O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2022 · Q511 Marks

A bag contains x five-cent coins and y ten-cent coins.

(a)(i)There is a total of 130 coins in the bag. Write down an equation, in terms of x and y, for the total number of coins in the bag.[1]
(a)(ii)The total value of the coins in the bag is $8.15 . Write down an equation, in terms of x and y, for the total value of the coins in the bag.[1]
(a)(iii)Solve the two simultaneous equations to find the number of each type of coin in the bag. Show your working.[3]
(b)A machine makes five-cent coins. It makes 720 coins per minute. The machine operates for 24 hours per day. Calculate the total value, in dollars, of the coins made by the machine in 300 days. Give your answer in standard form, correct to 3 significant figures.[3]
(c)The diameter of a five-cent coin is 21.2 mm, correct to the nearest 0.1 mm. The diameter of a ten-cent coin is 17.9 mm, correct to the nearest 0.1 mm. Marlon makes a line of 10 five-cent coins and a line of 10 ten-cent coins. Calculate the upper bound of the difference between the lengths of the two lines.[3]

Mark scheme

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

[1]
[1]
[3] M1 FT their equations provided both equations cannot be written in the form 5x + 10y = k or both equations cannot be written in the form x + y = k A2 A1 for either x = 97 or y = 33 nfww After A0 scored, SC1 for final answer two positive integers satisfying either x + y = 130 or 5x + 10y = 815
[3] B2 for 15 600 000 oe or 15 550 000 oe or 15 552 000 oe or answer (cao) 1.56 × 10⁸ or 1.55 × 10⁷ or 3.11 × 10⁸ or 3.11 × 10⁸ or 2.59 × 10⁵ or 5.18 × 10⁴ (nfww) or M1 for 720 × 24 × 60 × 300 × 0.05
[3] B1 for 21.25 and 17.85 seen M1 for [-](their 21.25 × 10 – their 17.85 × 10) oe

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