中一數學題 - Ans.fyi 參考答案

中一數學題

2012-10-08 1:18 am

1.In a soccer league，a team will get 3 points for a win，1 point for a draw and no point for a loss in a match.In the last season,team A had 6 times as many draws as losses and 5 times as many wins as losses.Let X be the number of losses team A had in the last season.

(a)Express the total points got by the team in the last season by using an algebraic expression.
In this season,team A plays the same number of games.But its number of losses in this season is 3 times of last season.But its number of draws is this season is half of last season.
b(i)Express the total points got by the team in this season by using an algebraic expression.
b(ii)In which season does team A preform better?

2.suppose there are n participants in a picnic, and the total expenditure required is $C,where C=1000+30n
(a) if $D denotes the expenditure shared by each student equally,express D in terms of n.
(b)A student claims that"the more the participants in the picnic, the greater the expenditure shared by each student" Do you agree?Explain briefly.

回答 (1)

micatkie

2012-10-08 2:04 am

✔ 最佳答案

1.
(a)
In the last season :
Number of losses = x
Number of draws = 6x
Number of wins = 5x

Number of points in the last season
= 3(5x) + 1(6x) + 0(x)
= 21x

(b)(i)
In this season :
Number of losses = 3x
Number of draws = (1/2)(6x) = 3x
Number of wins = (x + 6x + 5x) - (3x + 3x) = 6x

Number of points in this season
= 3(6x) + 1(3x) + 0(3x)
= 21x

(b)(ii)
The performance of team A in this season is the same as that in the lastseason.
This is because team A gets equal points (21x points) in each of the twoseason.

=====
2.
(a)
C = 1000 + 30n
D = C/n

Hence, D = (1000 + 30n)/n
D = (1000/n) + 30

(b)
No, I don' t agree.
When there are more participants, n increase.
This leads to (1000/n) decreases and thus D = [(1000/n) + 30] also decreases.

Conclusively :
the more the participantsin the picnic, the less the expenditure shared byeach student.

參考: micatkie

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