Question
Dhanu has a model railway.
(a) He has a train that consists of a locomotive and 4 coaches.
The mass of the locomotive is 87g and the mass of each coach is 52g.
(i) Work out the total mass of the train.
………………………………………. g
(ii) Work out the mass of the locomotive as a percentage of the total mass of the train.
……………………………………… %
(b) The train is 61cm long and travels at a speed of 18cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.
Calculate the length of the bridge.
……………………………………. cm
(c) A new locomotive costs \($64.\)
Calculate the cost of the locomotive in rupees when the exchange rate is 1 rupee = \($0.0154 .\)
Give your answer correct to the nearest 10 rupees.
……………………………….. rupees
(d) The cost of a railway magazine increases by 12.5% to \($2.70 .\)
Calculate the cost of the magazine before this increase.
\($ ………………………………………….\)
(e) Dhanu plays with his model railway from 0650 to 11 15.
He then rides his bicycle for 3 hours.
Find the ratio time playing with model railway : time riding bicycle.
Give your answer in its simplest form.
……………………. : …………………….
(f) The value of Dhanu’s model railway is \($550.\)
This value increases exponentially at a rate of r% per year.
At the end of 5 years the value will be \($736.\)
Calculate the value of r.
r = ………………………………………….
Answer/Explanation
(a)(i) 295
(a)(ii) 29.5 or 29.49…
(b) 11
(c) 4160
(d) 2.4[0]
(e) 53 : 36
(f) 6[.00] or 5.999…
Question
Darpan runs a distance of 12km and then cycles a distance of 26km. His running speed is x km/h and his cycling speed is 10km/h faster than his running speed. He takes a total time of 2 hours 48 minutes.
(a) An expression for the time, in hours, Darpan takes to run the 12km is\( \frac{12}{x}\) Write an equation, in terms of x, for the total time he takes in hours.
(b) Show that this equation simplifies to \(7x^{2}-25x-300=0\)
(c) Use the quadratic formula to solve \(7x^{2}-25x-300=0\) You must show all your working.
(d) Calculate the number of minutes Darpan takes to run the 12 km.
Answer/Explanation
(a) \(\frac{12}{x}+\frac{26}{x+10}=2.8\) oe isw
(b)\(12(x+10)+26x=2.8(x+10)\)or better
\(12x+120+26x=2.8x^{2}+28x\)
Question
A company employed 300 workers when it started and now employs 852 workers.
(a) Calculate the percentage increase in the number of workers.
(b) Of the 852 workers, the ratio part-time workers : full-time workers = 5:7.
Calculate the number of full-time workers.
(c) The company makes 40600 headphones in one year.
Write this number
(i) in words,
(ii) in standard form.
(d) In one month, the company sells 3000 headphones.
Of these, 48% are exported, \(\frac{3}{8}\)are sold to shops and the rest are sold online.
Calculate the number of headphones that are sold online.
(e) One year, sales increased by 15%. The following year sales increased by 18%.
Calculate the overall percentage increase in sales.
Answer/Explanation
1(a) 184
1(b) 497 2
1(c)(i) Forty thousand six hundred
1(c)(ii) \(4.06\times 10^{4}\)
1(d) 435
1(e) 35.7