Integrated mathematics scheme: IMS T2 - National STEM Centre

c.
P20 A.
B.
C.
P21 A.
1. 5a 2. 3a 3. -a 4. a+b
5. 2a + 3b 6. -2m +4n 7. -4m-n 8. 3y
9. x+ 11y 10. -2x+ y
1. 7·4 2. 18·6 3. 28·6 4. 25·6
5. 9 6. -4·7
1. 2 2. 3·5 3. -1 4. 3·5333
1. b = 3·7, ab = 8·51 2. b = 9·7, ab = 142·59
3. b = -7'8, ab = -49·92 4. b = 32, ab = 672
5. a = 6·7, ab = 35·51 6. a = 3·9, ab = 4·68
7. a = 4·6666, ab = 21 8. a = 3·56, ab = 9·256
The laws work for all values of a, band c
B. Diagram 1 shows 3(a + b) = 3a + 3b and a = xxx, b = 0000, i.e. Distributive
Law
E20 A. See P19 A.
Diagram 2 shows a + (b + c) = (a + b) + c, i.e. Associative Law (addition)
Diagram 3 shows 4 x (3 x 2) = (4 x 3) x 2, i.e. Associative Law (multiplication)
Diagram 4 shows 4 x (3 x 2) = (4 x 3) x 2 again in different form
Diagram 5 shows ab + ac = a(b + c), i.e. Distributive Law
Diagram 6 shows Associative Law (addition)
B. 1. There are
(i) 20 different pairs possible (5 x 4) (ii) 60 different threes
(5 x 4 x 3)
(iii) 120 different fou rs (5 x 4 x 3 x 2) (iv) 120 different fives
(5 x 4 x 3 x 2 x 1)
The words of 5 letters are bread, beard and bared.
C.
D.
2. Letters
1
2
3
4
5
6
See P19 B.
Arrangements
1
2
6
24
120
720
See P19 C. and ... 11. p-2q 12. q-6p
14. 0 15. -5·7u 16. -4u + 6v
13. -3r -35
25