Chapter 32 Exercise 32.1
Q. 1.
(i) 2x + 3y = 6
x=0
y=0
3y = 6
2x = 6
y=2
x=3
(0,2)
(3,0)
5
2x + 3y = 6
4
3
2
(0,2)
1
(3,0)
0
–3
–2
–1
0
1
2
3
4
5
6
4
5
6
7
–1
–2
(ii) 5x + 3y = 15
x=0
y=0
3y = 15
5x = 15
y=5
x=3
(0,5)
(3,0)
8
5x + 3y = 15
7
6
5
(5,0)
4
3
2
1
(3,0)
0
–3
–2
–1
0
1
2
3
–1
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
1
(iii) 7x − 3y = 21
x=0
y=0
−3y = 21
7x = 21
y = −7
x=3
(0,−7)
(3,0)
7x - 3y = 21
3
2
1
(3,0)
0
–3
–2
–1
0
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
(0,7)
–7
(iv) 2x − 5y = 30
x=0
y=0
−5y = 30
2x = 30
y = −6
x = 15
(0,−6)
(15,0)
1
(15,0)
0
–3
–2
0
–1
1
2
3
4
5
6
7
–1
–2
–3
–4
–5
(0,–6)
–6
2
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
8
9
10
11
12
13
14
15
16
(v) 3x − y = 0
x=0
4
x=1
−y = 0
3(1) − y = 0
3
y=0
3−y=0
2
(0,0)
3x – y = 0
(1,3)
−y = −3
1
y=3
(0,0)
0
(1,3)
–3
–2
–1
0
1
2
3
4
5
–1
–2
–3
(vi) 4x + 3y = 12
x=0
y=0
3y = 12
4x = 12
4
y=4
x=3
3
(0,4)
(3,0)
2
(0,4)
4x + 3y = 12
1
(3,0)
0
0
–1
1
2
3
4
5
–1
Q. 2.
(i) y = 2x + 6
x=0
y=0
y=6
2x = −6
(0,6)
x = −3
(−3,0)
y = 2x + 6
6
(0,6)
5
4
3
2
1
0
–5
–4
–3
(–3,0)
–2
–1
0
1
2
3
4
5
–1
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
3
(ii) y = −x + 2
x=0
y=0
y=2
x=2
(0,2)
(2,0)
y = –x + 2
6
5
4
3
2
(0,2)
1
(2,0)
0
–5
–4
–3
–2
–1
0
1
3
2
4
5
–1
1
(iii) y = __x + 3
2
x=0
y=0
1
__
x = −3
2
x = −6
y=3
(0,3)
3
(0,3)
2
y = 0.5x + 3
1
(−6,0)
(–6,0)
0
–6
–5
–4
–3
–2
–1
0
1
2
–1
–2
1
(iv) y = −__x + 3
3
x=0
y=0
1
__
y=3
3
(0,3)
x=3
x=9
(9,0)
5
4
y = –0.33x + 3
3
(0,3)
2
1
(9,0)
0
–5
–4
–3
–2
–1
0
1
2
3
–1
4
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
4
5
6
7
8
9
10
11
3
3
(v) y = −__x − 6
4
x=0
y=0
3
__
x = −6
4
3x = −24
y = −6
(0,−6)
x = −8
(−8,0)
y = –0.75x – 6
3
2
1
(–8,0)
–13 –12
–11
–10
–9
–8
–7
0
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
–1
–2
–3
–4
–5
–6
(0,–6)
–7
(vi) y = 5x
x=0
x=1
y=0
y=5
(0,0)
(1,5)
y = 5x
7
6
(1,5)
5
4
3
2
1
0
–1
(0,0)
0
1
2
3
4
–1
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
5
Q. 3.
Q. 4.
Q
6
1
5
0
–3 –2 –1
–1
4
3
2
1
0
1
2
–2
f: x → 3x – 1
0 1
–2 –1
–1
–3
–4
2
3
–5
4
–6
–2
–7
–3
–8
f: x → 2x – 3
–9
–4
–5
–6
(i) (4,4)
Q. 5.
Q
–7
(ii) (−2,1)
(iii) (2,−4)
(iv) (0,−3)
Q. 6.
(i) x + 3y = 12
x=0
y=0
3y = 12
x = 12
y=4
(12,0)
6
5
x + 3y = 12
4
3
(0,4)
(6,2)
2
x − 2y = 2
x=0
−2y = 2
y = −1
1
y=0
x=2
(2,0)
(0,−1)
0
–2
0
–1
x – 2y = 2
1
2
3
4
5
6
7
8
9
–1
–2
–3
POI: (6,2)
–4
–5
(ii) x + y = 6
2x + y = 8
x=0
y=0
x=0
y=0
y=6
x=6
y=8
2x = 8
(0,6)
(6,0)
(0,8)
x=4
POI : (2,4)
6
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
(4,0)
10
11
12
2x + y = 8 9
x+y=6
8
7
6
5
(2,4)
4
3
2
1
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
–1
–2
(iii) x − 3y = −12
x=0
2x + 3y = 30
y=0
x=0
y=0
−3y = −12
x = −12
3y = 30
2x = 30
y=4
(−12,0)
y = 10
x = 15
(0,10)
(15,0)
(0,4)
POI: (6,6)
–14–13–12–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1 2
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
–12
–13
(6,6)
3
4
5
6
7
8
9 10 11 12 13
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
7
(iv) 5x − 2y = −10
x−y=1
x=0
y=0
x=0
y=0
−y = 1
x=1
−2y = −10
5x = −10
y=5
x = −2
y = −1
(0,5)
(−2,0)
(0,−1)
(1,0)
POI: (−4,−5)
5x – 2y = –10
5
4
3
2
1
0
–6
–5
–4
–3
–2
0
–1
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
(–4,–5)
x–y=1
–6
(v) x + 2y = 8
x − 2y = 0
x=0
y=0
x=0
x=2
2y = 8
x=8
−2y = 0
2y = 2
y=4
(8,0)
y=0
y=1
(0,0)
(2,1)
(0,4)
POI: (4,2)
5
x + 2y = 8
4
3
(4,2)
2
1
0
–2
–1
0
1
2
3
4
–1
x – 2y = 0
–2
8
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
5
6
7
(vi) y = 2x + 4
y = 3x − 3
x=0
y=0
y=4
2x = −4
y = −3
3x = 3
(0,4)
x = −2
(0,−3)
x=1
x=0
y=0
(−2,0)
(1,0)
POI: (7,18)
y = 3x – 3
20
y = 2x + 4
18
(7,18)
16
14
12
10
8
6
4
2
0
–12
–10
–8
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
–2
–4
(vii) y = x + 1
y = −3x + 5
x=0
y=0
x=0
y=0
y=1
x = −1
y=5
(0,1)
(−1,0)
(0,5)
3x = 5
5
x = __
3
2
(1__,0)
3
POI: (1,2)
5
y = –3x + 5
4
3
2
(1,2)
1
0
–3
–2
0
–1
1
2
3
4
5
6
–1
y=x+1
–2
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
9
x=0
y=0
1
y = −__x + 2
2
x=0
y=1
x=1
y=2
(0,1)
(1,0)
(0,2)
(viii) y = −x + 1
y=0
1
__
x=2
2
x=4
POI: (−2,3)
(4,0)
y = –x + 1
5
4
y = –0.5x + 2
(–2,3)
3
2
1
0
–5
–4
–3
–2
0
1
2
3
4
–1
–2
y=0
2
y = __x
3
x=0
x=3
y = −4
2x = 4
y=0
y=2
(0,−4)
x=2
(0,0)
(3,2)
(ix) y = 2x − 4
x=0
(2,0)
POI: (3,2)
y = 2x – 4
5
4
3
2
(3,2)
1
0
–6
–5
–4
–3
–2
–1
0
1
–1
–2
–3
y = 0.67x
–4
–5
–6
10
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
2
3
4
5
6
7
8
9
(x) 3x − 4y = 0
1
y = −__x + 4
4
x=0
x=4
x=0
x=4
−4y = 0
3(4) − 4y = 0
y=4
y = −1 + 4
y=0
12 − 4y = 0
(0,4)
y=3
(0,0)
−4y = −12
(4,3)
y=3
POI: (4,3)
(4,3)
5
y = –0.25x + 4
4
(4,3)
3
2
1
0
–3
–2
–1
0
1
2
3
4
5
6
7
–1
3x –4y = 0 –2
Q. 7.
(i) No.
5x – 2y = –10
6
5x – 2y = 20
5
4
3
2
1
0
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
–1
–2
–3
–4
–5
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
11
(ii) Yes.
6
–3x + y = –6
–2x + y = –4
5
4
3
2
1
0
–4
–3
–2
0
–1
1
2
–3
–2
3
4
5
6
1
2
7
8
9
10
11
4
5
6
7
–1
–2
–3
–4
–5
(iii) Yes.
0
–8
–7
–6
–5
–4
–1
0
y = 4x –2
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
–11
12
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
3
y = 2x –5
(iv) No.
8
y = 2x –4
y = 2x + 8
7
6
5
4
3
2
1
0
–5
–4
–3
–2
0
–1
1
2
3
4
5
6
7
8
9
–1
–2
–3
Exercise 32.2
Q. 1.
(i) €180
(i) €136
(ii) €60
(ii) €175
(iii) 550 km
(iii) 900 units
(iv) y = 0.2x + 20
(iv) Cost = 0.164(1,500) + 22.12
= 268.12
(v) Cost = 0.2(1220) + 20
= €264
Q. 2.
Q
Q. 3.
(i) €11
(ii) €9
1
(iii) 4__ km
2
(iv) y = 2x + 3
(v) Cost = 2(10) + 3
= €23
Q. 4.
Q
(i) €40
(ii) €55
(iii) 400 units
(iv) y = 0.1x + 20
(v) Cost = 0.1(800) + 20
= €100
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
13
Q. 5.
(i)
Fahrenheit
220°
200°
180°
160°
140°
120°
100°
80°
60°
40°
20°
Celsius
0°
–20°
0°
10°
20°
30°
(ii) 32°F
Q. 6.
50°
70°
f(x) = 3x + 1
1
2
3
4
5
6
(i) 100
80°
90°
100°
(iv) 212°F
(iii)
0
60°
(iii) 5°C
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
–1
40°
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
–1
7
f(x) = 3x + 1
g(x) = 2x
0
1
2
3
4
5
(iv) €70
(ii) 5 days
Q
7
Q. 7.
Q. 8.
(i) €100
(i) €84
€84,000
000
(ii) €220
(ii) €92,000
(iii) 270 people
(iii) 2013
(iv) y = 0.6x + 100
(iv) Apartment: €101,000
(v) Cost = 0.6(350) + 100 = €310
Car:
€52,000
(i) €20,000
Total:
€153,000
(ii) €12,800
Yes, he will have enough.
(iii) €8,000
(iv) y = −2,400x + 20,000
14
Q. 9.
Q
9
(v) Value = −2,400(6) + 20,000
= €5,600
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
6
Exercise 32.3
Q. 1.
(i) Week Savings (€)
0
1
2
3
4
5
Savings (EURO)
550
300
350
400
450
500
550
500
450
400
350
300
250
200
(ii) €370
150
(iii) €480
100
50
0
Weeks
0
–0.5
Q. 2.
(i)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Cost (€)
50
80
110
140
170
Call-Out Change
1 hr
2 hrs
3 hrs
4 hrs
(ii)
0.5
180 Cost (EURO)
160
140
120
100
80
60
40
20
Time (hrs)
0
0
0.5
1
1.5
2
2.5
3
3.5
4
(iii) No. The line does not pass through (0,0).
Q
Q. 3
3.
(i)
Month
Jan.
Feb.
Mar.
Apr.
May
Comics (No.)
22
27
32
37
42
(ii) This is a linear pattern, since the first
difference is constant.
(iii) 22 + 11(5) = 77
4.5
5
5.5
(iv) €200
Q.
Q 4
4.
(i)
(v) €290
Time (in Weeks) Height (in cm)
0
50
1
55
2
60
3
65
4
70
(ii) 50 cm
(iii) Linear, since the first difference is
constant.
(iv) 50 + 9(5) = 95 cm
100 − 50 50
(v) _________ = ___ = 10 weeks
5
5
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
15
Q. 5.
(i)
Week 1
Week 2
Week 3
No. of kilometres run
18
21
24
(ii) Linear. The first difference is a constant.
(iii)
60
50
Km
40
30
20
10
0
0
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7
(iv) After the first three weeks of training, he may decide to increase the rate at which he trains.
In this case, the second part of the line graph would be steeper than the first part (the first 3
weeks).
Q. 6.
(i)
(ii)
Radiators (Nos)
0
1
2
3
4
5
6
7
2000
Cost (€)
1,000
1,125
1,250
1,375
1,500
1,625
1,750
1,875
Cost (EURO)
1800
1600
1400
1200
1000
800
600
400
200
No. of Radiators
0
–0.5
16
0
0.5
1
1.5
2
2.5
3
3.5
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
4
4.5
5
5.5
6
6.5
7
(iii) 1,000 + 10(125) = 1,000 + 1,250 = €2,250
3,000 − 1,000
(iv) _____________ = 16
125
Q. 7.
(i)
No. of Days
0
1
2
3
4
5
6
7
8
Cost (€)
50,000
70,000
90,000
110,000
130,000
150,000
170,000
190,000
210,000
(ii)
220000
Cost (EURO)
200000
180000
160000
140000
120000
100000
80000
60000
40000
20000
0
No. of days
0
1
2
3
4
5
6
7
8
9
10
(iii) After Day 3
(iv) 210,000 + 6(20,000) = €330,000
(v) 500,000 − 330,000 − 100,000 = €70,000 profit
Q. 8.
(i)
No. of
Seán Ciara
Days
0
10
0
1
15
7
2
20
14
3
25
21
4
30
28
5
35
35
6
40
42
7
45
49
8
50
56
9
55
63
10
60
70
(ii)
70
No. of Words
Ciara
Seán
60
50
40
30
20
10
No. of days
0
0
1
2
3
4
5
6
7
8
9
10
(iii) 5
100 − 10 90
(iv) _________ = ___ = 18 days
5
5
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
17
(i)
Q. 9.
Quantity
No. of
Supplied
Weeks
(litres)
0
200,000
1
215,000
2
230,000
3
245,000
4
260,000
5
275,000
6
290,000
Quantity Supplied (litres)
300000
250000
200000
150000
100000
50000
No. of Weeks
0
–0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
800,000 − 200,000 600,000
(ii) __________________ = ________ = 40 weeks
15,000
15,000
Q. 10.
Milk (litres)
Cheese (kg)
12,000
1,000
24,000
2,000
36,000
3,000
Cheese (kg)
3000
2500
2000
1500
1000
500
Milk (litres)
0
0
18
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000 36000
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
(ii)
No. of
Cost (€)
books
0
20,000
0
20,000
300
21200
600
22400
900
23600
1200
24,800
1500
26000
1800
27200
2100
28400
2400
29,600
2700
30,800
3000
32,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
0
300
600
900
1200
1500
1800
2100
2400
2700
3000
Number of Books
Mad Printers
No. of books Cost (€)
0
21000
300
21600
600
22200
900
22800
1200
23400
1500
24000
1800
24600
2100
25200
2400
25800
2700
26400
3000
27000
35,000
30,000
25,000
Cost (€)
(i)
Cost (€)
Q. 11.
20,000
15,000
10,000
5,000
0
0
300
600
900
1200 1500 1800 2100 2400 2700 3000
Number of Books
(iii) Cheap Print: €32,000; Mad Printers: €27,000
(iv) The cost of printing is the same for either company.
(v) Mad Printers
Exercise 32.4
Q. 1.
(i)
200
(ii) 159 km
Height (km)
(iii) 1.4 minutes
= 1 minute 24 seconds
180
160
140
120
100
80
60
40
20
0
Time (minutes)
0
–20
1
2
3
4
5
6
7
8
9
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
19
Q. 2.
(i)
Q
Q. 5.
1.4
Area Covered (sq. km)
(i) Quadratic (as it declines to a
minimum value and then rises)
(ii) Month 11
1.2
1
(iii) Month 5
0.8
(iv) ≈ 17 km2 = 30%
17
___
= 10%
3
170
____
= 100%
3
2
Answer ≈ 56__ km2
3
(v) Months 9, 10 and 11
0.6
0.4
0.2
0
Days
0
1
2
3
4
(ii) Exponential
(iii) 5 days: 2.24
Weeds grow more vigorously during
the summer. This is indicated during
months 9 to 11 in the graph.
6 days: 4.48
7 days: 8.96
Q
Q. 6.
Ans: 8.96 km2
Q. 3.
x
0
1
2
3
4
5
6
16
14
12
10
8
(i)
6
4
2
0
1
2
3
4
5
6
7
8
(ii) 7.3 m/s
(iii) 4 s
(iv) 2.6 and 5.4 seconds
Q. 4.
20
(i) 17,000
y
9
4
1
0
1
4
9
10
9
8
7
6
5
4
3
2
1
–1 0
1
2
3
4
5
6
(ii) Quadratic
(ii) 9 m
(iii) 12,000
(iii) 1 second and 5 seconds after release
(iv) 10 am. This is the time after which
the population declines.
(iv) 3 seconds after release
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
Q. 7.
(i)
Height (cm)
35
F
E
30
D
25
C
20
B
15
10
5
A
f
Day
0
0
0.5
1
1.5
2
2.5
3
3.5
4.5
4
5
(ii) 6 cm
(iii) Day 4 and 5
(iv) Day 0 and Day 1
(v) 27 cm
Q. 8.
x
–2
–1
0
1
2
3
y
7
0
–3
–2
3
12
12
11
10
f(x) = 2x2 – x – 3
9
8
7
6
5
(i) –2°C
4
3
(ii) x ≈ 0.25
2
1
∴ From approximately 05:15
(iii) From x = –1 to x = 1.5
∴ 2.5 hours
(iii) 1 hour + 1.5 hours = 2.5 hours
–2
–1
–1
0
1
2
3
–2
–3
Exercise 32.5
Q. 1.
(i) 50 + 20 + 20 + 50 = 140 km
(ii) 13:00
(iii) Along the line segment [DE]
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
21
Q. 2.
5
Distance (km)
4
3
2
1
0
0
5
10
15
20
25
30
35
40
45
50
55
Time (minutes)
Q. 3.
Left school for a class trip at 9.00 walked 2 km to the local museum which we reached at
10:00. Spent one hour there before leaving and travelling at a quicker pace to the bus stop
which was 3 km away. Got the bus at 12.00 and went on a coach tour over a scenic route
(10 km eventually from school) before returning to school at 14.00.
Q. 4.
Fig A → Statement 5
Fig B → Statement 4
Fig C → Statement 2
Fig D → Statement 1
Fig E → Statement 3
Q. 5.
(ii) 2.7 secs.
(iii) 45 m/s
Speed (m/sec)
(iv)
22
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5 A
0
0
G
F
E
D
C
B
1
2
3
Time (sec)
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
4
5
6
Q. 6.
(i) Race A: Oisín; Race B: Juan
(ii) Race A: 150 m; Race B: 250 m
(iii) Race A: Oisín 25 seconds; Juan 30 seconds
Race B: Oisín 45 seconds; Juan 40 seconds
150
(iv) Oisín: ____ = 6 m/s
25
150
____
Juan:
= 5 m/s
30
(v) 0 seconds: start of race
23 seconds: point of intersection of two graphs
(vi) Juan: He starts approximately 10 m ahead of Oisín at 0 seconds.
(vii) Juan: The slope of his graph at the start is greater than the slope of Oisin’s graph. This
shows that his rate of change is greater.
(viii) Oisín: The slope of his graph at the finish is greater than the slope of Juan’s graph.
Revision Exercises
Q. 1.
(i) x + y = 5
2x − y = −8
x=0
y=0
x=0
y=0
y=5
x=5
y=8
x = −4
(0,5)
(5,0)
(0,8)
(−4,0)
∴ POI: (−1,6).
8
(–1,6)
7
6
5
4
3
2
1
0
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
–1
–2
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
23
4x − y = −6
(ii) x − 2y = −5
x=0
y=0
x=0
y=0
−2y = −5
5
y = __
2
1
0,2 __
2
∴ POI: (−1,2)
x = −5
−y = −6
(−5,0)
y=6
(
)
4x = −6
3
6
x = −__ = −__
4
2
1
(−1__,0)
2
(0,6)
–4x + y = 6
6
5
4
3
(–1,2)
2
1
0
–7
–6
–5
–4
–3
–2
–1
0
1
2
x – 2y = –5
x=0
()
y=0
y=6
(0,6)
∴ POI: (3,2)
4
1
y = __ x + 1
3
x=0
(iii) 4x + 3y = 18
3y = 18
3
–1
4x = 18
18 9
x = ___ = __
4
2
1
(4__,0)
2
y=0
1
__
y=1
3
(0,1)
4x + 3y = 18
5
4
3
(3,2)
2
1
0
24
–4
–3
y = 0.33x + 1
–2
–1
x = −3
(−3,0)
6
–5
x = −1
0
1
–1
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
2
3
4
5
6
x=0
x=1
1
y = __x + 8
3
x=0
y=0
y=1
y=8
y=2+8
(0,0)
(1,1)
(0,8)
y = 10
(iv) y = x
x=6
(6,10)
∴ POI: (12,12)
12
(12,12)
10
8
6
y = 0.33x + 8
4
2
0
–8
–4
–6
–2
0
2
4
8
6
10
12
14
16
–2
–4
y=x
Q. 2.
40
(i) ___ = 8
5
(ii) They earn €8 per hour.
(iii) After 4 hrs: €32
(iv) y = 8x
x=8
y = 8(8)
Ans = €64
(v) The equation of the line method is more accurate if the correct equation is used. Reading
the graph, as drawn, will involve some error (most likely).
Q. 3.
(i)
(ii) Initial set-up costs.
Cost (EURO)
(iii) €19
70
(iv) €75
60
[y = 2(35) + 5 = 75]
40
30
20
10
Number of Magazines
0
0
5
10
15
20
25
30
35
40
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
25
Q. 4.
(i)
Time
Money owed
0
500
1st month
425
2nd month
350
3rd month
275
(ii)
Money Owed (EURO)
500
400
300
200
100
Months
0
0
1
2
3
5
4
6
7
8
9
10
(iii) More than 6 months. (Between 6 and 7 months)
Q. 5.
(i)
Time (hours)
Cost (€)
0
50
1
70
2
90
3
110
4
130
5
150
6
170
4
3
2
1
0
0
1
2
3
–1
–2
–3
–4
(i) 2.25°
(iii) Call−out charge.
(ii) –4° at 3 a.m
(iv) Additional cost per hour.
(iii) 1 a.m and 5 a.m
(i) 18:30
(ii) Between 18:45 and 19:00
600 km
(iii) _______ = 34.29 km/hr
1.75 hrs
26
5
(ii) y = 20x + 50
(v) y = 20(8.5) + 50 = €220
Q. 6.
Q.
Q 7.
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
4
5
6
Q. 8.
(i) Yes
2
y = 3x – 2
y = 2x – 3
1
0
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
0
2
4
6
8
10
12
–1
–2
–3
–4
(–1,–5)
–5
–6
(ii) No
8
6
4
2
y = 0.33x + 5
0
–4
–10
–8
–6
–4
–2
14
–2
–4
y = 0.33x – 4
–6
–8
(iii) Yes
6
4x + 3y = 11
4x + 3y = 9
5
4
3
2
1
0
–4
–3
–2
–1
0
–1
1
2
3
4
(2.5,–0.33)
5
6
7
–2
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
27
(iv) No
Reasons:
2.5
(i) Slopes are different.
(ii) Slopes are equal
(i.e. parallel lines).
2
1.5
(iii) Slopes are different.
1
(iv) Slopes are equal
(i.e. parallel lines).
0.5
0
–1
–0.5
0
0.5
1
1.5
2
2.5
3
3.5
–0.5
Q. 9.
(i) About 9 m
(ii) The train travels slowly for the first 20 seconds. Its speed then increases from around 25 seconds
into the journey. The fastest speed is between 50 and 60 seconds.
(iii) It is a train leaving a station.
Q. 10.
(a) John walks to school at a constant moderate speed. He looks at his watch, realises he will be
late if he doesn’t hurry up, so increases the pace at which he walks to school and walks the final
part of the journey at this faster speed.
(b) A car turning a sharp bend in the road slows down into the bend and speeds up out of it.
(c) The rate at which water fills a storage tank is constantly increasing.
(d) A pizza company charge a set delivery charge plus a rate of €x per pizza bought.
(e) A car is stuck in traffic and does not move.
(f )
A train travels at a constant speed before slowing down to a stop at a train station.
Q. 11.
Q.
Q 13.
16
(i)
Number of Birds
14
40
12
30
10
20
8
10
Day
0
6
0
1
2
3
4
5
4
(ii) Quadratic
2
–3 –2 –1
0
1
2
3
4
(i) 12.75
Day 7: 90 (66 + 24)
(iii) 10.30 p.m and 2.30 a.m.
(i) 450 g
(ii) 7 ounces
200
(iv) y = ____x
7
200
____
(v) y =
(50)
7
= 1,428.6 g
200
(iii) ____
7
28
(iii) Days 4 and 5
(iv) Day 6: 66 (46 + 20)
(ii) 00.30 a.m
Q. 12.
The second differences are constant.
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
Q. 14.
(i)
35
Height (cm)
30
25
20
15
10
5
0
0
5
10
15
20
25
30
35
(ii) It is constant.
(iii) ≈ 26.4 cm
(iv) 21.6 − 8 ≈ 13.6 cm
Q. 15.
(i) Days: 5
Cost: €600
∴ Cost per Day = €60 ÷ 5 = €120
(ii) €400
(iii) Cheaper Vans: Linear pattern (with fixed fee): There is an initial fixed fee of €400 followed
by a charge of €50 per day.
Vans R Us: Linear pattern (proportional): There is no fixed fee and a cost of €120 per day.
(iv) Cheaper Vans
(v) Vans R Us: Cost = 120 × Time
Cost = 120 × 15 = €1,800
Cheaper Vans: Cost = 400 + 50 × Time
Cost = 400 + 50 × 15 = €1,150
Q. 16.
(i) Exponential
(ii)
Day
No. of Words
0
4
1
8
2
16
3
32
4
64
5
128
6
256
7
512
8
1,024
9
2,048
10
4,096
11
8,192
12
16,384
No. of Words Known
500
400
300
200
100
Days
0
0
1
2
3
4
5
5
5
(iii) Day 12: 16,384
Active Maths 1 – Strands 1–5 – Ch 32 Solutions
29
Q. 17.
Q
Q. 18.
16
(i)
18
12
16
8
12
Height (metres)
14
10
4
0
8
0
1
2
3
4
6
5
4
–4
2
0
–8
Time (seconds)
0
1
2
3
4
5
–12
(ii) Quadratic
–16
(iii) Height = 6.25 m − 6.25
(iv) The pigeon had landed and is now
taking off again.
(i) 3.8
(ii) 10.4 m
(iii) 8.8 m
Q. 19.
(i)
50
No. of Cans
40
30
10
5
Level
0
0
1
2
3
4
5
6
7
8
9
(ii) 49 + 42 + 35 + 28 + 21 + 14 + 7 = 196 cans
(iii) Seven levels in total
∴ 7 × 12 = 84 cm
30
Active Maths 1 – Strands 1–5 – Ch 32 Solutions