O-Level Additional Math

[iFruit]

Sahimi:

Hi! pls help!!


If n is a number, show that for all values of n, (n3 + 11n) is divisible by 6. (sec Two maths)
Thks

n³ + 11n = n³ -n + 12n = n(n²-1)+12n = n(n-1)(n+1)+12n = (n-1)n(n+1)+12n


(n-1)n(n+1) is the product of 3 consecutive numbers which is always divisible by 6 ( you can use induction to prove if necessary) and 12n is divisible by 6.

So, n³ + 11n is divisible by 6

HTH

[Sahimi]

iFruit:

Sahimi:

Hi! pls help!!


If n is a number, show that for all values of n, (n3 + 11n) is divisible by 6. (sec Two maths)
Thks

n³ + 11n = n³ -n + 12n = n(n²-1)+12n = n(n-1)(n+1)+12n = (n-1)n(n+1)+12n


(n-1)n(n+1) is the product of 3 consecutive numbers which is always divisible by 6 ( you can use induction to prove if necessary) and 12n is divisible by 6.

So, n³ + 11n is divisible by 6

HTH

thks very much, iFruit.

[k1ndan]

E:{x:30<x<=100}

A:{x: Multiples of 3}
B:{x: unit digit is 10}

What is A’n B’?[/url]

[k1ndan]

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[k1ndan]

k1ndan:

http://i300.photobucket.com/albums/nn19/k1ndan/Maths_Sec2_Set1.jpg\">

Sorry, typo error, the condition should be if a=b, what is the value of W?

[k1ndan]

€ = {x : x is an integer, 30 < x≤100}

A: {x : x is divisible by 3}
{x: units digits of x is 0}

List the elements of A’ n C’

[Guan Hui]

since a+b=Q and Q=32 and a=b

a= 16, b=16
since c+b=P and P=46 and b=16
c=30
a+b+c= 16+16+30= 62(impossible since E=60)
E-(a+b+c)=W=60-62= -2 (unless negative is accepted as the ans?)


[/quote]

[Sahimi]

Hi pls help!


The two parallel sides of a trapezium are 3x and (5x + 8)cm each. Given the height between the parallel lines is (x - 1)cm. Show that the area is 4(x2 - 1).

[Augmum]

Sahimi:

Hi pls help!


The two parallel sides of a trapezium are 3x and (5x + 8)cm each. Given the height between the parallel lines is (x - 1)cm. Show that the area is 4(x2 - 1).

hi
let me try to attempt yr question.

Area of trapezium = half the sum of parallel lines x height = ½ X (3x +5x+ 8 ) x (x-1)
=8x+8 / 2 X (x-1)
=2(4x + 4)/2 X (x-1)
=(4x + 4) (x-1)
= 4 (x+1) (x-1)
=4 (x2 –x+x-1)
=4 (x2-1) (Ans)

[Sahimi]

Pls help !


Q1) Given that x2 + y2 = 185 and xy = -12, find the value of (x - y)2

Q2) If (a - b)2 = 72 and ab = 8.5, calculate the value of a2 + b2.

Q3) Given that 1043square - 1037square = 120y, find value the y without using calculator.