The Association of Business Executives Certificate

(d)


Q3 (a)
(b)
(c)
150 ÷ 0.006038 × 0.98 = 24,347.00 Yen.

6 tonnes per hectare × £170 per tonne = £1,020 per hectare

£1,020 per hectare

––––––––––––––– = 6.71 tonnes per hectare £152 per tonne

(i)		2,000 – 1,700			× 100 = 17.65%
	1,700
(ii)	2,000 ×		100 – 17.65				= £1,647
	100

Since £57.80 is 85% of the original price, then ^57.80 × 100 = £68.00

																				85
(i)	•			1000 × 8 × 9							= £720
					100
	•											8.2			^8
					1000 ×		1		+										– 1000 = £878.53
											100
	•										0.683						96
					1000 ×			1	+											– 1000 = £922.16
											100

2. 
   £922.16 – £720.00 = £202.16
   

						i			5
(d)	750 ×		1+						= 1, 264
					100

1+ ⁱ = 1.11

100

i = 11%

		i		5		1, 264			i	= 1.685^0.2
1+				=			1+
	100				750			100

i = 1.11 – 1× 100

(e) (i)

17,250 × 0.75 × 0.92^5 = £8,526.87

£8,527

(ii)

17, 250.00 – 8,526.87

×

100

= 50.6%

17, 250.00

1

(17, 250.00 × 0.75) – 8,526.87

100

(iii)

÷ 5

×

= 5.11%

17, 250.00

1

[Turn over

15 IQM0608

Q4 (a)

(i)

If p = 12:

q = 175 – (6 × 12)

q = 175

– 72

q =103 units

(ii)

q = 175 – 6p

6p = 175 – q

175

– q

1

p = ––––––

p = 29.17 – – q

6

6

(iii)

If q = 40 units

p = 29.17

1

× 40)

p = 29.17 – 6.67p = £22.50

– (–

6

(b)

(i)

2(4x – 9) = 42

8x – 18

= 42

8x = 42 + 18

x = 7.5

2. 
   x ² – 8x + 15 = 0, using factorisation
   

(x – 5)(x – 3) = 0 x = 3, 5

3. 
   4x ² + 9x – 8 = 0
   

q =	–9 ± 9^2 –		(		4		× 4 × –8		)		q =	–9 ± 209
		× 4
2									8

₌ –9 ± 14.46 q

8

q = 0.68 or – 2.93

(c) 5x – 3y = 2

30x – 18y = 12

(x6)

6x + 7y = 13

30x + 35y = 65

(x5)

–53y = –53

y = 1

substituting (y = 1) in

5x – 3y = 2

5x – 3 = 2x = 1

6x + 7y = 13

5x – 3y = 2

4

3

2

1

point of

intersection

0

–3

–2

–1

0

1

2

3

–1

–2

–3

–4

–5

IQM0608 16

(i)		Co-ordinates of intersection with the
		x-axis	y-axis
	5x – 3y = 2	(0.4, 0)	(0, –0.7)
	6x + 7y = 13	(2.2, 0)	(0, 1.9)

2. 
   The two lines intersect at (1, 1)
   

Q5 (a)

male ⁰/5

male ¹/6

female ⁵/5

male ²/7

male ¹/5

female ⁵/6

female ⁴/5

male ¹/5

male ²/6

female ⁴/5

female ⁵/7

male ²/5

female ⁴/6

female ³/5

1. 
   = ⁵/7 × ⁴/6 × ³/5 = ²/7
   

= /	× /	× /	Probability
			= 0
2 7	1 6	0 5

= /	× /	× /	= ^1/21
2 7	1 6	5 5
= ^2/7 × ^5/6 × ^1/5			= ^1/21

= /		× /		× /		= ^4/21
2	7	5	6	4	5
= /		× /		× /		= ^1/21
5	7	2	6	1	5

= /	× /	× /	= ^4/21
5 7	2 6	4 5
= ^5/7 × ^4/6 × ^2/5			= ^4/21

= ^5/7 × ^4/6 × ^3/5

= ^2/7

2. 
   = (²/7 × ¹/6 × ⁵/5) + (²/7 × ⁵/6 × ¹/5) + (⁵/7 × ²/6 × ¹/5)
   

• 
  ¹/21 + ¹/21 + ¹/21
  

• 
  ¹/7
  

2. 
   = (²/7 × ¹/6 × ⁵/5) + (²/7 × ⁵/6 × ¹/5) + (²/7 × ⁵/6 × ⁴/5) + (⁵/7 × ²/6 × ¹/5) + (⁵/7 × ²/6 × ⁴/5) + (⁵/7 × ⁴/6 × ²/5)
   

• 
  ¹/21 + ¹/21 + ⁴/21 + ¹/21 + ⁴/21 + ⁴/21
  

• 
  ⁵/7