Unit 5
4 marks · Normal3. A rectangle has a length (x + 5) cm and a width (x − 2) cm. A square of side x cm is cut out from it.
A vector describes a translation of the square to another position with vector (4, −1).
Find and simplify an expression for the area of the shaded part after the square is cut out.
The shaded area is 54 cm². Form and solve a quadratic equation to find the value of x.
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) (x + 5)(x − 2) − x² = x² + 5x − 2x−10 − x² = 3x − 10
(b) 3x − 10 = 54 ⇒ x = 21.33 cm
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Forms correct area expression
A1 (a) · 1 mark · Simplifies to 3x − 10
M2 (b) · 1 mark · Sets 3x − 10 = 54 and rearranges
A2 (b) · 1 mark · Solves for x accurately
Worked solution