Cambridge Additional Mathematics

4 Surds, indices, and exponentials Contents: A Surds B Indices C Index laws D Rational indices E Algebraic expansion and factori ...

102 Surds, indices, and exponentials (Chapter 4) Opening problem #endboxedheading The interior of a freezer has temperature¡ 10 ...

Surds, indices, and exponentials (Chapter 4) 103 EXERCISE 4A.1 1 Write as a single surd or rational number: a p 11 £ p 11 b p 3 ...

104 Surds, indices, and exponentials (Chapter 4) EXERCISE 4A.2 1 Simplify: a 2 p 2+3 p 2 b 2 p 2 ¡ 3 p 2 c 5 p 5 ¡ 3 p 5 d 5 p 5 ...

Surds, indices, and exponentials (Chapter 4) 105 Example 6 Self Tutor Write with an integer denominator: a 6 p 5 b 35 p 7 a 6 p ...

106 Surds, indices, and exponentials (Chapter 4) 2 Write with integer denominator: a 5 p 5 b 15 p 5 c ¡ 3 p 5 d 200 p 5 e 1 3 p ...

3 5 power, index or base exponent Surds, indices, and exponentials (Chapter 4) 107 Ifnis a positive integer, then an is the prod ...

108 Surds, indices, and exponentials (Chapter 4) Historical note 1=1^3 3+5=8=2^3 7+9+11= .. . 27 = 3^3 Nicomachusdiscovered an i ...

Surds, indices, and exponentials (Chapter 4) 109 Example 10 Self Tutor Write as powers of 2 : a 16 b 161 c 1 d 4 £ 2 n e 2 m 8 a ...

110 Surds, indices, and exponentials (Chapter 4) 6 Write without brackets: a (2a)^2 b (3b)^3 c (ab)^4 d (pq)^3 e ³m n ́ 2 f ³ a ...

Surds, indices, and exponentials (Chapter 4) 111 11 Write as powers of 2 , 3 and/or 5 : a^19 b 161 c 1251 d^35 e 274 f 2 c 8 £ 9 ...

112 Surds, indices, and exponentials (Chapter 4) Example 14 Self Tutor Write as a single power of 2 : a^3 p 2 b p^1 2 c^5 p 4 a^ ...

Surds, indices, and exponentials (Chapter 4) 113 5 Without using a calculator, write in simplest rational form: a 4 3 (^2) b 8 5 ...

114 Surds, indices, and exponentials (Chapter 4) 2 Expand and simplify: a (2x¡1)(2x+3) b (3x+ 2)(3x+5) c (5x¡2)(5x¡4) d (2x+3)^2 ...

Surds, indices, and exponentials (Chapter 4) 115 3 Factorise: a 4 x+ 9(2x)+18 b 4 x¡ 2 x¡ 20 c 9 x+ 9(3x)+14 d 9 x+ 4(3x)¡ 5 e 2 ...

Once we have the same base we then equate the indices. 116 Surds, indices, and exponentials (Chapter 4) Anexponential equationis ...

Surds, indices, and exponentials (Chapter 4) 117 EXERCISE 4F 1 Solve forx: a 2 x=8 b 5 x=25 c 3 x=81 d 7 x=1 e 3 x=^13 f 2 x= p ...

DYNAMIC GRAPHING PACKAGE “ ” means “approaches”. ! x y 1 1 -3 -2 -1 2 3 2 4 6 8 y=2x O 118 Surds, indices, and exponentials (Cha ...

Surds, indices, and exponentials (Chapter 4) 119 2 Explore the family of curves of the form y=2x+d wheredis a constant. For exam ...

1 -2 -1 1 2 2 3 4 5 y x y= 2 x A B y x y=-3 y=2-x-3 2 2 -2 O -2 All exponential graphs are similar in shape and have a horizonta ...