Algebra 2

5 marks · Hard

The formula for the area of a parallelogram is , where is the base and is the height.

(a)

Given , , express the area in terms of using index notation.

[2 marks]

(b)

If , solve for . Give all possible positive values for .

[3 marks]

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) 20x^3

(b) x=\sqrt[3]{9} \approx 2.08

Also accept: Final answers may be left in surd form if not rational.

Common mistakes: Not combining the indices correctly; Giving a negative value for x

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Substitutes base and height into area formula.

A1 (a) · 1 mark · Correct application of index laws to get .

M1 (b) · 1 mark · Equates to 180 and attempts to solve for .

M2 (b) · 1 mark · Correctly isolates and takes cube root.

A1 (b) · 1 mark · Gives correct positive value(s) of .

Worked solution

a) Substitute , into the area formula:

b) Set and solve for :