Algebra 9
3 marks · EasyThe statement is: "The sum of any two even numbers is always even."
Write an algebraic expression for two even numbers.
Show algebraically that their sum must be even.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 2m and 2n (where m, n are integers)
(b) 2m + 2n = 2(m+n) so the sum is a multiple of 2 (even)
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correctly writes two even numbers in the form 2m, 2n or equivalent.
M1 (b) · 1 mark · Adds the two expressions correctly to get 2m + 2n = 2(m+n) or equivalent.
A1 (b) · 1 mark · Clearly concludes sum is even because it is 2 times an integer.
Worked solution
a) Let the two even numbers be 2m and 2n, where m and n are integers.
b) Their sum is 2m + 2n = 2(m + n). Since m + n is an integer, 2(m + n) is even.