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**Question 1:**An alloy has a mass of 17.2g and a density of 5.74g/cm

^{3}. The mass is correct to 1 decimal place. The density is correct to 2 decimal places. Calculate the upper and lower bounds of the volume of the alloy. Give your answers to 3 decimal places.

**Question 2:**A tourist travels 6,500km in 1.1hours. Both measurements are correct to 2 significant figures. Calculate the upper and lower bounds of the average speed travelled. 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 = 19.0 Newtons correct to 1 decimal place and A=83.03m

^{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:**A water tank holds 65 litres of water rounded to the nearest 5 litres. An empty cup holds 380 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 length and width of a rectangle are 130cm and 4.0cm respectively. Both measurements are correct to 2 significant figures. Calculate the upper and lower bounds of the perimeter of the rectangle. 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 = 58.7 amps correct to 1 decimal place and V=26.04 volts correct to 2 decimal places. By considering bounds calculate the resistance, R, to a suitable degree of accuracy. Give a reason for your answer.

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# Answers

**Question 1:**Upper bound = 3.008cm

^{3}, lower bound = 2.985cm

^{3}

**Question 2:**Upper bound = 6,238.095km/h, lower bound = 5,608.696km/h

**Question 3:**Upper bound = 0.22945N/m

^{2}, lower bound = 0.22822N/m

^{2}P=0.23N/m

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

**Question 4:**Upper bound = 180 cups, lower bound = 162 cups

**Question 5:**Upper bound = 278.100cm, lower bound = 257.900cm

**Question 6:**Upper bound = 0.44408 ohms, lower bound = 0.44315 ohms R=0.44 ohms correct to 2 s.f. because the upper and lower bounds are equal when rounded to this accuracy

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