Page 55 - ACE YR IGCSE A TOP APPR' TO MATHS

(c) y y
1 6

Y
4
x
0 90° 180° 270° 360° 2 X

x
–1 0 2 4 6
[3]
→ → →
7 7 Vectors and Transformations (b) YZ = YO + OZ
–4
3
= ( ) ( )
+
Vectors –4 0
–1
1 (a) Coordinates of B = ( )
–4
2 + 1
→
= ( –5 – 20 ) |YZ| = √1 + 16
( ) = 4.12 [3]
3
= –25 [1] 4 (a) XP = XO + OP
→ →
→
→ → → ( ) ( )
–3
8
(b) BC = BA + AC = 5 + 7
–8
–1
= ( ) ( ) = ( )
+
5
20
–15
( ) 12
–9
= 5 |XP| = √25 + 144
→
→ = 13 [3]
|BC| = √81 + 25 → 1 →
= 10.3 [3] (b) XF = 2 FP
( ) ( )
1 –20 –5
=

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[1]
(a) (i)
→
→
→
→
4 4 1 XO + OF = 1 (FO + OP)
→ 20 2
(ii) YX = ( ) [1] OF – 1 FO = 1 OP – XO
→ →
→
→
–4
(b) 5 – AB = –1 2 2
–1 + 3A = 4B 3 → 1 → →
Solve the simultaneous equations. 2 OF = 2 OP + OX
AB = 6 → → →
6 OF = 1 OP + 2 OX
A = 3 3
B
( ) ( )
6
–1 + 3 ( ) = 4B = 1 –3 + 2 –8
3 –5
3 7
B
( )
–B + 18 = 4B 2 19
= – [3]
4B + B – 18 = 0 3
2
9 5. (a) –1
B = 2 or B = – y
4 8 P
A = 3 or A = – 8 [5]
3 6
→ → →
3 (a) OY = OX + XY 4
0
8
2
+
– 2
= ( ) ( ) ( ) 2 R Q (6, 2)
2
4
10
( )
4
= 4 0 2 4 6 8 10 x [1]
Answers 175
Answers.indd 175 15/03/2022 11:08 AM