MODUL PROGRAM IBNU SINA ADDITIONAL MATHEMATICS
MODULE 3 SIMULTANEOUS EQUATIONS
Terbitan :YAYASAN PELAJARAN JOHOR JABATAN PELAJARAN NEGERI JOHOR
SIMULTANEOUS EQUATIONS
FORM 4
MODULE 3 IBNU SINA TOPIC : SIMULTANEOUS EQUATIONS Express Note :
Solve the quadratic equation using factorisation, completing the square or the formula x =
−b ±
b
2
− 4ac
2a
PAPER 2 1.
Solve the simultaneous equations
2.
Solve the simultaneous equations 3 x + y = 9 and
3.
Solve the simultaneous equations 2y
4.
Solve the simultaneous equations 3 p − 5q
5. 6. 7.
x
2y = 8 and 3 x 2
+
−
x = 1 =
Solve the simultaneous equations
3 p
−
2q
q
=
p
Solve the simultaneous equations 2q − p =
2q
−
p
p
9.
Solve the simultaneous equations 2 x − y = 7 and
2
−
2
xy = 0
−
3 p2
−
x
x
11pq
=
1
= −
y
p + q
=
52
=
=
2
1
q
2 x+ y = x
x
x +
2y
1 and
Solve the simultaneous equations
Solve the simultaneous equations
+
4 and 6q 2
Solve the simultaneous equations 3 x + 2y = 12 and
4 y 2
x − y = 3
+
x
and 2y 2
8.
10.
2
+
4 y − 9
−
=
2
=
7
x( x
+
xy + y
y
2
−
0 and
3 y 2
6y
x
y ) = 11 x
+
2
=
7 .Give your
answer correct to three significant figures 11.
Solve the simultaneous equations 2 x + 3 y = 9 and
−
x
1
= −
y
12.
Solve the simultaneous equations 2 x + 3 y + 1 = 0 and
13.
Give your answer correct to two decimal places. Given that (-1, 2k ) are the solutions to the simultaneous equations 2
x+
14.
py − 29
=
4=
px −
xy,find
2
x+
6
xy+ 6
y
2
=
0.
the values of k and p .
Find the coordinates of the points of intersection between the line the curve
=
y x
=
4 and
8(1 − x )
END OF MODULE 3
PROGRAM IBNU SINA TAHUN 2010(ALL A’s)
Page 2
SIMULTANEOUS EQUATIONS
FORM 4
MODULE 3 - ANSWERS TOPIC : SIMULTANEOUS EQUATIONS PAPER 2
1. 2. 3. 4. 5. 6. 7.
x x
=
x
=−
p
=−
x
=3
p
p
y
=
, y
=
=3,
2
3 2
8 9
, y
, y
1 , q 1 2
; x
2 3
; x
=−
, q
=
=−
5
3
=
x
=
2
, y
=
9.
x
=
2
, y
=−
10.
x
= 11 .556
11.
x
=3
12.
x
= 1.12
13.
k
14.
(
4
3
4
=
= −4
=
, y
=
=
1 , q
=
6
1
=
1
=
=
; x
1 ; x = 18 , y
=
−1
=−
=
0.639
1
=
12
, y
, y
27
, q
3
4 , q
=3
2
, y
=−
; p
; x
, y 1
7
=
3 ; x = 19 , y
, y
, p
1
=
; p
3
1 ; p
8.
=
4
=
=
, y
= −6
; x
2
1
; x
4
=−
, q
, y
1
=
31
= 3.76
1.31
=−
9
=−
1.08 ; x = −1.79 , y
=−
4
, y
; k = −2 , p
=
0.86
8
=−
1 ,2) , ( 1, 4) 2
−−
END OF MODULE 3
PROGRAM IBNU SINA TAHUN 2010(ALL A’s)
Page 3
