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**Question 1:**An alloy has a mass of 850g and a volume of 95cm

^{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:**A tourist travels 230km at a speed of 75km/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 3:**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 = 56.2 Newtons correct to 1 decimal place and A=98.93m

^{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 4:**The length of a rectangle is 897cm correct to the nearest cm. The width of the rectangle is 10cm correct to the nearest 5cm. Calculate the upper and lower bounds of the area of the rectangle. 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 = 74.5 amps correct to 1 decimal place and R=50.36 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 water tank holds 84.7 litres of water correct to 3 significant figures. An empty cup can hold 45 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.

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# Answers

**Question 1:**Upper bound = 9.243g/cm

^{3}, lower bound = 8.667g/cm

^{3}

**Question 2:**Upper bound = 3.241hrs, lower bound = 2.903hrs

**Question 3:**Upper bound = 0.56861N/m

^{2}, lower bound = 0.56754N/m

^{2}P=0.57N/m

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

**Question 4:**Upper bound = 11,218.750cm, lower bound = 6,723.750cm

**Question 5:**Upper bound = 3,754.71075 volts, lower bound = 3,748.92975 volts V=3,750 volts correct to 3 s.f. because the upper and lower bounds are equal when rounded to this accuracy

**Question 6:**Upper bound = 190 cups, lower bound = 186 cups

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