O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2025 · Q209 Marks
ABCD and EFGD are rectangles. [Figure showing two rectangles, EFGD enclosing ABCD, with dimensions labelled as x, 2x-3, x+3, x-2]
- (a)(i)Show that CD = x-1.[1]
- (a)(ii)The area of rectangle ABCD is 1/5 of the area of rectangle EFGD. Form an equation in x and show that it simplifies to x²-6x+3 = 0.[3]
- (b)(i)Use the quadratic formula to solve the equation x²-6x+3 = 0. You must show all your working and give your answers correct to 2 decimal places.[3]
- (b)(ii)Calculate the shaded area.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [1] With no error seen leading to x-1
- [3] M1 e.g. 5 × 3(x – 1) = (2x – 3)(x + 3) oe B1 2x²-3x+6x-9 or better A1 With no errors or omissions at any stage in the working
- [3] B2 [--]6±√(-6)²-4×1×3 / 2×1 oe or B1 for (-6)²-4×1×3 or better or for [--]6+√k / 2 oe or [--]6-√k / 2 oe B1 5.45 and 0.55
- [2] M1 for substituting their x value into correct area formula, where x > 2 e.g. (2x-3)(x+3)-3(x-1) oe
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