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**Question 1:**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 = 251 Newtons and A=97.1m

^{2}, both measurements are correct to 3 significant figures. By considering bounds calculate the pressure, P, to a suitable degree of accuracy. Give a reason for your answer.

**Question 2:**The length and width of a rectangle are 140cm and 9.8cm respectively. Both measurements are correct to 2 significant figures. Calculate the upper and lower bounds of the area of the rectangle. Give your answers to 3 decimal places.

**Question 3:**A water tank holds 34.2 litres of water correct to 3 significant figures. An empty cup can hold 56 centilitres of water correct to 2 significant figures. Calculate the maximum and minimum number of cups of water that can be completely filled from the water tank.

**Question 4:**An alloy has a mass of 10kg and a density of 7,950kg/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 5:**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 = 72.3 amps correct to 1 decimal place and R=95.87 ohms correct to 2 decimal places. By considering bounds calculate the voltage, V, to a suitable degree of accuracy. Give a reason for your answer.

**Question 6:**A tourist travels 4,100km at a speed of 1.5km/h. Both measurements are correct to 2 significant figures. Calculate the upper and lower bounds of the time taken. Give your answers to 3 decimal places.

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# Answers

**Question 1:**Upper bound = 2.59145N/m

^{2}, lower bound = 2.57849N/m

^{2}P=2.6N/m

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

**Question 2:**Upper bound = 1,428.250cm, lower bound = 1,316.250cm

**Question 3:**Upper bound = 61 cups, lower bound = 60 cups

**Question 4:**Upper bound = 0.002m

^{3}, lower bound = 0.001m

^{3}

**Question 5:**Upper bound = 6,936.55625 volts, lower bound = 6,926.24625 volts V=6,900 volts correct to 2 s.f. because the upper and lower bounds are equal when rounded to this accuracy

**Question 6:**Upper bound = 2,862.069hrs, lower bound = 2,612.903hrs

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