F.1 mathematics

1. If x divided by 3 minus 5 equals 1/8 of x, the value of x

Sol:

x ÷ 3 － 5 ＝ x/8

x/3 － 5 ＝ x / 8

8x － 120 ＝ 3x

5x ＝ 120

x ＝ 24

Ans: x ＝ 24

2. simiplify the following expressions

( a ) (2t)^3 / 6t^2

( b ) [ - m² - ( - m )² ] / ( - 3m² )

Sol:

( a )

(2t)^3 / 6t^2

＝ 8t^3 / 6t^2

＝ 4t/3

( b )

[ - m² － ( - m )² ] / ( - 3m² )

＝ ( - m² － m² ) / ( - 3m² )

＝ ( - 2m² ) / ( - 3m² )

＝ 2/3

Ans: ( a ) 4t/3 ( b ) 2/3

3. Two cars A and B 50km apart are travelling towards each other

on the same road. Car A travels at d km/h while car B travels 60

km/h. If the two cars will meet after 30 minutes, find the value of d.

Sol:

30 min. ＝ 1/2 hr

d ＋ 60 ＝ 50 ÷ 1/2

d ＋ 60 ＝ 100

d ＝ 40

Ans: d ＝ 40

2008-01-12 15:07:25 補充：
點解第二題的第二個step會變左8t^3? 個hins係咩?Ans: 因為三次方是在括號外面, 所以括號裡頭既數字都要三次方(2t)^3 → 2 既三次方等於 8, t 既三次方等於 t^3合起來就等於 8t^3

2008-01-12 15:08:20 補充：
另外, 2 ( b ) 點解 [ - m^2 － ( - m ) ^2 ]/ ( - 3m^2 ) 會變左( - m^2 － m^2 ) / ( - 3m^2 )?Ans: 我們睇這 ( - m ) ^2 這個部份, ( - m )^2 就係 ( - 1 m )^2( - 1 m )^2 → - 1 既二次方等於 1, m 既二次方等於 m^2合起來就等於 1m^2 ＝ m^2 ( 1 可得唔寫 )so, 你 substitute m^2 入左 ( - m ) ^2 既位置便可得( - m^2 － m^2 ) / ( - 3m^2 )?