Power of Maths Paper 1 OL

Power of Maths: Paper 1 – Answers

Exercise 5 1. (a) n(n + 7), 638 (b) n(2n + 10), 2368 (c) n(10n – 27), 8190 (d) n (13 − n)

________ 4

(e) n(3n − 19) _________

2

(i) n(n + 1) _______

12 2

, 3861 (f ) n(2n + 1) _________

8 , 657 ( j) n(3n − 9) _________

2

(g) n(12 – n), –925 (h) n(2x + 3n − 3) _____________

, –270 , 388

, 12x + 198 , 825 2. (a) 2550 (b) 2500 (c) 500 500 (d) 3575 (e) 201 000

3. (a) 5, 2 (b) 10, 14, 18, 22 (c) –35 (d) –105 4. (a) €2250 (b) €1 904 000; €63 200 (c) €377 500 (d) 63; 1020 (e) 14, 1225 (f ) 4092 5. (a) (i) 2

(ii) 7 (iii) 2 (iv) 5 (v) n(5n − 1) ________

2 (vi) 3404 (b) (i) –5

(ii) –5 (iii) –5 (iv) 6 (v) 79 (vi) 6n – 11 (vii) 2816 (viii) n(3n – 8) (ix) 29 200 (c) (i) 3 (ii) 8 (iii) 2600 (iv) 3 (v) 5 (vi) 2 (vii) 69

Exercise 6

1. (a) First differences: 2, 3, 4, 5, … .; second differences: 1, 1, 1, … (b) First differences: 5, 7, 9, 11, ….; second differences: 2, 2, 2, … (c) First differences: 2, 4, 6, 8, ….; second differences: 2, 2, 2, … (d) First differences: 8, 14, 20, 26, ….; second differences: 6, 6, 6, … (e) First differences: –3, –5, –7, –9, ….; second differences: –2, –2, –2, … (f) First differences: –6, –10, –14, –18, ….; second differences: –4, –4, –4, … (g) First differences: –4, –6, –8, –10, ….; second differences: –2, –2, –2, … (h) First differences: 2, 3, 4, 5, ….; second differences: 1, 1, 1, … (i) First differences: 5, 8, 11, 14, ….; second differences: 3, 3, 3, … (j) First differences: 3t + 1, 5t + 1, 7t + 1, 9t + 1, ...; second differences: 2t, 2t, 2t, … 2. (a) 43, 65 (b) 70, 90 (c) 115, 167 (d) 65, 98 (e) –27, –23 3. (a) 2, 5, 10, 17 (b) 2, 8, 18, 32 (c) –1, –1, 1, 5 (d) 2, –1, –6, –13 (e) 0, 1, 6, 15 4. (b) 1, 3, 6, 10, 15, 21 (c) (i) First differences: 2, 3, 4, 5, 6 (ii) Second differences: 1, 1, 1, 1; The sequence is a quadratic sequence.

Revision Questions

1. (c) N = 3n + 2 (d) 32 (e) 22 2. (a) 7 – 2n (b) 3, 1, –1, –3 (d) Slope = –2 (e) 3 _

2 (i) 11 __

2

(ii) 3 _

2 3. (b) 7, 9, 3, 1, 7, 9, 3, 1 (c) 3 (d) 0, 4, 4, 0, 0,

4, 4, 0; 4 4. (b) Any term – previous term = constant = –5 (c) (i) 1000 (ii) –5 (d) 945 litres

346

(e) 101st day 5. (c) 2n (d) n + 2 (e) 3n + 2 (f ) 98 hours 6. (a) 2000, 2350, 2700, 3050 (b) Any term – previous term = constant = 350 (c) a = 2000, d = 350 (d) 350n + 1650 (e) 5150 m (f ) 7th day (g) 47 100 m (h) 7 7. (c) N = 6l + 2

(d) n = 14l – 1 (e) n = 7N − 17 _______

3

or N = 3n + 17 _______

7

(f ) 314 (g) 80 (h) 137 8. (a) –11, –20 (b) –11, –9 (c) –11, 2 (d) 2n – 13 (e) 1, 11 9. (a) (i) –7 (ii) 3 (iii) 42 (iv) 42 (v) 2289 (b) 736 10. (a) (ii) 22 – 2n (iii) –14°C (b) (i) 25 (ii) 13 (iii) 25 (iv) 325 11. (a) (i) –5 (ii) 7 (b) –5, 2, 9, 16 (c) 2895 12. (a) 4, 7, 10 (b) 61 (c) 650

Section 5 Chapter 11

Exercise 1

1. (a) 62∙8 km/h (b) €5∙40; 90c per can (c) No (d) 160-page refi ll pad (e) 870 ml bottle (f ) 416 m2 (g) 36∙25% (h) 2

(c) 5∙4 × 106 m2 (d) 2∙6 × 10– 4 m2 (e) 6∙8 × 10– 4 m3 (f ) 5 × 103 kg (g) 5∙6 × 10– 6 m3 (h) 5 × 103 cm3 (i) 5 × 10–3 m3 3. (a) 20 m/s (b) 30 m/s (c) 27 7

_ 9 m/s = 27∙8 m/s (d) 12∙5 m/s (e) 36 km/h

(f ) 56∙16 km/h (g) 10∙8 km/h (h) 90 km/h (i) 20 5

_ 6 m/s = 20∙8 m/s (j) 32∙4 km/h 4. 13 gallons

5. 6697∙6 km 6. 8847∙6 m 7. 4∙16 8. 2∙44 m; 1∙62 feet 9. (a) 52 500 m2 (b) 5∙25 × 10–2 km2 (c) 5∙25 hectares (d) 13 acres 10. 120 yards 11. (a) 1∙08 × 109 km/h (b) 6∙7 × 108 mph

Exercise 2

1. (a) ₤659∙36 (b) $1091∙20 (c) CAD 1216∙80 (d) R12 248 2. (a) €366∙57 (b) €788∙64 (c) €1457∙42 (d) $5406∙13 (e) ₤120∙85 (f ) 1783∙70 rupees 3. (a) $1620∙43 (b) €513∙75 4. (a) (i) €66∙73 (ii) 707∙30 HKD (b) 2248 THB (c) 2544∙91 THB 5. (a) €645∙21 (b) €678∙43 (c) €33∙22 6. (a) 5

(e) €1 = ₤0∙80; Exchange rate from ₤ to € is constant over this period

_ 4 (b) y = 5

Exercise 3

1. €270∙60 2. ₤346∙80 3. €219∙56 4. €357 5. €378∙51 6. €62∙39 7. €60∙86 8. (a) €38 610 in Luxembourg (b) €40 920 in Finland 9. €35 593∙22; €42 711∙86 10. €21 049

_ 4 x (c) €250 (d) ₤240

_ 3 2. (a) 5 × 10–2 m (b) 2∙7 × 10–3 km

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