Cambridge International Mathematics

700 ANSWERS

4

agradient of OA=4, gradient of BC=4 ) OAkBC

OA=BC=

p

17 units

bgradient of OA=4

gradient of AB=¡^14 and 4 £¡^14 =¡ 1

) OA and AB are perpendicular.

c Froma, a pair of opposite sides ara parallel and equal in

length, ) OABC is a parallelogram.

Fromb, angle OAB is a right angle

) the parallelogram is a rectangle.

d(^12 ,2)and(5,3) e 2 x+8y=17and 4 x¡y=17

5a

by=4 c OA=AB=BC=CO=5units

) OABC is a rhombus

d(4,2)and(4,2)

eDiagonals of a rhombus bisect each other

f y=^12 xand 2 x+y=10

6agradient of AC=k

3

, gradient of BC=¡k

3

bAs the right angle must be at C, k

3

=^3

k

) k^2 =9and so k=3fask> 0 g

c isosceles d x=0

7aCisat(0, 2

p

3) bMisat(1,

p

3) and N(¡ 1 ,

p

3)

c x=0,

p

3 x¡ 3 y=¡ 2

p

3 ,

p

3 x+3y=2

p

3

REVIEW SET 14A

1ax=¡ 1 b¡^45 cx-int=3, y-int=2, m=¡^23

d 8 x¡ 3 y=¡ 7

2 y=¡^12 x+4(or x+2y=8) 3 y=3x¡ 5

4 y=¡ 2 x+3 52 x¡ 3 y=¡ 18 (ory=^23 x+6)

67 k=¡ 11

8 y=¡ 4

92 x¡ 3 y=18

10

11

a AB=BC=5units ) ¢ABC is isosceles

b Xisat(^12 ,^12 )

c gradient of BX=7, gradient of AC=¡^17

) BX and AC are perpendicular.

d BX is a line of symmetry with equation y=7x¡ 3.

12

a gradient of AB=^25 , gradient of DC=^25 , ) ABkDC.

Also AB=CD=

p

29 units

b gradient of AB=^25 , gradient of BC=¡^52 , and as these

are negative reciprocals, AB is perpendicular to BC.

Also AB=BC=

p

29 units.

c ABCD is a square

d 7 x¡ 3 y=27, 3 x+7y=24, 4 x¡ 10 y=3,

10 x+4y=51

REVIEW SET 14B

1ay=0 bm=¡ 2 ,c=5 c 4 x+7y=6

2 y=2x+2

3ay=¡ 2 x+7 b y=¡^23 x+2^13 c y=^32 x¡ (^712)
4 k=¡ 1
5 P=¡^23 t+3^13
6 x-intercept is 5 ,
y-intercept is¡ 2
7ay=3 bx=¡ 1 c y=1: 6 x+20
8 m=¡^43 9am=2 by=¡^12 x+3
10 x^0123
y 7531
11 5 x+3y=19
12 a
O
y
x
246
2
-2
8
PQ
SR
O
y
x
246
2
8
4 CB
A
-1 1 2 3 4 x
-1
-2
-3
O
y
3 ¡-¡2 ¡=¡6xy
-1 1 2 3 4 x
1
-1
-2
()4 ¡1 ¡,
y
@¡= ¡Er_\!¡-¡2
O
O
y
x
246
2
4
8
A
B
C
D
-2
x
-2 2 4 6
8
6
4
2
y
O
yx¡=¡-2 ¡+¡7
-8 -4 4 x
8
4
-4
-12
B,()-5 -6
A,()-11 ¡2
D,()-3 ¡8
O C,()3 ¡0
6 x
4
2
-1
-2
2 ¡-¡5 ¡=¡10xy
y
O
O
y
x
246
2
4
-4 -2
B
C
A X
IB MYP_3 ANS
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Y:\HAESE\IGCSE01\IG01_an\700IB_IGC1_an.CDR Friday, 21 November 2008 9:24:52 AM PETER