英文數學(升中一)

1. (5x2)+(5x4)+(5x6)+(5x8)+...+(5x998)
= (5x2)(1+2+3+4+...+499) <-- This step is factorization
= 10 (1+ 499) x 499 /2
= 2500x499
=1247500


2. Find the units digit of the expression 1x2x3x...x2012x2013.Briefly explain your answer.

Hint:Consider the product of the first 5 integers.
As 1 x 2 x 3 x 4 x 5 = 120 = 12 x 10
thus, the expression must be multiplied by 10.
the units digit of multiplicatoin of 10 must be 0.

3.1 L is equal to 1 立方米.
wrong, 1ml = 1cm^3
1m^3 = 1000000cm^3
so 1m^3 = 1000000ml = 1000L


4. In a bookstore, the number of Chinese books is 50 more than twice the
number of English books.If there aer 350 Chinese books, find the number of
English books in the bookstore.(列方程)
let y be the number of english books.
2y+50 = 350
2y=300
y=150
so there are 150 english books

5. Complete the following table.
e.g / 問題.
Marked price $100 / 2200
Selling price $80 / 1980
Discount $20 / $220
Discount percentage 80% / 10%

2013-08-06 15:17:12 補充：
1. As all the terms contain 5x2 , we can factorize it.
so (5x2)+(5x4)+(5x6)+(5x8)+...+(5x998)
= (5x2)(1+2+3+4...+499)
Then, to solve (1+2+3+4...+499)
we can consider the following, 1+ 499, 2+ 498, 3+ 497.....
totally, there are 249 pairs of the numbers.
(the remaining should be 250)

2013-08-06 15:17:17 補充：
As 1+ 499, 2+ 498, 3+ 497 ... are equal to 500,
thus, (1+2+3+4...+499) = 500x 249 +250=124750
so (5x2)(1+2+3+4...+499)
= 10x 124750 =1247500