S1 Math (Algebra)

1. An even number can be written as 2n , where n is an integer.
a). Write down the even number which is just less than 2n.
as 2n is an even number
the even number which is just less than 2n must be 2n - 2

b). Write down the even number which is just greater than 2n.
as 2n is an even number
the even number which is just less than 2n must be 2n + 2

2) The sum of the the first n natural numbers is 1/2n(n+1). Find the sum of the first 12 natural numbers .

as The sum of the the first n natural numbers is 1/2n(n+1)
when n = 12
The sum of the the first n natural numbers
= the sum of the first 12 natural numbers
= 1/2(12)(12+1)
= 78

3)A sum of $830 was distributed among 35 children , each child over 10 years age received $25 and those below 10 years got $16 each.How many children were over 10 years of age ?

Let the number of children over 10 years of age be x
then the number of children below 10 years = 35 - x

so 830 = 25 * (35-x) + 16*x
830 = 875 - 25x + 16x
9x = 45
x = 5
so there were 10 children over 10 years of age

希望幫到你

2007-12-27 14:15:37 補充：
唔好意思~發現第三題掉轉左黎計Let the number of children over 10 years of age be xthen the number of children below 10 years = 35 - xso 830 = 25 * x + 16*(35-x)830 = 25x + 560 - 16x9x = 270x = 30so there were 30 children over 10 years of age

1a) 2n-2 = 2(n-1)
1b) 2n+2 = 2(n+1)

2) sub n = 12, ans = (1/2)(12)(12+1) = 78

3)
let number of child over 10 years of age be x
let number of child below 10 years of age be y
x+y = 35 ----------------- (E1)
25x+16y = 830 ------- (E2)
25*(E1) - (E2) : 25x+25y-25x-16y = 25*35-830
9y = 45
y = 5
x = 35-5 = 30
So there are 30 children over 10 years of age