Integrated mathematics scheme: IMS T2 - National STEM Centre

M36 A. 1. Drawing to confirm Pythagoras' theorem.
2. Checking drawings
3. Note that (a) If A < 90°, BC 2 < AC 2 + AB 2
(b) If A> 90°, BC 2 > AC 2 + AB 2
B. 1. (a) 4·47 em (b) 5·83 em (c) 7·21 em (d) 4·95 em
2. Use b 2 = c 2 - a 2 or a 2 = c 2 - b 2
(a) a = 9·75 em (b) b = 8·66 em (c) a = 18·3 em
(d) b=93·67cm (e) b=27·2mm (f) 16km
M37 A. 1. 5·83 m
2. Yes, the base will be 4·5 m from the wall
3. 5·6m
B. 1. 4·7 m, 4·3 m 2. 21·6 m
3. Roughly 88 m
C. 1. 5·83 units 2. 4·24 units 3. 3·6 units
5. 3·6 units 6. 6·4 units 7. 5 units
4. 1·41 units
8. 6·3(25) units
P25 A. 1. c = 3·97 em so area = ~ac = 8·93 cm 2
2. C = 48° 3. No, the third angle is 80°
B. 1. DAX = 55°
ADX = 35° ABY = 55°
XDC = 55° YBC = 35°
XCD = 35° BCY = 55°
2. The angles are either 90°, 65° or 25°
3. BAD = 30° DAC = 20° ADC = 90°
4. ABD = 45° DCA = 43°
4. 9·22 em
C. 1. True
2. Not true except in special cases where the angles are 45°, 45° and
90°
3. True 4. True
P26 A., B. and C. practical work
D. 1. (a) 8·06cm
2. 4·39 m
3. (a) 5·385 units
(b)
(b)
38·01cm
2·83 units
(c) 6·74 em
(c) 3·61 units (d) 5·83 units
E26 A. See P25 A.
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