O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2023 · Q89 Marks
The diagram shows a small rectangle inside a large rectangle. The height of the large rectangle is x cm. The length of the large rectangle is 4 times its height. The width of the shaded border is 3 cm. The area of the small rectangle is 80 cm². [Figure Rectangles with Border]
- (a)Form an equation in x and show that it simplifies to 2x² - 15x - 22 = 0.[4]
- (b)Solve the equation 2x²-15x-22 = 0 . Show your working and give your answers correct to 2 decimal places.[3]
- (c)Calculate the shaded area.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [4] M2 B1 for x-6 or 4x-6 seen
- B1 for 4x x x - 80 oe
- M1 FT expansion of (4x – c)(x – d)
- FT dep on a maximum of one omission or a numerical error in previous equation
- A1 A0 if any errors or omissions
- [3] B2 for -(-15)±√(-15)²-4×2×-22 / (2×2) oe
- B1 for (-15)²-4x2x-22 oe
- or for -(-15)±√their discriminant / (2×2) oe
- B1 -1.26 and 8.76
- [2] M1 for (their 8.76)×(4×their 8.76)-80 oe
- or 30×their 8.76-36 oe
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