- Expand and simplify the following expressions
- a) ????(5???? − 2) − 5???????? (2 marks)
- b) 2????(3???? + 4) + 3????(1 − 3????) − 6???? + 1 (3 marks)
- Solve the following equations:

Answers should be given as integers or simplified fractions (do NOT use decimals).

- a) 7???? − 8 = −120 (2 marks)
- b) 5(3 − 2????) = 4???? − 1 (3 marks)Page 3 of 9
- c)

2(2???? + 4) = −

(3???? + 6)

4

- A rigger is a person who specialises in lifting and moving large or heavy objects. The equipment available to riggers on construction sites is often limited, so they rely on equations to help them figure out how to safely lift and move objects. The rigging equation for calculating the mass of a hollow steel pipe is given below:

???? = 24????????(???? − ????)

Where ???? is the mass of the pipe in tonnes (t), ???? is the length, ???? is the outside diameter, and ???? is the wall thickness of the pipe, all measured in metres (m).

- a) What is the mass of a 6 m pipe with an outside diameter of 0.3 m and a wall thickness of 5 cm? Give your answer to the nearest tonne.

- b) Transpose the equation to make ???? the subject. (2 marks)
- c) A steel pipe needs to be moved into place on a construction site using a crane. The rigger has a sling available that is approved for use on pipes that have an outside diameter less than 1 m. If the steel pipe to be moved is 8 m long, has a wall thickness of 0.04 m, and has a mass of 7.5 t, can the rigger safely move the pipe?

Use mathematics to explain how you determined your answer.

- a) A mobile phone plan costs $50 per month plus 7 cents per text message.

(i) Complete the equation below to represent the total monthly cost, C, of this mobile plan. Define any other variables that you use.

???? =

(ii) Use your equation to find how many text messages were sent in the last month if the bill came to $67.50.

- b) (i) The River Leven, L, is 26 km longer than the River Tamar, T.

Write an equation to show the length of L in terms of T (e.g. L=…)

(ii) The River Derwent is 249 km long, and if you double this length you

have triple the length of the River Tamar and River Leven combined.

Convert this sentence into an algebraic equation using the same

variables as above.

(iii) Combine your equations and solve to find the length of the River Tamar.

To stimulate his daughter in the pursuit of problem solving, a maths teacher offered to pay her $10 for every question she solved correctly, and to fine her $7 for every incorrect solution. After she had completed 32 problems the maths teacher was starting to regret his decision, he now owed his daughter $133! Use algebraic techniques to find out how many problems the daughter solved correctly.

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