Cambridge Additional Mathematics

Simplify 7!¡6! 6 by factorising. Counting and the binomial expansion (Chapter 10) 261 5 Write as a product by factorising: a 5! ...

262 Counting and the binomial expansion (Chapter 10) EXERCISE 10C.2 1 Use the formula ¡n r ¢ = n! r!(n¡r)! to evaluate: a ¡ 3 1 ...

Counting and the binomial expansion (Chapter 10) 263 Suppose we want to find the number of different permutations on the symbols ...

264 Counting and the binomial expansion (Chapter 10) Example 11 Self Tutor The alphabet blocks A, B, C, D, and E are placed in a ...

Counting and the binomial expansion (Chapter 10) 265 7aHow many different permutations on the letters A, B, C, D, E, and F are t ...

266 Counting and the binomial expansion (Chapter 10) 13 3 boys and 3 girls are to sit in a row. How many ways can this be done i ...

Counting and the binomial expansion (Chapter 10) 267 Acombinationis a selection of objectswithoutregard to order. For example, t ...

268 Counting and the binomial expansion (Chapter 10) Example 14 Self Tutor A committee of 4 is chosen from 7 men and 6 women. Ho ...

Counting and the binomial expansion (Chapter 10) 269 6aHow many different teams of 5 can be selected from a squad of 12? b How m ...

270 Counting and the binomial expansion (Chapter 10) Consider the cube alongside, which has sides of length (a+b)cm. The cube ha ...

Counting and the binomial expansion (Chapter 10) 271 c Write down the triangle of coefficients to row 6 : n=1 n=2 n=3 11 121 133 ...

272 Counting and the binomial expansion (Chapter 10) Example 16 Self Tutor Find the: a 5 th row of Pascal’s triangle b binomial ...

Counting and the binomial expansion (Chapter 10) 273 7 Find (2 + p 3)^3 4+ p 3 , giving your answer in the form a+b p 3 c , wher ...

274 Counting and the binomial expansion (Chapter 10) Example 17 Self Tutor Write down the first three and last two terms of the ...

The “term independent of ” is the constant term. x Counting and the binomial expansion (Chapter 10) 275 EXERCISE 10G 1 Write dow ...

¡n 2 ¢ =n(n¡1) 2 for all integersn> 2. (2) (1) 276 Counting and the binomial expansion (Chapter 10) Example 20 Self Tutor Fin ...

Counting and the binomial expansion (Chapter 10) 277 17 The coefficient ofx^2 in the expansion of (1 + 2x)n is 112. Findn. 18 Th ...

278 Counting and the binomial expansion (Chapter 10) Review set 10B #endboxedheading 1 Alpha-numeric number plates have two lett ...

Vectors 11 Contents: A Vectors and scalars B The magnitude of a vector C Operations with plane vectors D The vector between two ...

280 Vectors (Chapter 11) Opening problem An aeroplane in calm conditions is flying at 800 km h¡^1 due east. A cold wind suddenly ...