Unit 7
5 marks · EasyA rectangular field is 20 metres longer than it is wide. The area of the field is 1200 m².
Let the width of the field be metres. Form a quadratic equation in \( x \ ) for the area of the field and solve it to find the width and length of the field.
The width you obtained in part (a) is used as the input in the function . Work out the value of , giving your answer to 2 decimal places.
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) width 30 m, length 50 m · must show correct quadratic set-up, expanding and solving for positive root only, answers for width and length both in metres
(b) y = 1000 · must show substitution of x=30, correct cubic operation, rounded to 2 decimal places
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Forms the correct quadratic equation: or equivalent.
M2 (a) · 1 mark · Solves the quadratic (expands/brings to standard form and factorises or uses the quadratic formula). (follow-through)
A1 (a) · 1 mark · States both width (30 m) and length (50 m), positive values only. (follow-through)
M3 (b) · 1 mark · Substitutes value of into the cubic function correctly. (follow-through)
A2 (b) · 1 mark · Evaluates and gives to 2 decimal places. (follow-through)
Worked solution
Let the width be metres.
Then the length = metres.
Expand:
Factorise:
So (since width cannot be negative), length = 30 + 20 = 50.
Now substitute into :
Final value: .