O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2016 · Q511 Marks
Factorise fully 8x²y - 12x⁵.
- (a)Factorise fully 8x²y - 12x⁵.[1]
- (b)Solve 4x − 2(x + 5) = 3.[2]
- (c)Solve 7 − 5y < 20.[2]
- (d)(i)A rectangle has length 2x cm, perimeter 18cm and area 10cm². Show that 2x² - 9x + 5 = 0.[2]
- (d)(ii)Solve 2x² – 9x + 5 = 0, giving your answers correct to 2 decimal places.[3]
- (d)(iii)Find the difference between the length and the width of the rectangle.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] (a) 4x²(2y - 3x³) final answer
- [2] (b) x = 6.5 or 13/2 or 6½
- [2] (b) M1 for 4x – 2x – 10 = 3 or better
- [2] (c) y > -2.6 or y > -13/5 or y > -2 3/5 final answer
- [2] (c) M1 for -5y < 20 – 7 oe or better
- [2] (c) Or SC1 for 2.6 or – 2.6 oe seen
- [2] (d)(i) EITHER Width = (18-4x)/2 oe
- [2] (d)(i) OR Width = 10/(2x) oe
- [2] (d)(i) (18-4x)/2 × 2x = 10 oe
- [2] (d)(i) 4x + 20/(2x) = 18 oe
- [2] (d)(i) A1 isw
- [3] (d)(ii) 3.85 and 0.65 cao
- [3] (d)(ii) B2 for 3.850 to 3.851 and 0.649 to 0.650
- [3] (d)(ii) or one correct answer or 3.9 and 0.6
- [3] (d)(ii) Or if in form (P±√Q)/r or (P+√Q)/r or (P-√Q)/r
- [3] (d)(ii) B1 for p = 9 and r = 4 or q = 41
- [1] (d)(iii) 6.35 to 6.45 or – 6.45 to - 6.35 oe
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