Name: Date:

**Question 1:**An alloy has a mass of 70kg and a density of 4,740kg/m

^{3}. The density is correct to the nearest 10kg. The mass is correct to the nearest 5kg. Calculate the upper and lower bounds of the volume of the alloy. Give your answers to 3 decimal places.

**Question 2:**The formula to calculate voltage, V, (measured in volts) is V = IR where I is the current (in amps) and R is the resistance (in ohms).

I = 432 amps and R=40.4 ohms, both measurements are correct to 3 significant figures. By considering bounds calculate the voltage, V, to a suitable degree of accuracy. Give a reason for your answer.

**Question 3:**A tourist travels 39.3km at a speed of 1.90km/h. The distance is correct to 1 decimal place. The speed is correct to 2 decimal places. Calculate the upper and lower bounds of the time taken. Give your answers to 3 decimal places.

**Question 4:**A water tank holds 70 litres of water rounded to the nearest 5 litres. An empty cup holds 520 millilitres of water rounded to the nearest 10ml. Calculate the maximum and minimum number of cups of water that can be completely filled from the water tank.

**Question 5:**The formula to calculate pressure, P, (in Newtons/metre

^{2}) is P =

A

F

where F is the force in Newtons and A is the area in metres^{2}.

F = 97.9 Newtons correct to 1 decimal place and A=28.94m

^{2}correct to 2 decimal places. By considering bounds calculate the pressure, P, to a suitable degree of accuracy. Give a reason for your answer.

**Question 6:**The length of a rectangle is 3.1cm correct to 1 decimal place. The width of the rectangle is 6.38cm correct to 2 decimal places. Calculate the upper and lower bounds of the perimeter of the rectangle. Give your answers to 3 decimal places.

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# Answers

**Question 1:**Upper bound = 0.015m

^{3}, lower bound = 0.014m

^{3}

**Question 2:**Upper bound = 17,494.625 volts, lower bound = 17,411.025 volts V=17,000 volts correct to 2 s.f. because the upper and lower bounds are equal when rounded to this accuracy

**Question 3:**Upper bound = 20.765km/h, lower bound = 20.604km/h

**Question 4:**Upper bound = 140 cups, lower bound = 128 cups

**Question 5:**Upper bound = 3.38517N/m

^{2}, lower bound = 3.38055N/m

^{2}P=3.4N/m

^{2}correct to 2 s.f. because the upper and lower bounds are equal when rounded to this accuracy

**Question 6:**Upper bound = 19.070cm, lower bound = 18.850cm

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