Unit 6
4 marks · Easy(a) A number n is such that n^2 = 121. Let S be the set of all integer values of n.
(b) Using n = 11, write all possible members of set A = {x | x = 2^k, 0 ≤ k ≤ n, k is an integer}.
List set S.
Write down all members of set A.
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.
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(a) S = {-11, 11}
(b) A = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048}
Common mistakes: missing negative value; incomplete powers sequence
Show mark scheme and worked solution
Marking points
B1 (a) · 2 marks · Lists both integer solutions {-11, 11} for n.
M1 (b) · 1 mark · Writes correct sequence of 2^k for k = 0 to n = 11.
A1 (b) · 1 mark · All correct members: 1 to 2048 inclusive.
Worked solution
(a) n^2 = 121 ⇒ n = 11 or n = -11. Thus S = {-11, 11}.
(b) For k = 0,1,2,...,11: 2^0=1, 2^1=2, ... up to 2^11=2048. So A = {1,2,4,8,16,32,64,128,256,512,1024,2048}.