O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2017 · Q59 Marks
Express as a single fraction in its simplest form `4/(x-2) - 5/(x+1)`.
- (a)Express as a single fraction in its simplest form `4/(x-2) - 5/(x+1)`.[2]
- (b)Solve `2x(x + 1) = 3(4 – x)`.[3]
- (c)(i)Anil and Yasmin buy some pens and notebooks from the same shop. Anil buys 3 pens and 2 notebooks for $4.80 . Yasmin buys 5 pens and 4 notebooks for $9.00 . Form a pair of simultaneous equations to represent this information.[1]
- (c)(ii)Solve the simultaneous equations to find the cost of a pen and the cost of a notebook.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [2] (a) (14-x)/((x-2)(x+1)) Final answer
- M1 for (4(x+1)-5(x - 2))/((x-2)(x+1)) or better soi
- [3] (b) -4 or 1.5 oe
- B1 for 2x² + 5x −12 [= 0]
- Or M1 for (2x-3)(x + 4) [= 0]
- OR M1 for FT factorising their 3-term quadratic equation
- Or for correct FT substitution into formula oe
- and A1FT for solutions from their quadratic equation
- [1] (c)(i) 3p + 2n = 4.8[0] or 3p + 2n = 480
- 5p + 4n = 9[.00] or 5p + 4n = 900
- [3FT] (c)(ii) 0.6[0]
- 1.5[0]
- M1 for a correct method to eliminate one variable
- A1 for either p = 0.6[0] or n = 1.5[0] www
- After A0, B1FT for a correct substitution to find the other variable
- After 0, SC1 for a pair of values that satisfy either equation
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