Unit 6
4 marks · Easy(a) Simplify the algebraic expression: (x^2y^3)^1/2 × (y^2x)^1/2. (b) List all the members of set A = {even numbers between 2 and 12}.
Write your answer in its simplest index form.
List all the elements of 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.
Show answer
(a) x^{1.5}y^{2.5}
(b) {2, 4, 6, 8, 10, 12}
Common mistakes: incorrect index laws; missing elements
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses correct law of indices in simplification.
A1 (a) · 1 mark · Gives final answer as x^{1.5}y^{2.5}.
M1 (b) · 1 mark · Identifies all even numbers between 2 and 12 inclusive.
A1 (b) · 1 mark · Writes all members of A without omissions or extras.
Worked solution
(a) (x^2y^3)^{1/2} × (y^2x)^{1/2} = x^{1}y^{1.5} × y^{1}x^{0.5} = x^{1+0.5}y^{1.5+1} = x^{1.5}y^{2.5}.
(b) A = {2, 4, 6, 8, 10, 12}.