Revision Test 5 : Transposition and simultaneous equations
This assignment covers the material contained in Chapters 12 and 13. The marks available are shown in brackets at
the end of each question.
1. Transpose p − q + r = a − b for b.
( 2 )
2. Make π the subject of the formula r =
c
2π
(2)
3. Transpose V =
1
3
πr
2 h for h.
( 2 )
4. Transpose I =
E − e
R + r
for E.
( 2 )
5. Transpose k =
b
ad − 1
for d.
( 4 )
6. Make g the subject of the formula t = 2π
L
g
(3)
7. Transpose A =
πR 2 θ
360
for R.
( 2 )
8. Make r the subject of the formula
x + y =
r
3 + r
(5)
9. Make L the subject of the formula
m =
μL
L + rC R
(5)
10. The surface area A of a rectangular prism is
given by the formula A = 2(bh + hl + lb). Evaluate b when A = 11 750 mm
2
, h = 25 mm and
l = 75 mm.
(4)
11. The velocity v of water in a pipe appears in
the formula h =
0.03 Lv 2
2 dg
. Evaluate v when
h = 0.384, d = 0.20, L = 80 and g = 10.
(3)
12. A formula for the focal length f of a convex
lens is
1
f
=
1
u
+
1
v
. Evaluate v when f = 4 and
u = 20.
(4)
In problems 13 and 14, solve the simultaneous equations.
13. (a) 2x + y = 6
(b) 4x − 3y = 11
5x − y = 22
3x + 5y = 30
(9)
14. (a) 3a − 8 +
b
8
= 0
b +
a
2
=
21
4
(b)
2 p + 1
5
−
1 − 4q
2
=
5
2
1 − 3 p
7
+
2q − 3
5
+
32
35
= 0
(18)
15. In an engineering process two variables x and y
are related by the equation y = ax +
b
x
, where a
and b are constants. Evaluate a and b if y = 15
when x = 1 and y = 13 when x = 3.
(5)
16. Kirchhoff’s laws are used to determine the current
equations in an electrical network and result in the
following:
i 1 + 8 i 2 + 3 i 3 = −31
3 i 1 − 2 i 2 + i 3 = −5
2 i 1 − 3 i 2 + 2 i 3 = 6
Determine the values of i 1 , i 2 and i 3
(10)