F3 Quiz1 Ans
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F.3 Mathematics – Quiz 1 (Answer)
Page 1
Kwok Tak Seng Catholic Secondary School F.3 Mathematics Quiz 1 – Integral Indices and Surds (Answer) 1.
9a6b2 ÷ 10a3b8 9 = a 6 − 3 b 2 −8 10
= 3 4 a 2×4 b 3×4 × a 3 b 5×3 c 7×3 = 3 4 a 2×4 b 3×4 × a 3 b 5×3 c 7×3 = 3 4 a 8+ 3 b12 +15 c 21
9 = a 3b −6 10
=
= 81a 11b 27 c 21
9a 3 10b 6 (a–3b4)–2 ÷ (ab–3)4
3.
4.
= a −3×−2 b 4×−2 ÷ a 4 b −3×4 = a 6 b −8 ÷ a 4 b −12 = a 6 − 4 b −8− ( −12 ) = a 6 − 4 b −8− ( −12 ) = a 2b 4
u −6 v 3 (2u − 4 v 2 ) − 2
5. =
u −6 v 3 2 − 2 u − 4×−2 v 2×−2
= 3 − 4 a 12 b −8 ×
= 4u −14 v 7
a 4 −3 ) 9b − 2 a 4×−3 3 2×−3 b − 2×−3
a −12 3 −6 b 6
= 3 −4 a 12 b −8 × a −12 ÷ 3 −6 b 6 = 3 −4 −( −6 ) a 12 + ( −12 ) b −8− 6
4v 7 u 14
= 3 2 a 0 b −14 9 = 14 b
75 + 45 + 48 − 243 = 5 3 +3 5 +4 3 −9 3 =3 5
( 6 − 3 )( 6 + 2 )
9.
(3a −3 b 2 ) − 4 × (
= 3 − 4 a −3×−4 b 2×−4 ×
= 2 2 u −6 − 8 v 3 − ( −4 )
7.
(5p2q–3)–1(3p–3q)0 = (5 p 2 q −3 ) −1 (1) = 5 −1 p 2×−1 q −3×−1 = 5 −1 p −2 q 3 q3 = 5p2
6.
= u − 6 v 3 ÷ 2 −2 u 8 v −4
=
(3a2b3)4 × (ab5c7)3
2.
8.
4 96 × 12 = 4 16 × 6 × 4 × 3 = 16 6 × 2 3 = 32 6 × 3 = 32 9 × 2 = 96 2 ( 8 − 2)2
10.
= 6× 6 + 6× 2 − 3× 6 − 3× 2 = 36 + 12 − 18 − 6 = 6 + 4×3 − 9× 2 − 6 = 6+2 3 −3 2 − 6
= ( 8 ) 2 − 2( 8 )( 2 ) + ( 2 ) 2 = 8 − 2( 8 × 2 ) + 2
= 10 − 2 16 = 10 − 2 × 4 =2
10
11.
3 5 = =
10 3 5
1
12. ×
10 × 5 3× 5
5 5
3 3+4 2 =
1 3 3+4 2
×
3 3−4 2 3 3−4 2
F.3 Mathematics – Quiz 1 (Answer)
=
Page 2
2 5 3
=
=
13.
5 3−2 7 =
=
=
=
5 3−2 7
×
3+ 2 7 3+ 2 7
5(3 + 2 7 ) (3 − 2 7 )(3 + 2 7 ) 5(3 + 2 7 ) (3 − 2 7 )(3 + 2 7 ) 5(3 + 2 7 ) (3 2 ) − (2 7 ) 2
=
15 + 10 7 9 − 28
=
15 + 10 7 − 19
=−
15 + 10 7 19
14. (a)
4ab(−2a) + 10a2 (
= −8 a 2 b +
10 × −3 2 7 a b− a 5 3
= −8 a 2 b − 6 a 2 b − = −14a 2 b −
(b)
−3 −7 b) + ( a) 5 3
7 a 3
7 a ------(**) 3
Substitute a = 3 and b = − 1 7 − 14(3) 2 (− ) − (3) 3 3
1 7 = 14(9)( ) − (3) 3 3
= 42 − 7 = 35
1 into (**), 3
3 3−4 2 (3 3 + 4 2 )(3 3 − 4 2 ) 3 3−4 2 (3 3 ) 2 − (4 2 ) 2
=
3 3−4 2 27 − 32
=
3 3−4 2 −5
=
4 2 −3 3 5
Page 1
Kwok Tak Seng Catholic Secondary School F.3 Mathematics Quiz 1 – Integral Indices and Surds (Answer) 1.
9a6b2 ÷ 10a3b8 9 = a 6 − 3 b 2 −8 10
= 3 4 a 2×4 b 3×4 × a 3 b 5×3 c 7×3 = 3 4 a 2×4 b 3×4 × a 3 b 5×3 c 7×3 = 3 4 a 8+ 3 b12 +15 c 21
9 = a 3b −6 10
=
= 81a 11b 27 c 21
9a 3 10b 6 (a–3b4)–2 ÷ (ab–3)4
3.
4.
= a −3×−2 b 4×−2 ÷ a 4 b −3×4 = a 6 b −8 ÷ a 4 b −12 = a 6 − 4 b −8− ( −12 ) = a 6 − 4 b −8− ( −12 ) = a 2b 4
u −6 v 3 (2u − 4 v 2 ) − 2
5. =
u −6 v 3 2 − 2 u − 4×−2 v 2×−2
= 3 − 4 a 12 b −8 ×
= 4u −14 v 7
a 4 −3 ) 9b − 2 a 4×−3 3 2×−3 b − 2×−3
a −12 3 −6 b 6
= 3 −4 a 12 b −8 × a −12 ÷ 3 −6 b 6 = 3 −4 −( −6 ) a 12 + ( −12 ) b −8− 6
4v 7 u 14
= 3 2 a 0 b −14 9 = 14 b
75 + 45 + 48 − 243 = 5 3 +3 5 +4 3 −9 3 =3 5
( 6 − 3 )( 6 + 2 )
9.
(3a −3 b 2 ) − 4 × (
= 3 − 4 a −3×−4 b 2×−4 ×
= 2 2 u −6 − 8 v 3 − ( −4 )
7.
(5p2q–3)–1(3p–3q)0 = (5 p 2 q −3 ) −1 (1) = 5 −1 p 2×−1 q −3×−1 = 5 −1 p −2 q 3 q3 = 5p2
6.
= u − 6 v 3 ÷ 2 −2 u 8 v −4
=
(3a2b3)4 × (ab5c7)3
2.
8.
4 96 × 12 = 4 16 × 6 × 4 × 3 = 16 6 × 2 3 = 32 6 × 3 = 32 9 × 2 = 96 2 ( 8 − 2)2
10.
= 6× 6 + 6× 2 − 3× 6 − 3× 2 = 36 + 12 − 18 − 6 = 6 + 4×3 − 9× 2 − 6 = 6+2 3 −3 2 − 6
= ( 8 ) 2 − 2( 8 )( 2 ) + ( 2 ) 2 = 8 − 2( 8 × 2 ) + 2
= 10 − 2 16 = 10 − 2 × 4 =2
10
11.
3 5 = =
10 3 5
1
12. ×
10 × 5 3× 5
5 5
3 3+4 2 =
1 3 3+4 2
×
3 3−4 2 3 3−4 2
F.3 Mathematics – Quiz 1 (Answer)
=
Page 2
2 5 3
=
=
13.
5 3−2 7 =
=
=
=
5 3−2 7
×
3+ 2 7 3+ 2 7
5(3 + 2 7 ) (3 − 2 7 )(3 + 2 7 ) 5(3 + 2 7 ) (3 − 2 7 )(3 + 2 7 ) 5(3 + 2 7 ) (3 2 ) − (2 7 ) 2
=
15 + 10 7 9 − 28
=
15 + 10 7 − 19
=−
15 + 10 7 19
14. (a)
4ab(−2a) + 10a2 (
= −8 a 2 b +
10 × −3 2 7 a b− a 5 3
= −8 a 2 b − 6 a 2 b − = −14a 2 b −
(b)
−3 −7 b) + ( a) 5 3
7 a 3
7 a ------(**) 3
Substitute a = 3 and b = − 1 7 − 14(3) 2 (− ) − (3) 3 3
1 7 = 14(9)( ) − (3) 3 3
= 42 − 7 = 35
1 into (**), 3
3 3−4 2 (3 3 + 4 2 )(3 3 − 4 2 ) 3 3−4 2 (3 3 ) 2 − (4 2 ) 2
=
3 3−4 2 27 − 32
=
3 3−4 2 −5
=
4 2 −3 3 5
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