O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2019 · Q511 Marks
x²+7x-13 = (x+a)²+b Find the value of a and the value of b.
- (a)(i)x²+7x-13 = (x+a)²+b Find the value of a and the value of b.[2]
- (a)(ii)Hence solve the equation x² +7x-13 = 0. Show your working and give your answers correct to 3 significant figures.[2]
- (b)Simplify `(4x²-9)/(2x²-11x+12)`.[3]
- (c)Solve `2x/(x+4) + 6/(x-1) = 2`.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [2] [a =] 3.5 oe [b =] -25.25 B1 for (x + 3.5)² or a = 3.5
- [2] x= -3.5±√25.25 M1 FT their completed square expression 1.52 -8.52 A1 After 0 scored, B1 for 1.52 and -8.52
- [3] (2x+3)/(x-4) final answer nfww B1 for (2x + 3)(2x – 3) oe factorisation seen B1 for (2x-3)(x – 4) oe factorisation seen
- [4] x = 16 M1 for 2x(x - 1) + 6(x + 4) = 2(x + 4)(x – 1) M1FT for 2x²-2x + 6x + 24 = 2x² + 8x - 2x – 8 M1FT for 24 + 8 = 6x – 4x (may be 8x – 6x)
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