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**Question 1:**A crate is in the shape of a cuboid. It has a square base 2,860 millimetres wide, rounded to the nearest 10mm. The crate has a height of 1315 millimetres rounded to the nearest 5mm. Calculate the upper and lower bounds of the volume of the crate, in cubic metres. Give your answers to 3 decimal places.

**Question 2:**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 = 20.7 Newtons correct to 1 decimal place and A=98.99m

^{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 3:**A tourist travels 5,800km at a speed of 4.5km/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.

**Question 4:**The length and width of a rectangle are 990cm and 9.3cm 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 5:**An alloy has a mass of 11.5g and a density of 3.34g/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 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 = 38.9 amps correct to 1 decimal place and V=40.34 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 = 10.814m

^{3}, lower bound = 10.698m

^{3}

**Question 2:**Upper bound = 0.20963N/m

^{2}, lower bound = 0.20860N/m

^{2}P=0.21N/m

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

**Question 3:**Upper bound = 1,314.607hrs, lower bound = 1,263.736hrs

**Question 4:**Upper bound = 2,008.700cm, lower bound = 1,988.500cm

**Question 5:**Upper bound = 3.463cm

^{3}, lower bound = 3.423cm

^{3}

**Question 6:**Upper bound = 1.03848 ohms, lower bound = 1.03556 ohms R=1.04 ohms correct to 3 s.f. because the upper and lower bounds are equal when rounded to this accuracy

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