O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2017 · Q912 Marks
A pump takes 12 minutes to add 3000 litres of water to a pond. How long will it take the same pump to add 1750 litres of water to a pond?
- (a)A pump takes 12 minutes to add 3000 litres of water to a pond. How long will it take the same pump to add 1750 litres of water to a pond?[2]
- (b)(i)Write down an expression, in terms of x, for the number of minutes the small pump takes to fill the empty tank.[1]
- (b)(ii)It takes 15 minutes longer to fill the empty tank using the small pump than it does with the large pump. Form an equation in x and show that it simplifies to 3x² + 60x – 10 000 = 0.[3]
- (b)(iii)Solve the equation 3x² + 60x – 10 000 = 0. Give each answer correct to 2 decimal places.[3]
- (b)(iv)Find the length of time the large pump takes to fill the empty tank. Give your answer in minutes and seconds, correct to the nearest second.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [2] M1 for (12 / 3000) × 1750 oe
- [2] 7 cao
- [1] 2500 / x
- [3] M1 Or equivalent unsimplified equation
- [3] M1 FT elimination of their fractions with algebraic denominators
- [3] A1 Correct simplification leading to 3x² + 60x – 10 000 = 0 AG
- [3] B1 for √60² - 4 × 3 × (-10000) soi
- [3] B1 for (-60 ± √their123600) / (2×3)
- [3] 48.59 and -68.59 final answer
- [3] M2 for 2500 / (their 48.59 + 20)
- [3] or M1 for 2500 / their 48.59
- [3] 36 minutes 27 seconds
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