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**Question 1:**An alloy has a mass of 870g and a volume of 90cm

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

**Question 2:**The length and width of a rectangle are 550cm and 8.0cm 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 72.8 litres of water correct to 3 significant figures. An empty cup can hold 33 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:**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 = 501 Newtons and A=76.1m

^{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 5:**A tourist travels 890km at a speed of 95km/h. The distance is correct to the nearest 10km. The speed is correct to the nearest 5km/h. Calculate the upper and lower bounds of the time taken. Give your answers to 3 decimal places.

**Question 6:**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 = 475 amps and R=46.2 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.

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# Answers

**Question 1:**Upper bound = 10.000g/cm

^{3}, lower bound = 9.351g/cm

^{3}

**Question 2:**Upper bound = 4,467.750cm, lower bound = 4,332.750cm

**Question 3:**Upper bound = 224 cups, lower bound = 217 cups

**Question 4:**Upper bound = 6.59435N/m

^{2}, lower bound = 6.57255N/m

^{2}P=6.6N/m

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

**Question 5:**Upper bound = 9.676hrs, lower bound = 9.077hrs

**Question 6:**Upper bound = 21,991.875 volts, lower bound = 21,898.175 volts V=22,000 volts correct to 2 s.f. because the upper and lower bounds are equal when rounded to this accuracy

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