1.1 Number & Algebra Toolkit

Let , where   and 

Find the value of W. Give your answer as a fraction.

Give your answer from part (a) to

A prism has a cross sectional area of and volume of .

Calculate the length of the prism.

The cross-sectional area of the prism is in the shape of a trapezium and its parallel sides measure 2 m and 2.4 m.

Calculate the height of the trapezium. Give your answer in cm.

Mary has found the exact answer for  is  .

Write down the exact answer of as a decimal.

Give your answer from part (a) correct to

It is given that  and , where  and  .

Find the size of the angles  and .

A circle has radius  equal to

Find the exact value of the area of the circle, giving your answer in terms of .

A medium rare steak should have an internal temperature of  to . Max decides to go to 10 different steak houses, he measures the internal temperature of a medium rare steak at each establishment and records the following:

51.0,   52.1,  62.9,  49.0,  59.8,  50.2,  54.3,  47.7,  48.6,   65.4

Find the mean internal temperature of Max’s recordings.

Max goes to 5 more steak houses and calculates the mean of all 15 restaurants to be 

Calculate the mean internal temperature from the 5 additional steak houses Max went to.

Max records one last steak that has an internal temperature of

Calculate the interval of  such that the mean internal temperature for all 16 steaks is within the temperature range for a medium rare steak.

The diameter of Earth is  m, correct to four significant figures.  The circumference of Mars is  m, correct to four significant figures. 

Modelling Earth and Mars as perfect spheres, find the difference between the volume of Earth and the volume of Mars, giving your answer in the form , where .

Solve the following systems of linear equations using technology.

Write    as a sum of partial fractions.