O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2020 · Q612 Marks
Solve the inequality 6x-7 > 5-2x.
- (a)Solve the inequality 6x-7 > 5-2x.[2]
- (b)Chen buys 4 notebooks and 3 pens for $17.50 . Liu buys 2 notebooks and 5 pens for $14. Form a pair of simultaneous equations and solve them to find the cost of a notebook and the cost of a pen. Show your working.[4]
- (c)(i)Show that x/(x+2) - 3/(x-5) = 4 can be rearranged to 3x²-4x-34 = 0.[3]
- (c)(ii)Solve the equation 3x²-4x-34 = 0. Show your working and give your answers correct to 2 decimal places.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [2] x > 1.5 oe final answer M1 for 6x + 2x > 5 + 7 or better After 0 scored, SC1 for answer [...]1.5 oe
- [4] 4n + 3p = 17.5[0] 2n + 5p = 14 B1 Correct method to eliminate one variable M1 FT their equations n = 3.25 p = 1.5[0] A2 A1 for either n = 3.25 or p = 1.5[0] Or after A0, SC1 for a pair of values that satisfy either equation or for correct answers with no working
- [3] M1 Use of common denominator x(x-5)-3(x+2) / (x+2)(x-5) [=4] M1 Correct elimination of fractions and expansion of brackets x^2 – 5x - 3x – 6 = 4x^2 + 8x – 20x – 40 or better A1 A0 if any errors or omissions in working
- [3] -(-4)/(-4)^2-4×3×-34 / (2×3) B2 B1 for √(-4)^2-4×3×-34 or for -(-4)±√their 424 / (2×3) or for (3x - 2/3)^2 oe 4.1[0], -2.77 B1
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