Cambridge International Mathematics

Exponents and surds (Chapter 6) 129 6 Express the following in simplest form, without brackets: a (2b^4 )^3 b μ 3 x^2 y ¶ 2 c (5 ...

130 Exponents and surds (Chapter 6) Example 10 Self Tutor Simplify, giving answers in simplest rational form: a 70 b 3 ¡^2 c 30 ...

Exponents and surds (Chapter 6) 131 10 000 = 10^4 1000 = 10^3 100 = 10^2 10 = 10^1 1=10^0 1 10 =10 ¡ 1 1 100 =10 ¡ 2 1 1000 =10 ...

132 Exponents and surds (Chapter 6) Example 13 Self Tutor Simplify the following, giving your answer in standard form: a (5£ 104 ...

Scientific and graphics calculators are able to display very large and very small numbers in standard form. Likewise, if you per ...

134 Exponents and surds (Chapter 6) 3 Find, in standard form, with decimal part correct to 2 places: a (5: 31 £ 104 )£(4: 8 £ 10 ...

Exponents and surds (Chapter 6) 135 Historical note #endboxedheading The namesurdand theradicalsignp both had a rather absurd pa ...

136 Exponents and surds (Chapter 6) ADDING AND SUBTRACTING SURDS ‘Like surds’ can be added and subtracted in the same way as ‘li ...

Exponents and surds (Chapter 6) 137 Discovery Properties of surds #endboxedheading Notice that p 4 £9= p 36 = 6 and p 4 £ p 9=2£ ...

138 Exponents and surds (Chapter 6) Example 19 Self Tutor Simplify: a p 32 p 2 b p 12 2 p 3 a p 32 p 2 = q 32 2 = p 16 =4 b p 12 ...

Exponents and surds (Chapter 6) 139 2 Simplify: a 3 p 3 £ 2 p 2 b 2 p 3 £ 3 p 5 c p 2 £ p 3 £ p 5 d p 3 £ p 2 £ 2 p 2 e ¡ 3 p 2 ...

140 Exponents and surds (Chapter 6) Example 22 Self Tutor Expand and simplify: a p 2( p 2+ p 3) b p 3(6¡ 2 p 3) a p 2( p 2+ p 3) ...

Exponents and surds (Chapter 6) 141 Example 26 Self Tutor Expand and simplify: a (3 + p 2)(3¡ p 2) b (2 p 3 ¡5)(2 p 3+5) a (3 + ...

142 Exponents and surds (Chapter 6) When an expression involves division by a surd, we can write the expression with aninteger d ...

Exponents and surds (Chapter 6) 143 Example 29 Self Tutor Write 1 ¡ 2 p 3 1+ p 3 in simplest form. 1 ¡ 2 p 3 1+ p 3 = μ 1 ¡ 2 p ...

144 Exponents and surds (Chapter 6) 3 Simplify: a (¡2)^3 b ¡(¡1)^8 c (¡1)^3 £(¡2)^2 £¡ 33 4 Simplify, giving your answers in sim ...

Exponents and surds (Chapter 6) 145 Review set 6B #endboxedheading 1 Find the integer equal to: a 73 b 32 £ 52 2 Write as a prod ...

Challenge #endboxedheading 146 Exponents and surds (Chapter 6) Discovery Continued square roots#endboxedheading X= s 2+ r 2+ q 2 ...

Formulae and simultaneous equations 7 Contents: A Formula substitution [2.5] B Formula rearrangement [2.5] C Formula derivation ...

148 Formulae and simultaneous equations (Chapter 7) Aformulais an equation which connects two or more variables. The plural of f ...