(a) Apples cost $x per kilogram and oranges cost $y per kilogram. The total cost of 5 kg of apples and 10kg of oranges is $40. (b) Solve -8 < 4(x-3) < 7. (c) Solve 4/(x-1) + 2/(2x+3) = 1. Show all your working and give your answers correct to 2 decimal places.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [1] 5x + 10y = 40 leading to x + 2y = 8
2. [4] Apples $2.80, Oranges $2.60
3. B1 4x + 3y = 19
4. M1 Correct method to eliminate one variable
5. A2 A1 for either x = 2.8[0] or y = 2.6[0] nfww
6. After A0 scored, SC1 for a pair of values that satisfy either correct equation or for correct answers with no working or with incorrect
7. [3] 1 < x < 4 3/4 oe final answer
8. B2 for 1 < x or x < 4 3/4 oe
9. or M1 for -8/4 [...] x - 3 [...] 7/4 or better or -8 + 12 [...] 4x [...] 7 + 12 or better
10. [6] 5.65 and -1.15
11. B3 2x²-9x-13 [= 0]
12. B2 for (4(2x+3)+2(x-1)) / ((2x+3)(x-1)) [=1] or better
13. or B1 for 4(2x + 3) + 2(x – 1) oe or for (2x + 3)(x – 1) or better
14. B2FT their 3-term quadratic
15. B1FT for √(-9)² - 4×2×-13 oe or for -(-9)±√(their discriminant) / (2×2)
16. or for (x + (-9)/(2×2))² + ((-13)/(2×2)) - ((-9)/(2×2))²