F.3 maths - Ans.fyi 參考答案

F.3 maths

2009-12-12 7:51 pm

1. In a fitness course, a student will get a pass if his average score in the five tests is not less than 40. If Raymond's scores in the first four tests are 38,46,29 and57, what is the minimum score he must get in the fifth test in order to get a pass?

2.The sun of the digits of the ones and the tens of a two-digit number is 8 and this two-digit number is less than 40.
(a) Let x be the digit of the ones in the two-digit number. Repersent the range of values of x by an inequality .
(b) Find all the possible values of this two-digit number.

3.Samson is now x years old. Samson's sister is three year elder then him. Given that the sum of their ages is not greater than 31, find the greatest value of x .

4.Two cars travelling in opposite directions at speeds 50 km/h and 70 km/h respectively meet on a road. After at least how many minutes is their minimum distance 3 km apart?

回答 (1)

用戶9112

2009-12-12 8:11 pm

✔ 最佳答案

(1) Average score required = 40
Total score required for 5 tests = 40 * 5 = 200
Minimum test score for the 5th test = 200 - 38 - 46 - 29 - 57
= 30
(2)(a) The ones digit is x
The tens digit is then 8 - x
The value of the number is 10(8 - x) + x = 80 - 9x
Since the number is a 2 digit number, 80 - 9x >= 10
70 >= 9x
7.78 >= x
7 >= x
The range of the number is 80 - 9(0) >= Number >= 80 - 9(7)
80 >= Number >= 17
(b) The numbers are 80, 71, 62, 53, 44, 35, 26, 17
(3) The age of Samson's sister is x + 3
Sum of their ages = x + x + 3 <= 31
2x + 3 <= 31
2x <= 28
x <= 14
The greatest value of x is 14
(4) Let the time required be x minutes
The distances travelled by both cars are 50 * x /60 and 70 * x/60 km respectively
50x/60 + 70x/60 = 3
120x/60 = 3
2x = 3
x = 1.5
At least after 1.5 minutes will they be 3km apart

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