Maths 急~~~Exam

1. Simplify (3r-s)^2/12r-4s

(3r-s)^2/12r-4s

=(3r-s)^2/4(3r-s)

=(3r-s)/4

2.Use simultaneous equation:
y=5x+2=6x+3

5x+2=6x+3

x=-1

Sub x=-1 into y=5x+2

y=-3

so,x=-1,y=-3


3.Use simultaneous equation:
x=3/4y+1=1/2y+3

{x=3/4y+1
{x=1/2y+3


Sub x=3/4y+1 into x=1/2y+3

3/4y+1=1/2y+3

3y+4=2y+12

y=8

Sub y=8 into x=3/4y+1

x=7

So,x=7,y=8

4.Use the method of substitutation and the method of elimination.

{r+5s=2 --------------(1)
{4r-3s=31----------------(2)

From(1),
r+5s=2

r=2-5s----------------(3)

sub (3) into (2)

4(2-5s)-3s=31

8-20s-3s=31

-23s=23

s=-1

Sub s=-1 into (3)

r=2-5(-1)

r=7

so,r=7,s=-1


5.A metal rod of length 0.5m expands to 0.535m when the temperature is increased from 25℃to 165℃. Find the rate of expansion in mm/℃.

the increase of length:(0.535-0.5) x 1000 mm=35 mm

the increase in temperature:(165-25)*C=140*C

The rate of expansion:
= 35/140 mm/*C

=1/4 mm/*C

The required answer is 1/4mm/*C

2007-01-04 19:54:33 補充：
For question(5),the answer can also be written as 0.25mm/*C