Checkpoint Maths 2 Answer
Short Description
Cambridge Checkpoint...
Description
D - Ans 4 web - 001-024.qxd
17/8/04
11:13 am
Page 1
Checkpoint Maths 2 Answers SECTION ONE
5
Chapter 1 – Shape, space and measures 1 Exercise 1.1 1
2
Sunday
0200
1012
1400
2212
Monday
0200
1012
1348
2200
Tuesday
0310
1122
1510
2322
Wednesday
0336
1148
1321
2133
(d) 1845
(e) 2330
(f) 1650
Thursday
0255
1107
1515
2327
(a) 1900
(b) 1200
(c) 0005
Friday
0057
0909
1436
2248
(d) 2210
(e) 0815
(f) 2015
Saturday
0638
1450
1648
0100
(g) 0745
(h) 1945 (a) 1 hour 2 min (b) 1620 (c) 1926
(a) 0840
(d) 2225 7
(c) 0800
Pupils’ own questions and answers.
(a) 1630
Chapter 2 – Number 1
(b) 1606 (c) 1803 (a)
Depart
Exercise 2.1 (b)
Arrive
Depart
Arrive
0523
0631
5.23 am
6.31 am
0715
0823
7.15 am
8.23 am
0904
1012
9.04 am
10.12 am
1028
1136
10.28 am
11.36 am
1 2
3
(a) 14.8
(b) 31.14
(c) 9.66
(d) 100.01
(e) 44.44
(f) 9.1
(a) 11.1
(b) 10.9
(c) 15.04
(d) 0.01
(e) 11.7
(f) 10
(g) 12
(h) 0
(a) 17.02
(b) 159.36
(c) 43.56
(e) 35.1
(f) 5.1
(h) 10
1445
1553
2.45 pm
3.53 pm
(d) 4
1622
1730
4.22 pm
5.30 pm
(g) 18.63
1809
1917
6.09 pm
7.17 pm
2017
2125
8.17 pm
9.25 pm
Exercise 2.2 1
4
Dubai (local time)
(c) 0955
(b) 0820
3
London
(b) 0535
Exercise 1.2
2
Dubai (local time)
(a) 0830
6
1
London
Stansted
0500
0715
0915
1040
1315
Luton
0630
0845
1045
1210
1445
Gatwick
0805
1020
1220
1345
1620
Heathrow
0850
1105
1305
1430
1705
2 3
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
(a) 20
(b) 30
(c) 24
(d) 14
(e) 43
(f) 18
(a) 18
(b) 9
(c) 11
(d) 0
(e) 27
(f) 1
(a) 15
(b) 18
(c) 2
(d) 35
(e) 15
(f) 6 1 of 24
D - Ans 4 web - 001-024.qxd
2
4
17/8/04
11:14 am
Section 1 – Shape, space and measures 2
(a) (12 8) 2 8
Exercise 3.3
(b) 5 (2 4) 30
1
Pupils’ perpendicular bisector constructions.
2
The orientation of pupils’ diagrams may differ from the ones shown below.
(c) 2 (3 4 5) 4 (d) (10 4) (3 3) 36 (e) (9 6 3) 2 4 10 (f) (9 6 3) (2 4) 2 5
Page 2
(a)
(b)
(d)
(e)
(a) 20 8 2 6 22 (b) (20 8) 2 6 12 (c) (20 8) (2 6) 1.5 (d) 20 (8 2 6) 10 (e) 20 8 (2 6) 19
6
(a) 8 3 4 6 14 (b) (8 3) 4 6 38 (c) (8 3) (4 6) 22 (d) 8 3 (4 6) 2
Exercise 2.3 1 2
(a) 4
(b) 4
(c) 3
(d) 8
(e) 12
(f) 6
(a) 13
(b) 37
(c) 12
(d) 12.8
(e) 0.125
(f) 0.5
(f)
Chapter 3 – Shape, space and measures 2 Exercise 3.1 1
Circumference
2
Radius, radii
3
Chord
4
Diameter
5
Arc
6
Sector
7
Segment
8
Tangent
(g)
Exercise 3.2 1
Pupils’ drawings.
2
Pupils’ drawings.
3
Pupils’ own patterns.
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
2 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 3
Section 1 – Using and applying mathematics/ICT
3
Pupils’ construction of a regular octagon.
4
(a), (b) Pupils’ constructions.
Chapter 5 – Using and applying mathematics/ICT 1
(c) Point of intersection is the same distance from points A, B and C.
Investigation
5
Pupils’ constructions.
6
Pupils’ constructions.
Chapter 4 – Handling data 1 Exercise 4.1 1
Primary
2
Secondary
3
Secondary
4
Primary
5
Secondary
Only one possible solution for each number is given below. There are many other correct possibilities. Some solutions have included the use of the factorial (!) which, although not covered in the text, could be introduced for more able students. 1 44 44
4 4 2 4 4
4 3 4 4 4
44 4 4 4
4 5 4 4 4
44 6 4 4
4 7 4 4 4
8 (4 4) 4 4
4 9 4 4 4
44 4 10 4
Pupils’ suggested research.
4 11 4! 4 4
44 4 12 4
Q p.19
4 13 4! 4 4
14 4 4 4 4
Question (c).
15 44 4 4
16 4 4 4 4
Q p.19
4 17 4 4 4
4 18 4 4 4
4 19 4! 4 4
20
4 21 4! 4 4
22 4 4 4 4
23 (4! 4 4) 4
24 4 4 4 4
Q p.19
Pupils’ own questions.
Q p.19 Pupils’ own questions.
Exercise 4.2 Pupils’ rewritten questions.
25
4 4 4
4
4 4 4 4
44 26 4! 4
Exercise 4.3
4 27 4! 4 4
28 4 4 4 4
Pupils’ own questions. Ensure questions are clear, simple, unbiased and relevant.
4 29 4 4! 4
30 4 4 4 4
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
3
3 of 24
D - Ans 4 web - 001-024.qxd
4
17/8/04
11:14 am
Page 4
Section 2 – Number 2
SECTION TWO
ICT activity Pupils’ constructions. As the vertex is dragged, the shape of the triangle changes but the circumference of the circle still passes through each of the three vertices.
Chapter 6 – Number 2 Exercise 6.1 1
Review 1A 1
(a) 1645
(b) 0030
2
0620
3
0900
4
(a) (3 4) 5 35 (b) (8 6) (7 4) 22 (c) 5 (8 3) 4 51
5
Pupils’ construction of a regular hexagon.
6
arc sector
chord
2
Pupils’ questionnaires. Pupils’ examples of a biased question which should not be used.
(d) A thousandth
(e) One thousand
(f) A thousandth
(g) A thousandth
(h) One thousand
(i) A millilitre
(j) One million
(a) kg
(b) cm
(c) m or cm
(d) ml
(e) t
(f) m
(g) litre
(h) km
(i) litre
(j) cm
Pupils’ lines and measurements.
4
Pupils’ estimates. Answers may vary considerably.
Exercise 6.2
tangent
8
(b) A hundredth
3
1
7
(a) One hundred (c) One thousand
(a) 1 m is 100 cm so to change from m to cm multiply by 100 to change from cm to m divide by 100. (b) 1 m 1000 mm so to change from m to mm multiply by 1000. so to change from mm to m divide by 1000. (c) 1 cm 10 mm so to change from cm to mm multiply by 10. to change from mm to cm divide by 10.
Review 1B
(a) 40 mm
(b) 62 mm
(c) 280 mm
(d) 1200 mm
2040 on Wednesday
(e) 880 mm
(f) 3650 mm
3
2300
(g) 8 mm
(h) 2.3 mm
4
(a) (7 8) (3 2) 3
(a) 2.6 m
(b) 89 m
(c) 2300 m
(d) 750 m
(e) 2.5 m
(f) 400 m
(g) 3800 m
(h) 25 000 m
1
1625
2
(b) (7 8) 3 2 7
2
3
(c) 7 8 (3 2) 8.6 5
Pupils’ constructions of a perpendicular bisector.
6
Pupils’ examples.
(a) 2 km
(b) 26.5 km
7
Pupils’ questionnaires.
(c) 0.2 km
(d) 0.75 km
8
Pupils’ examples of a badly written question, i.e. not clear, not relevant or biased.
(e) 0.1 km
(f) 5 km
(g) 15 km
(h) 75.6 km
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
4
4 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 5
Section 2 – Algebra 1
5 1 kg is 1000 g so to change kg to g multiply by 1000 to change g to kg divide by 1000. 6 (a) 2000 kg
(b) 7200 kg
(c) 2.8 kg
(d) 0.75 kg
(e) 450 kg
(f) 3 kg
(g) 6.5 kg
(h) 7000 kg
7 (a) 2600 ml
Exercise 7.2 1 2 3
(b) 700 ml
(c) 40 ml
(d) 8 ml
8 (a) 1.5 litres
4
(b) 5.28 litres
(c) 0.75 litres
(d) 0.025 litres
5
9 138.3 tonnes 6
10 (a) 720 ml (b) 0.53 litres
7
Chapter 7 – Algebra 1 Exercise 7.1 1 (a) a 2
(b) a 3
(d) a 6
(e) a 5
2 (a) b 7
(b) b 7
(d) b 5
(e) b 8
3 (a) c 4
(b) c 8
(d) c 4
(e) c 8
4 (a) d 2 (d) d 11
(b) d 4 (b) e 4
(d) e 4
(e) e 3
6 (a) f 3
(b) f 3
(d) f 4
(e) f 7
7 (a) g 4
(b) g 12
(d) g 4
(e) g 6
(d) h 5
(b) h 4 (b) k 4
(d) k 4
(e) k 2
10 (a) m 9 (d) m 1
(b) m 17
(b) a 3
(d) a 2
(e) a 2
(a) b 5
(b) b 2
(d) b 2
(e) b 3
(a) c 2
(b) c 5
(d) c 4
(e) c 3
(a) d 2
(b) d 3
(d) d 3
(e) d 3
(a) e 1
(b) e 3
(d) e 3
(e) e 2
(a) f 1.5
(b) f 1
(d) f 3
(e) f 5
(a) g 1
(b) g 5
(d) g 14
(e) g 1
(c) a 1 (c) b 1 (c) c 3 (c) d 5 (c) e 2 (c) f 1 (c) g 5
Exercise 7.3 (b) a 4 (e) a 1
(c) a 4
2 (a) b 2 (d) b 3
(b) b 3 (e) b 12
(c) b 5
3 (a) c 3 (d) c 8
(b) c 5 (e) c 1
(c) c 9
4 (a) d 9 (d) d 1
(b) d 7 (e) d 5
(c) d 4
5 (a) e 3 (d) e 3
(b) e 2 (e) e 2
(c) e 2
6 (a) f 8 (d) f 4
(b) f 7 (e) f 6
(c) f 3
(c) g 3
7 (a) g 4 (d) g 3
(b) g 14 (e) g 5
(c) g 3
(c) h 5
8 (a) h 2 (d) h 3
(b) h 3 (e) h 3
(c) h 10
(c) k 5
9 (a) j 8 (d) j 14
(b) j 15 (e) j 27
(c) j 32
10 (a) k 6 (d) k 15
(b) k 4 (e) k 16
(c) k 6
(c) b 7 (c) c 3 (c) d 9 (c) e 2 (c) f 6
(e) h 11
9 (a) k 6
(a) a 2
1 (a) a 3 (d) a 5
(e) d 9
5 (a) e 2
8 (a) h 2
(c) a 4
(c) m 13
(e) m 4
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
5
5 of 24
D - Ans 4 web - 001-024.qxd
6
17/8/04
11:14 am
Page 6
Section 2 – Shape, space and measures 4
Chapter 8 – Shape, space and measures 3
Chapter 9 – Shape, space and measures 4
Exercise 8.1
Exercise 9.1
(a) 18.85 cm
(b) 78.54 cm
(c) 125.66 mm
(d) 3.14 m
(a) 25.13 cm
(b) 21.99 cm
(c) 75.40 mm
(d) 39.58 m
(a) 31.4 cm
(b) 35.7 cm
(c) 61.7 cm
(d) 121.4 mm
(e) 13.7 cm
(f) 100.7 cm
4
(a) 235.6 cm
(b) 424 times
5
6.3 cm
6
37.70 m
1 2 3
1
2
3
Exercise 8.2 1
(a) 28.3 cm2
(b) 176.7 cm2
(c) 2.0 mm2 (e) 167.4 cm 2
(d) 918.6 cm2 2
(f) 0.1 cm2
(a) 100.5 cm2
(b) 78.5 cm2
(c) 58.9 cm2
(d) 62.1 cm2
(e) 1.9 cm
2
(f) 43.4 cm2
4
Exercise 8.3 1
(a) 25 cm2 (b) 19.6 cm2 (1 dp) (c) 5.4 cm2 (1 dp)
2
11.4 cm2
3
(a) 25.1 cm2 (1 dp)
Exercise 9.2 1
(b) 21.5% (1 dp) 4
(a) 268 cm2 (b) 81 cm
5
5969 m2
6
Ring 1 37.7 cm2 Ring 2 62.8 cm2 Ring 3 88.0 cm2
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
6 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 7
Section 2 – Shape, space and measures 4
2
7
Exercise 9.3 1
2
3
4
5
6
3
4
Exercise 9.4 The diagrams that follow show only two possible nets for the three-dimensional shapes in the question. Other nets are possible. 1 5
6
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
7 of 24
D - Ans 4 web - 001-024.qxd
8
17/8/04
11:14 am
Page 8
Section 2 – Shape, space and measures 4
2
4
5
3
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
8 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 9
9
Section 2 – Using and applying mathematics/ICT
6
P/D
Perimeter/diagonal for even-sided regular polygons
3.15 3.10 3.05 3.00 2.95 2.90 2.85 2.80
0
2
4
6 8 Number of sides
10
12
14
Perimeter/diagonal for odd-sided regular polygons 3.50 3.45
P/D
3.40 3.30 3.25 3.20
3.15 3.10
0
2
4
6 8 Number of sides
10
12
14
The results for odd and even-sided regular polygons can be combined on a graph as follows:
Chapter 10 – Using and applying mathematics/ICT 2
Perimeter/diagonal for regular polygons 3.6 3.5 3.4
Investigation
3.3
Pupils will produce a variety of nets. The net using the smallest amount of card is shown below:
3.1
P/D
3.2
3.0 2.9 2.8 2.7 2.6 2.5
35 51 cm 8
20
8
20
56 cm
ICT activity 1–7 Pupils generate their own regular polygons and measure the perimeter and diagonal length of each. 8
(a) Pupils’ results should show that, as the number of sides of the regular polygon increases, so the value perimeter diagonal gets closer to .
0
2
4
6 8 Number of sides
10
12
14
Review 2A 1
(a) 40 mm
(b) 284 mm
(c) 850 mm
2
(a) 7200 kg
(b) 2.8 kg
(c) 50 kg
3
(a) 2300 ml
(b) 400 ml
(c) 8.9 ml
4
1600 ml
5
(a) a 4
(b) b 13
(c) m 5
6
38.96 cm (2 dp)
7
452.39 cm2
8
18.8 cm2 (1 dp)
(b) The value perimeter diagonal gets closer to , but the results for even and odd-sided regular polygons differ because they approach differently. This is shown in the following graphs. Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
9 of 24
D - Ans 4 web - 001-024.qxd
10
9
17/8/04
11:14 am
Page 10
Section 3 – Algebra 2
Different nets are possible to this one.
10 Different nets are possible to this one.
4 cm
5 cm 5 cm
4 cm
5 cm
4 cm 12 cm
10 cm
5 cm
4 cm
10 Different nets are possible to this one.
SECTION THREE 5 cm 10 cm
4 cm
Chapter 11 – Algebra 2 Exercise 11.1 1
(a) a is less than 6 (b) b is greater than 5
4 cm
(c) c is not equal to 10 2
Review 2B
(a) x is less than or equal to 7 (b) y is greater than or equal to 3
1
(a) 3500 m
(b) 0.75 m
(c) 0.28 m
2
(a) 800 g
(b) 4100 g
(c) 70 g
3
(a) 0.7 litres
(b) 20 litres
(c) 0.005 litre
4
2.32 litres
5
(a) a 8
6
42.16 cm (2 dp)
7
226.19 cm2
8
(a) 345.6 m
9
Different nets are possible to this one.
(c) z is less than or equal to 10 3
(a) d is greater than 4 (b) e is less than 7 (c) f is not equal to 8
(b) b 1.5
(c) c 5
4
(a) m is less than 8 (b) n is greater than 5 (c) f is not equal to 5
5
(b) 5656 m2
(a) s is less than or equal to 6 (b) t is greater than or equal to 9 (c) u is not equal to 3
4 cm
Exercise 11.2 12 cm
1
2
3
4
5
6
7
8
9
10
Exercise 11.3 4 cm
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
1
a 10
2 b 7
3
c 5
4
d 6
5
e 10
6 f 76
7
g 12
8
h5
9
j 4
10 k 7 10 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 11
Section 3 – Algebra 3
Exercise 11.4
11
Exercise 11.6
1 2
3
4
5
6
7
2
3
4
5
6
7
2 3
1
3 a 6
2 4b 7
3
6 c9
4 0 d3
5
2 e 1
6 3 f 3
7
1 g 4
8 3 h 2
5 i 1
2
3
4
5
6
7
9
2
3
4
5
6
7
Exercise 11.7
2
3
4
5
6
7
10 4 j 4
4 5 6 2
3
4
5
6
7
2
3
4
5
6
7
2
3
4
5
6
7
0.5
0.6
0.7
0.8
0.9
1.0
2.2
2.3
2.4
2.5
2.6
2.7
7 8 9
1
11 a 18
2 21 a 40
3
160 h 200
4 14 t 28
5
300 n 400
6 155 h 185
7
7 n 11
8 1 n 8
9
10 d 12
10 40 n 50
Chapter 12 – Algebra 3 Exercise 12.1
10
1 (a) p m q
(b) q m p
2 (a) p m d
(b) m d p
3 (a) s r 3t
rs (b) t 3 (b) c 2d x
7
xc 4 (a) d 2
12
d 3b 5 (a) a 2
d 2a (b) b 3
6
p 5s 6 (a) r 3
3r p (b) s 5
m 7 (a) r p 2
m (b) p r 2
w 8 (a) r 2p 5
1 w (b) p r 2 5
9 (a) r w dt
wr (b) t d
Exercise 11.5 1 2
3
4
5
6
7
2 2
3
4
5
6
3 7
8
9
10
11
4 1
2
3
4
5
5 2
3
4
5
6
7
6 2
3
4
5
6
7
7 –6
–5
–4
–3
–2
–1
8 –9
–8
–7
–6
–5
–4
–2
–1
0
1
2
3
–1
0
1
2
3
4
9 10 Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
yc 10 (a) m x
c (b) m yx
Exercise 12.2 1
(a) a c b
(b) b c a
2
(a) a b c
(b) c a b 11 of 24
D - Ans 4 web - 001-024.qxd
12
17/8/04
11:14 am
Page 12
Section 3 – Shape, space and measures 5
s 3 (a) p qr
s (b) r pq
4 (a) q r 3p
rq (b) p 3
5 (a) p t mn
tp (b) n m
r 3q 6 (a) p 2
r 2p (b) q 3
7 (a) m rn
m (b) n r
vw 8 (a) d s
ds (b) v w
tw 9 (a) m n
mn (b) w t
1 10 (a) w t mn
1 (a) q r p
(b) q s 2r
2 (a) r 4p 2q
(b) q 2p 3s
r 3 (a) q p
qs (b) r p
r3 4 (a) p q
q4 (b) r p
5 (a) n r m
e 62°
6 f 55°
7
g 90°
8 h 144°
9
i 154°
10 j 35°
Exercise 13.2
1 1 (b) m t n w
Exercise 12.3
5
1
a 110°
2 b 145°
3
c 55°
4 d 95°
5
e 100°
6 f 125°
7
g 106°
8 h 150°
9
i 90°
10 j 60°
Exercise 13.3 1
Pupils’ drawings and measured angles.
2
Pupils’ drawings and measured angles.
3
Pupils’ drawings and measured angles.
4
Pupils’ own observations leading to: vertically opposite angles are equal.
Exercise 13.4 1
Pupils’ drawings and measured angles.
(b) n m p
2
Pupils’ drawings and measured angles.
3p n 6 (a) m 2
3x q (b) p 2
3
Pupils’ drawings and measured angles.
4
uv 7 (a) x y
rs (b) p q
Pupils’ own observations leading to: corresponding angles are equal.
2p 5 8 (a) q 6
6q 5 (b) p 2
3x 7y 9 (a) z 4
3x 4z (b) y 7
8q 10 (a) r 2p
(b) q 2pr 8
Chapter 13 – Shape, space and measures 5 Exercise 13.1
Exercise 13.5 1 a 40°
b 140°
2 c 60°
d 120°
3 e 40°
f 140°
4 g 48°
h 132°
5 j 144°
k 36°
6 l 70°
m 110°
7 n 80°
o 100° p 100° q 80°
8 r 43°
s 137°
w 145° x 145° y 35°
1
a 130°
2
b 140°
9 v 35°
3
c 135°
4
d 70°
10 a 36°
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
t 137°
u 43° z 145° 12 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 13
13
Section 3 – Using and applying mathematics/ICT 3
Chapter 14 – Handling data 2
3
(a)
Rainfall compared with hours of sunshine
Exercise 14.1 Pupils’ own explanations should accompany each answer.
Rainfall (mm)
1
(a) Likely to be a positive correlation. (b) No correlation. (c) Likely to be a positive correlation. (d) Likely to be a negative correlation, though there will be exceptions for vintage motorcycles.
0
(e) Different correlations possible – check explanation for justification. 4
(a)
(h) Likely to be a positive correlation.
Time (min)
Distance from school plotted against travel time 45 35 25 15 5 0
14
100 80 60 40 20 10
20 30 40 50 60 Adult illiteracy rate (%)
70
(b) Pupils’ explanations.
5
10 15 20 Distance (km)
25
30
Male life expectancy (years)
Distance from school plotted against travel time 45 35 25 15 5 0
5
10 15 20 Distance (km)
(c) Pupils’ explanations. (d)
(c) Pupils’ explanations.
Time (min)
12
120
0
(b) Strong/moderate positive correlation. (d)
4 6 8 10 Hours of sunshine
Correlation between adult illiteracy and infant mortality Infant mortality per 100
(g) Up to adulthood there is a positive correlation. However, once adulthood is reached there is no correlation. (a)
2
(b) Very little/no correlation. Pupils’ explanations.
(f) Likely to be a negative correlation.
2
8 7 6 5 4 3 2 1
25
(e) About 11 km
Correlation between male and female life expectancy in different countries 75 65 55 45 35 30
40 50 60 70 80 90 Female life expectancy (years)
30
Chapter 15 – Using and applying mathematics/ICT 3 Investigation Pupils will each produce a table of results and a graph of their results. Answers to questions will depend on class results.
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
13 of 24
D - Ans 4 web - 001-024.qxd
14
17/8/04
11:14 am
Page 14
Section 4 – Number 3
ICT activity
6
(b) Strong positive correlation
Pupils produce their own angle booklets. 7
Review 3A 1 (a) 2
3
(b)
(c)
(a) c b a pn (c) q m
w (d) t 2(mn 5) q 70°
r 110°
(b) s 104°
t 38°
u 38°
(c) Likely to be no correlation; pupils’ explanations.
SECTION FOUR Chapter 16 – Number 3
4
b 100° c 80° d 35° e 105° f 40° g 35° h 80°
5
(a)
Exercise 16.1 1
(b) 2
6
(a) Likely to be a positive correlation; pupils’ explanations. (b) Likely to be a negative correlation (with the exception of vintage cars); pupils’ explanations. (c) Many factors may affect this. For a given painter at a particular point in time, though, it is likely to be a positive correlation. Pupils’ explanations.
Review 3B 1
(a) x 50%
2
(a) 4
(b) 21 x 55 5
6
7
3
4 5
0.8
0.9
8
qp (a) r 3 t(n 2) (c) v m
1.0
(b) €160
(d) €60
(e) €450
(a) 3 years
(b) 4 years
(d) 6 years
(e) 312 years
1.2
1 t (b) r 5 2 m 1 2q (d) p r 5 3
1 2
(a) 5%
(b) 6%
(d) 712%
(e) 412%
(c) 8%
(a) €400
(b) €800
(c) €466.67
(d) €850
Exercise 16.3 1
€20 loss
2
€6 loss
4
€5 loss
5
€1400 loss
3
€3 profit
1
70%
2 50%
3 75%
4 25%
5
50%
6 60%
7 25%
8 75%
9
75%
10 70%
Exercise 16.5 62.5%
2
60%
(b) p 57° q 57° r 87° s 93°
3
50%
a 130° f 115°
4
30%
5
33.3% (1 dp)
q 150°
b 130° c 50° g 115° h 65°
(c) 5 years
Exercise 16.2
1
(a) r 30°
(c) €90
9
1.1
(a) €30
Exercise 16.4
(b) 0.7
(a) Likely to be a negative correlation; pupils’ explanations. (b) Likely to be a positive correlation; pupils’ explanations.
(d)
xw (b) b 3
(a) p 70°
(a) Weak negative correlation
d 65° e 65° i 65°
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
14 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 15
Section 4 – Algebra 4
6 28.6% (1 dp)
15
Exercise 17.4
7 40%
1 (a) 3(3m 5)
(b) 2(8 3p)
8 35%
2 (a) 2(2p 3)
(b) 6(3 2b)
9 42%
3 (a) 3(2y 1)
(b) 2(2a 3b)
10 37.5%
4 (a) 3(a b)
(b) 4(2a 3b 5c)
5 (a) a(3b 4c 5d)
(b) 2p(4q 3r 2s)
6 (a) b(b c)
(b) 2a(2a 5b)
7 (a) ab(c d e)
(b) m(2m 3)
8 (a) 3ab(c 3d)
(b) 5a(a 2b)
9 (a) 2ab(4a 3b)
(b) p2(2q2 3r2)
Chapter 17 – Algebra 4 Exercise 17.1 1 (a) 2(2a 5)
(b) 5(2a 3)
(c) 3(3a 7)
2 (a) 3(2b 1)
(b) 5(2b 1)
(c) 5(5b 2)
3 (a) 5(3c 5)
(b) 4(3c 2)
(c) 8(a 3)
4 (a) 4(2 d)
(b) 2(3 2d)
(c) 6(3 2d)
5 (a) 2(3a 2b)
(b) 7(c 2d)
(c) 4(3a 4b)
6 (a) 4(6p 7q) (b) 6(a 5b)
(c) 7(3d 2e)
7 (a) 3(2a 3b 4c)
(b) 2(4a b 2c)
(c) 3(2p 3q 5r) 8 (a) 4(3m 4n 9r)
(b) 7(a 2b 5c)
(c) 8(8p 4q 2r) 9 (a) 3(3a b 6c)
(b) 4(6p 8q 3r)
(c) 3(a b c) 10 (a) 6(a 2b 3c)
(b) 7(p q r)
10 (a) 12(a 2)
(b) 21(2a 3)
11 (a) 11a(1 b)
(b) 4a(1 4 2b)
12 (a) 5b(a 2c 3b)
(b) 2b2(4a 3)
13 (a) a(a 1)
(b) b(1 b)
14 (a) b (1 b)
(b) a(a2 a 1)
15 (a) p(p2 2p 3)
(b) m(7m2 9m 4)
16 (a) 3a(2a2 a 4)
(b) 5a(a2 2a 5)
17 (a) 28ab(2a b)
(b) 12b(6a 3c 4d)
18 (a) 2a (2b 3c)
(b) 7m2n(2mn 3)
19 (a) 6ab(ab 2)
(b) 3c2(1 5c)
20 (a) 5a(b c)
(b) 13bc(b 2c)
2
3
(c) 15(2p 4q r)
Exercise 17.5 Exercise 17.2
1 (a) (a b)(c d)
(b) (p q)(r s)
1
(a) x(2a 3b 4c)
(b) b(7a 8c)
2 (a) (m n)(p q)
(b) (a c)(b d)
2
(a) q(3p 4 5s)
(b) n(2m 3r 5p)
3 (a) (a 2)(b c)
(b) (a 3)(b c)
3
(a) x(4a 3x)
(b) b(4a 3b)
4 (a) (a 4)(b c)
(b) (a 3)(b c)
4
(a) p(6p 5q)
(b) m(7n 2m)
5 (a) (p q)(m n)
(b) (p q)(n m)
5
(a) x(x a)
(b) p(qr p)
6 (a) (a b)(c d)
(b) (r t)(s v)
7 (a) (x y)(w v)
(b) (a b)(a c)
Exercise 17.3
8 (a) (x y)(z x)
(b) (p r)(q p)
1
(a) 2y(2x 3z)
(b) 3q(3p 4r)
9 (a) (m n)(n r)
(b) (p r)(x y)
2
(a) 5m(3n 2p)
(b) 7c(2b 3c)
10 (a) (a 3c)(b 2c)
(b) (a d)(b 1)
3
(a) 6p(q 5p)
(b) 5x(3x 2y)
4
(a) 4xy(3x 2y)
(b) 5ab(2b 5a)
5
(a) 7a(x 2y 3z)
(b) 3x2(10a 2b 3c)
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
15 of 24
D - Ans 4 web - 001-024.qxd
16
17/8/04
11:14 am
Page 16
Section 4 – Handling data 3
Exercise 17.6
Exercise 19.2
1
(a) (3a b)(b c)
(b) (2p q)(3r s)
1
1 36
2
(a) (x y)(z y)
(b) (4a b)(2c b)
2
5 8
3
(a) (r 2s)(3t r)
(b) (2m 3n)(q 2m)
3 (a)
4
(a) (5f g)(f 2 h)
(b) (ab c)(d c)
5
(a) (2gh i)(jk i)
(b) (a b)(c b)
Chapter 18 – Shape, space and measures 6 Exercise 18.1 1 2 3
(a) 24 cm3
(b) 150 cm3
(d) 4000 cm3
(e) 1500 cm3
(a) 120 cm3
(b) 120 cm3
(d) 4000 cm3
(e) 3861 cm3
(c) 40 cm3 (c) 270 cm3
1 5
(b)
2 5
(c)
2 25
(d)
3 5
Exercise 19.3 1
7 25
2
8 25
3
5 25
4
1 25
5
2 25
6
2 25
7
3 25
8 Mutually exclusive
9
2 25
10
1 25
11
17 25
12
15 25
or 35
13
25 25
14
20 25
or 45
15
8 25
16
13 25
or 15
or 1
(a) 339.3 cm3 (1 dp)
(b) 2827.4 cm3 (1 dp)
17
12 25
18
7 25
(c) 954.3 cm3 (1 dp)
(d) 924.7 cm3 (1 dp)
19
4 25
20
3 25
2
1 36
4
20 36
(e) 155.0 cm3 (1 dp)
Exercise 19.4
Exercise 18.2 1
224 cm3
2
225 cm3
3
3200 cm3
4
1500 cm
3
5
3930 cm3 (3 sf)
1
1 36
3
4 36
5
1 36
6
11 36
7
1 18
8
16 36
or 49
9
1 18
10
16 36
or 49
or 19
or 59
Exercise 19.5
Exercise 18.3 1
8 cm
2
(a) 5 cm
(b) 6.5 cm
3
(a) 9 cm
(b) 81 cm2
4
10 cm
5
1.51 cm (2 dp)
Chapter 19 – Handling data 3 Exercise 19.1 1
Independent
3
They are mutually exclusive events.
2
Independent
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
1
1 8
2
1 12
3
19 96
4
1 96
5
3 8
6
2 12
or 16
7
46 96
or 2438
8
6 96
or 116
9 0 (it is impossible to throw a red face on the dodecahedron) 10
96 96
or 1 16 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 17
Section 5 – Algebra 5
Chapter 20 – Using and applying mathematics/ICT 4
Review 4B 1
7 years
Investigation
2
66.5%
1 2
3
(a) 8 cm2
(b) 40 cm3
(c) 32 cm2
(d) 320 cm3
(a) Small triangular cross-section 21 cm2 Enlarged triangular cross-section 84 cm2 (b) Volume of small prism 168 cm Volume of enlarged prism 1344 cm3 3
3,4 Pupils investigate the relationship between scale factor of enlargement and its effect on the area factor and volume factor of enlargement. If the scale factor of enlargement is n, the area factor of enlargement is n2 and the volume factor of enlargement is n3.
The screenshot below shows an example of the formulae that can be used:
Pupils prepare a report based on their findings.
Review 4A 1
€2600
2
4.2%
3
66.7% (1 dp)
4
600%
5
(a) 4(4a 3)
7
251.3 cm3 (1 dp)
8
(a) Pupils’ examples.
4
(a) (r 3s)(2t r)
5
48 cm3
6
8.9 cm
7
(a)
4 10
8
(a)
4 6
or 25
or 23
(b)
(b) (4ab2 c)(a d)
2 10
or 15
(b) 26 or 13
(c)
6 10
(c)
2 9
or 35
SECTION FIVE Exercise 21.1 1
Pupils’ tables of sets of co-ordinates leading to y 2x
2
Pupils’ tables of sets of co-ordinates leading to y 12x 1
3
Pupils’ tables of sets of co-ordinates leading to yx2
4
Pupils’ tables of sets of co-ordinates leading to y 12x 3
5
Pupils’ tables of sets of co-ordinates leading to y x
6
Pupils’ tables of sets of co-ordinates leading to y 12x 3
7
Pupils’ tables of sets of co-ordinates leading to y4
8
Pupils’ tables of sets of co-ordinates leading to x 3
9
Pupils’ explanations.
(b) x(4x 1)
(c) 2bc(3b 1 2c) (a) (2c a)(3b c)
(b) 7r(2r 3)
(c) 3t(2t2 3t m)
Chapter 21 – Algebra 5
ICT activity
6
(a) 4(2p q)
17
(b) (4p q2)(2p r)
Exercise 22.2 (b) Pupils’ examples.
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
1
Sloping
2
Sloping
3
Vertical
4
Sloping 17 of 24
D - Ans 4 web - 001-024.qxd
18
17/8/04
11:14 am
Page 18
Section 5 – Algebra 5
5 Horizontal
4
y
6 Vertical
4
y=3
7 Sloping
2
8 Horizontal 9 Sloping
–2
10 Sloping
0
2
4
x
–2
Exercise 21.3 1
5
y 6
y 4
4
y=x+2
2
y – x = –1
2 –2 –4
–2
0
2
4
x
–2 2
4 x = –2
4
2
0
y = 2x – 3 2
–4
–2
0
2
4
x
–2
6 x
4
6 x
4
y
y
–2 3
2
–2 6
2
–2
0
7
y 6
y 4 4
2y = x + 6
2 2
–2
0
y= 2
1 2x
+1 4
x
–4
–2
0
2
4
x
–2
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
18 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 19
Section 5 – Algebra 5
y 6
8
Exercise 21.5 1
4
2
0
2
4
(a) y 3x 1
(b) Gradient 3
(a) y 12x 2
(b) Gradient 12
(c) y intercept 2
x 4
–2
(a) y 4x 4
(b) Gradient 4
(c) y intercept 4 5
y 6
9
(b) Gradient 1
(c) y intercept 1 3
–2
(a) y x 1 (c) y intercept 1
y = –x + 3
2
–4
19
(a) y x 3
(b) Gradient 1
(c) y intercept 3 6
Pupils’ observations.
4
Exercise 21.6 2
0
–2
1
y = –2x + 2 2
4
x
–2 10
y 4 2
2
–4
0
–2
–2
2 4 y + x = –1
x
–4 3
Exercise 21.4 Pupils’ own line graphs accompany questions 1–10.
(a) Gradient 2
y intercept 1
(b) Gradient 3
y intercept 1
(c) Gradient 12
y intercept 3
(d) Gradient 1
y intercept 0
(e) Gradient 1
y intercept 12
(f) Gradient 3
y intercept 4
(g) Gradient 1
y intercept 4
(h) Gradient 1
y intercept 0
(a) Gradient 2
y intercept 4
(b) Gradient 1
y intercept 2
(c) Gradient 3
y intercept 0
(d) Gradient 2
y intercept 4
(e) Gradient 3
y intercept 1
(f) Gradient 1
y intercept 1
(g) Gradient 5
y intercept 4
(h) Gradient 2
y intercept 4
(a) Gradient 1
y intercept 2
(b) Gradient 2
y intercept 1
(c) Gradient 3
y intercept 1
(d) Gradient 1
y intercept 0
1 Gradient 1
2 Gradient 2
(e) Gradient 4
y intercept 8
3 Gradient 12
4 Gradient 2
(f) Gradient 3
y intercept 3
6 Gradient 4
(g) Gradient 0
y intercept 4
5 Gradient
12
7 Gradient 13 9 Gradient 0
8 Gradient 3
(h) Gradient
1 2
y intercept 3
10 Gradient infinite
11 Pupils’ own observations. Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
19 of 24
D - Ans 4 web - 001-024.qxd
20
17/8/04
11:14 am
Page 20
Section 5 – Handling data 4
Chapter 22 – Shape, space and measures 7 Exercise 22.1 1
a 40°
2
b 43°
3
c 30°
4
d 45°
5
e 25°, f 35°
6
g 27°, h 27°, i 36°
Exercise 22.2
2
e 48° h 132°
f 84° i 48°
5
k 108°
l 108°
6
m 120° r 60°
n 60° s 120°
Name of polygon
Number of triangles
Total sum of interior angles
1
150 cm2
2
138 cm2
triangle
1
180°
3
288 cm2
4
quadrilateral
2
2 180° 360°
4
108 cm2
5
pentagon
3
3 180° 540°
5
703.7 cm2 (1 dp)
6
hexagon
4
4 180° 720°
6
155.5 cm2 (1 dp)
8
octagon
6
6 180° 1080°
7
480 cm2
9
nonagon
7
7 180° 1260°
8
262 cm2
10
decagon
8
8 180° 1440°
12
dodecagon
10
10 180° 1800°
The number of sides is always 2 more than the number of triangles.
3
Sum of the interior angles Size of each interior angle
3
p 120° t 120°
q 60°
Chapter 23 – Shape, space and measures 8
3
Number of sides
g 132° j 48°
Exercise 23.1
1 Number of sides
4
4
5
6
8
9
10
12
Exercise 23.2 1
9 cm
2
3 cm
3
(a) 11.3 cm (1 dp)
(b) 2226 cm2
4
(a) 13 cm
(b) 450 cm2
5
2 mm
180° 360° 540° 720° 1080° 1260° 1440° 1800°
Chapter 24 – Handling data 4 60° 90° 108° 120° 135° 140° 144° 150°
Size of each 120° 90° 72° 60° exterior angle
45°
40°
36°
Exercise 22.3
30°
Exercise 24.1 1
Discrete
2 Continuous
3
Discrete
4 Continuous
5
Continuous
6 Continuous
7
Discrete
8 Continuous
9
Continuous (usually) 10 Discrete
1
a 75°
2
b 70° c 120°
Exercise 24.2
3
d 104°
Pupils’ examples.
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
20 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 21
21
Section 5 – Handling data 4
Exercise 24.3 1
5
Distances travelled to school 70 60 Frequency
6
Frequency 0 1
12 10 8 6 4 2
7
8
0– 10– 3
30– 50– Mark (%)
70–
90 – 100
Heights of students
40
0– 1– 2– 3– 4– 5– 6– 7 – 8 Distance (km)
Mass (kg) 0– 1– 2– 3– 4– 5– 6– 7– 8– 9– 10–11
Maths test results
2 4 3 5 8 4 2 1
0
Time (secs)
8– 10– 12– 14– 16– 18– 20– 22–24
Frequency
0
3
14
8
1
2
2
0
Number of books
0– 10– 20– 30– 40– 50–60
Frequency
8
14
26
20
8
4
9
30
Points scored
0– 10– 20– 30– 40– 50– 60– 70–80
20
Frequency
0
1
3
5
11
6
4
2
10
Exercise 24.4 0 19
Mean annual temperatures in two cities 30
Temperatures in 50 towns in July Frequency
20 15 10
city A
5
15–
20– 25– 30– 35 – 40 Temperature (°C)
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
0– 10 – 20 – 30 – 40 –5 0
20
–
0 –
20 18 16 14 12 10 8 6 4 2 0
city B
25
–
4
0–
17 0–
Height (cm)
1
18
16 0–
15 0–
0– 14
13
0–
0
10
Frequency
30 20 0
2
Frequency
40
10
0 65– 70– 75– 80– 85– 90 – 95 Scores
Frequency
50
–
Frequency
Scores in a golf competition 20 18 16 14 12 10 8 6 4 2
Temperature (°C)
21 of 24
D - Ans 4 web - 001-024.qxd
22
17/8/04
11:14 am
Page 22
Section 5 – Reviews
2
Ages of spectators compared
Frequency (1000s)
30
football
25
golf
20
1
Pupils’ observations based on their results.
2
Pupils’ examples.
ICT activity Pupils’ analyses of test results.
15 10
Review 5A
5
Age
60 70 – –8 0
30 – 40 – 50 –
10 – 20 –
0–
0
1
yx2
2
(a)
y 4
3 Pupils’ sketches of frequency polygons. 4 Pupils’ sketches of frequency polygons. 5
0
–2
school A
2
x
4
–2 school B
y
(b)
4
8
y = 12 x + 2
7–
Distance (km)
6–
5–
4–
3–
2–
1–
2
0–
Frequency
Distances travelled by pupils to two schools 45 40 35 30 25 20 15 10 5 0
y = 2x – 1
2
–4
–2
Pupils’ explanations. ‘On average’, pupils at school A travel less distance to school than those at school B. 6 Pupils’ sketches of frequency polygons.
0
2
–2 3
(a) Gradient 4, y intercept 5
7 Pupils’ sketches of frequency polygons.
(b) Gradient 1, y intercept 0
8 Pupils’ sketches of frequency polygons.
(c) Gradient 12, y intercept 1 (d) Gradient 2, y intercept 1
9 Pupils’ sketches of frequency polygons. 10 Pupils’ sketches of frequency polygons.
Chapter 25 – Using and applying mathematics/ICT 5
4 x
4
120°
5
a 75°, b 135°
6
226.2 cm2
7
8 cm
Investigation Pupils’ calculations based on their packaging. Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
22 of 24
D - Ans 4 web - 001-024.qxd
17/8/04
11:14 am
Page 23
Section 5 – Reviews
8
23
Maths test results Frequency
8 6 4 2 0
0–
10–
20–
30–
40– 50– Score
60–
70–
80– 90 – 100
Review 5B 1
y 2x 2
2
(a)
y 4 y=x+3 2
–4
0
–2
4 x
2
–2 y
(b)
4 y = –x + 3 2
–2
0
2
4
x
–2 3
(a) Gradient 3, y intercept 1 (b) Gradient 1, y intercept 4 (c) Gradient 2, y intercept 2 (d) Gradient 2, y intercept 12
4
72°
5
a 100°, b 80°, c 220°
6
176 cm2
7
628.3 cm2
8
Pupils’ reports.
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
23 of 24
D - Ans 4 web - 001-024.qxd
24
17/8/04
11:14 am
Page 24
Section 6 – Handling data
SECTION SIX – CHECKPOINT QUESTIONS
Shape, space and measures 1 (a) a 60°, b 60°, c 60° (b) Equilateral
Number
2 172 cm2
1
5 or 6
3 6 cm
2
About 47 000 feet
4 4 cm
3
(a) (i) Each small division on the scale shows 10 grams (ii) Arrow X shows a mass of 280 grams
5 12 cm2
(b) Pupils’ scales marked to show 70 g.
7 (a) 13 km/litre (b) 117 km
(c) (i) 39 cents (ii) 11 cents 4
(a) (i) 32 litres (ii) $36
8 (a) (i) 80°
(ii) 30°
(b) (i) 35°
(ii) 55°
9 (a) 384 cm
(b) 54 (km) 40 (min) 60 (km/h)
1
(c) 8 cm
3
3x(5x 2)
4
x2 5x 6
5
(2ab c)(4b c)
6
3
7
(a) p 12
8
(a) 2, 1, 1, 2
(b) 512 cm3 (b) 14 350 m2
(a) Primary (b) (i) Pupils’ explanations (ii) Pupils’ own questions
(b) 7x 6 20
2
(iii) 55°
Handling data
(a) (7x 6) cm
vu t a
2
10 (a) 444.2 m
Algebra 1
6 4 minutes
2
(a) Pupils’ scatter diagrams with line of best fit drawn. (b) 14
(b) q 7
(c) r 3
(b) Pupils’ graphs with line y x 2 drawn. (c) 23
Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational
24 of 24
View more...
Comments
