O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2022 · Q810 Marks
Lara and Marco each cycle 50km on a cycle trail. Lara cycles at an average speed of x km/h. Marco cycles at an average speed of (x-3) km/h.
- (a)Write down an expression for the time, in hours, Lara takes to complete the trail.[1]
- (b)Marco takes 15 minutes longer than Lara to complete the trail. Hence form an equation and show that it simplifies to x² - 3x - 600 = 0.[4]
- (c)Solve the equation x² - 3x - 600 = 0. Show your working and give your answers correct to 2 decimal places.[3]
- (d)Find the time Marco takes to complete the trail. Give your answer in hours and minutes, correct to the nearest minute.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] (a) 50/x or 50x⁻¹ final answer
- [4] (b) M2 for (50/(x-3)) - (50/x) = 15/60 oe B1 for 50/(x-3) soi M1 DEP on previous M2 FT elimination of fractions or use of common denominator A1 A0 if any errors or omissions
- [3] (c) 26.04 and -23.04; B2 for -(-3)±√((-3)²-4×1×-600)/(2×1) oe or B1 for ((-3)²-4×1×-600) oe or for -(-3)±√their2409/(2×1) oe or for (x-3/2)² - (3/2)² - 600 = 0
- [2] (d) 2 [hours] 10 [minutes] cao; M1 for substitution of their positive root into 50/(x-3) or 50/x + 0.25 oe or B1 for final answer 1 [hour] 55 [minutes]
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