Cambridge International Mathematics

Transformation geometry (Chapter 20) 409 ENLARGEMENTS WITH CENTRE THE ORIGIN Suppose P(x,y) moves to P^0 (x^0 ,y^0 )such that P^ ...

410 Transformation geometry (Chapter 20) 2 Copy triangle T onto squared paper. a Enlarge T about centre C(7,2)with scale factor ...

Transformation geometry (Chapter 20) 411 Example 9 Self Tutor Consider the triangle ABC with A(1,1),B(5,1)and C(1,4)under a stre ...

412 Transformation geometry (Chapter 20) EXERCISE 20E 1 Copy these diagrams and perform the stretch with the given invariant lin ...

Transformation geometry (Chapter 20) 413 b The object triangle OAB is mapped onto the image triangle OAB^0. Describe fully the s ...

414 Transformation geometry (Chapter 20) What to do: 1 On the same set of axes graph: a y= 1 x b y= 1 x +2 c y= 1 x ¡ 3 d What t ...

Transformation geometry (Chapter 20) 415 To help draw the graphs in the following exercise, you may wish to use thegraphing pack ...

416 Transformation geometry (Chapter 20) 8 For the following, copy and draw the required function: a sketch y=f(x¡2) b sketch y= ...

Transformation geometry (Chapter 20) 417 An enlargement with centre O(0,0)and scale factork=2 maps¢ABC onto¢A^0 B^0 C^0. ¢A^0 B^ ...

418 Transformation geometry (Chapter 20) a S maps¢ABC to (1), R maps (1) to (2). So, RS maps¢ABC to (2). This is a reflection in ...

This is T 4 followed by T 2 ,orT 2 T 4. second transformation first transformation y O x B B' A Transformation geometry (Chapter ...

O y x O y 123 6 x ABA' B' DCD' C' 1 3 420 Transformation geometry (Chapter 20) 8 Suppose R is a clockwise rotation of 90 oabout ...

Quadratic equations and functions 21 Contents: A Quadratic equations [2.10] B The Null Factor law [2.10] C The quadratic formula ...

Equations of the form ax+b=0where a 6 =0are calledlinear equationsand haveonly onesolution. For example, 3 x¡2=0is the linear eq ...

b 2 ¡ 3 x^2 =8 ) ¡ 3 x^2 =6 fsubtracting 2 from both sidesg ) x^2 =¡ 2 fdividing both sides by¡ 3 g which has no solutions asx^2 ...

EXERCISE 21B.1 1 Solve for the unknown using the Null Factor law: a 3 x=0 b a£8=0 c ¡ 7 y=0 d ab=0 e 2 xy=0 f abc=0 g a^2 =0 h p ...

Example 5 Self Tutor Solve forx: a x^2 +3x=28 b 5 x^2 =3x+2 a x^2 +3x=28 ) x^2 +3x¡28 = 0 ) (x+ 7)(x¡4) = 0 ) x+7=0 or x¡4=0 ) x ...

EXERCISE 21B.2 1 Solve forx: a x^2 ¡ 7 x=0 b x^2 ¡ 5 x=0 c x^2 =8x d x^2 =4x e 3 x^2 +6x=0 f 2 x^2 +5x=0 g 4 x^2 ¡ 3 x=0 h 4 x^2 ...

Try as much as we like, we will not be able to solve quadratic equations such asx^2 +4x¡7=0using the factorisation methods alrea ...

USE OF THE QUADRATIC FORMULA If b^2 ¡ 4 ac is a rational perfect square then p b^2 ¡ 4 ac will be rational, and so the solutions ...