Cambridge International Mathematics

Trigonometry (Chapter 15) 329 8aIfμis any acute angle as shown, find the length of: i OQ ii PQ iii AT b Explain howtanμor tangen ...

330 Trigonometry (Chapter 15) We can measure a direction by comparing it with thetrue north direction. We call this atrue bearin ...

Trigonometry (Chapter 15) 331 EXERCISE 15E 1 Draw diagrams to represent bearings from O of: a 136 o b 240 o c 051 o d 327 o 2 Fi ...

332 Trigonometry (Chapter 15) Example 11 Self Tutor A cube has sides of length 10 cm. Find the angle between the diagonal AB of ...

Trigonometry (Chapter 15) 333 5 All edges of a square-based pyramid are 12 m in length. a Find the angle between a slant edge an ...

334 Trigonometry (Chapter 15) a The projection of AH onto the base plane EFGH is EH ) the required angle is AHE.b b The projecti ...

Trigonometry (Chapter 15) 335 2 For each of the following figures, name the angle between the given line segment and the base pl ...

336 Trigonometry (Chapter 15) EXERCISE 15F.3 1 A cube has sides of length 10 cm. Find the angle between the plane defined by BGD ...

Trigonometry (Chapter 15) 337 6 Find: a sinμ b tanμ c the exact coordinates of P. 7 Find the diameter of this circle. 8 9 Find t ...

338 Trigonometry (Chapter 15) 3 Find the measure of all unknown sides and angles in triangle KLM: 4 The angle of elevation from ...

Algebraic fractions 16 Contents: A Simplifying algebraic fractions [2.9] B Multiplying and dividing algebraic fractions [2.9] C ...

340 Algebraic fractions (Chapter 16) The same principle can be applied to algebraic fractions: If the numerator and denominator ...

Algebraic fractions (Chapter 16) 341 Example 2 Self Tutor Simplify: a (x+ 3)(x¡2) 4(x+3) b 2(x+3)^2 x+3 a (x+ 3)(x¡2) 4(x+3) = x ...

342 Algebraic fractions (Chapter 16) FACTORISATION AND SIMPLIFICATION It is often necessary to factorise either the numerator or ...

Algebraic fractions (Chapter 16) 343 Example 6 Self Tutor Simplify: x^2 ¡x¡ 6 x^2 ¡ 4 x+3 Don’t forget to expand your factorisat ...

344 Algebraic fractions (Chapter 16) 4 Simplify: a x^2 ¡x x^2 ¡ 1 b x^2 +2x+1 x^2 +3x+2 c x^2 ¡ 4 x+4 2 x^2 ¡ 4 x d x^2 +4x+3 x^ ...

Algebraic fractions (Chapter 16) 345 DIVISION For example, m 2 ¥ n 6 = m 2 £ 6 n fStep 1g = m£ 6 2 £n fStep 2g = m£ 6 2 £n fStep ...

346 Algebraic fractions (Chapter 16) The rules for addition and subtraction of algebraic fractions are identical to those used w ...

Algebraic fractions (Chapter 16) 347 Example 10 Self Tutor Simplify: a 2 a + 3 c b 7 x ¡ 5 2 x a 2 a + 3 c = 2 £c a£c + 3 £a c£a ...

348 Algebraic fractions (Chapter 16) 3 Simplify: a x 3 +2 b m 2 ¡ 1 c a 3 +a d b 5 ¡ 2 e x 6 ¡ 3 f 3+ x 4 g 5 ¡ x 6 h 2+ 3 x i 6 ...