O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2017 · Q1012 Marks
A rectangular picture, ABCD, is placed inside a rectangular frame. [Figure of a rectangular picture inside a frame] The length, AB, of the picture is three times its height, x cm. The width of the frame is 2 cm.
- (a)The total area of the picture and the frame is 476 cm². Form an equation in x and show that it simplifies to `3x² + 16x – 460 = 0`.[4]
- (b)Solve the equation `3x² + 16x – 460 = 0`.[3]
- (c)Find the height and length of the frame.[2]
- (d)The frame is made from wood. The wood is 5 mm thick. The mass of 1 cm³ of the wood is 0.7 g. Calculate the mass of wood used in the frame.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [4] (a) 3x² +16x-460 = 0 correctly derived
- B1 for (x + 4)(3x + 4) ое
- and M1 for expanding brackets and collecting like terms
- and M1 for their area = 476
- A1 for correct simplification leading to 3x² + 16x-460 = 0
- [3] (b) 10 and (-46/3) ое (-15.3)
- B2 for (x – 10)(3x +46)
- Or M1 for such as (x+a)(3x+b) with ab = − 460 or 3a + b = 16
- A1FT for solutions from their factors
- [2FT] (c) [Height = ] 14
- [Length = ] 34
- B1FT for either, or for both correct but in the wrong places
- [3FT] (d) 61.6 or 16(their +ve root + 1)×0.35
- M2 for (their 476 – their 10 × their 30) × 0.5 × 0.7 oe
- Or M1 for their 476 – their 10 × their 30 oe
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