.
13.(i) 21% (ii) €1 700
14.€ 3 340
17B Taking it further 1. 6·8 × 106
people
2. (i) €26 250 (ii) €23 028.75 (iii) €14 309.33
5. (i) €1 056.25 (ii) 7 hours (iii) €268.71 (iv) €60.44 (v) €1 019.20
6. (i) €36 575 (ii) €43 616
7. A = €7 000, B = €600, C = €7 600, D = €2 734·50, E = €380, F = €266, G = € 3 380·50, H = €4 219·50
8. (i) €694 (ii) €138.71 (iii) €854.71 (iv) 30%
10. (i) €65 684.90 (ii) €50 184.29 (iii) €477.53 (iv) €20 000
9. (i) €5 520 (ii) €10 000
386 Linking Thinking 2
3. €5 451.37 4. (i) €16 153.36 (ii) 4.7%
6. (ii) 1⋅7 m 7. (ii) 0⋅7 m 8. 0⋅2 m apart 9. 3⋅5 cm 10.(i) 1 cm = 10 km (ii) Fits on page easily (iii) 17 km
Practice questions 18.2
1. (i) 20 (ii) 10 (iii) 9⋅6
2. (i) 6 (ii) 3 (iii) 8
3. (i) 12 (ii) 7 (iii) 12
4. (i) 9 (ii) 9 (iii) 26
5. (i) 8; 8, 12 (ii) 6; 6, 9 (iii) 8; 12, 16
6. (i) 3, 12 (ii) 5, 6 (iii) 4, 15
7. (i) Not parallel (ii) Parallel (iii) Parallel
8. (i) E and F are parallel (ii) 4⋅5 km
9. (i) 10 m (ii) 5⋅76 m
10.7 11.5
Practice questions 18.3 1. (i)
Similar 2. (i)
(ii) Not similar (iii) Similar Similar
(ii) Similar (iii) Not similar (iv) Similar (v) Similar (vi) Not similar
3. (i) 4⋅5 cm (ii) 8 cm (iii) 12 cm (iv) x = 27; y = 30
4. (i)
|∠QRP| = |∠ZRT| vertically opposite;
(ii) 10 (iii) 15
|∠PQR| = |∠RZT| alternate; |∠QPR| = |∠RTZ| alternate
5. Yes 6. 6⋅4 m 7. 7·68 m 8. (ii) 5⋅33 m 9. 15⋅5 cm 10.x = 4⋅3 m; y = 9⋅6 m
Revision questions
2. (ii) 1.4 m 3. (i) 5 (ii) 12 (iii) 5⋅5
4. (i) 20 (ii) 27 (iii) 10
5. (i) 6 (ii) 16 (iii) 8
6. 16⋅28 m 7. (i) Yes, right angle and other angle equal
(ii) 38 cm
8. 564 m 9. (i) Triangles PTQ and PRS are similar so we can use proportional sides
(ii) 350 m 10.(ii)
(iii) ∆TBS ∶ ∆ABC = 2 ∶ 3 18B Taking it further
2. (i) 8 (ii) 4 (iii) 9
3. (i) 20 (ii) 20
4. (i) 13 (iii) 10 (iv) 13
5. (i) 8 (ii) 11
6. (i)
|∠BCA| = |∠DCE|, vertically opposite
(ii) 38⋅8 m 7. (ii) 800 cm
8. (ii) Yes, |∠ABC| = |∠BDE| (alternate angles)
(iii) 15 (iv) 12⋅6
9. 6⋅4 cm
10.|BD| and |DE| 11.|∠ACB| = |∠CBD| (90°); |∠ABC| =
|∠CBD| (same angle) so ∆ABC similar to∆CBD; |∠BCA| = |∠DCA| (90°); |∠BAC| = |∠DAC| (same angle) so ∆ABC similar to ∆ACD
Unit 19 Trigonometry
Practice questions 19.1 1. (i) 11⋅4 (ii) 7⋅9 (iii) 12 (iv) 5⋅1 (v) 15⋅2 (vi) 2⋅6
2. (i) √
_ 61
(ii) 10√ (iii) 3√ (iv) 6√ (v) 2√ (vi) 2√
_ 10
_ 6
_ 3
_ 15
_ 5
|∠BAC| = |∠CED|, right angle;
|∠ABC| = |∠TBS| same angle; |∠BTS| = |∠BAC|, corresponding
1. (ii) 1 cm = 20 km; fits onto page (iii) 30 km
18A Core skills 1. (ii) 4 cm (iii) 2 cm
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