QUESTIONS:

• 1 Expand and simplify the following expression
• a) (5   − 2) − 5   

           b) 2 (3   + 4) + 3  (1 − 3  ) − 6   + 1      

2.  Solve the following equations:

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

           a) 7 − 8 = −120       

           b) 5(3 − 2 ) = 4   − 1      

           C) 2(2+4)=-(3+6)

3.  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    he nearest tonne.

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

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

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

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

          b) 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=…)

• 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.

• Combine your equations and solve to find the length of the River Tamar.

5. 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!

b) A café owner blends two brands of coffee together to save money. Brand A coffee costs $7 per kilogram, and brand B costs $11 per kilogram. The total weight of the blended coffee is 15 kilograms and the total cost is $129. How many kilograms of each brand did the owner use?

7. a) Consider the equation:      1=₁₀  −5

• What is the gradient of the line described by this equation? Sketch the direction of the slope of this line.

• What are the coordinates of the y-intercept of this line?

1. c) Find the gradient of the line that passes through the points (-7, 8) and (-3, 18)

1. Expand and simplify the following expressions
2. a) (5   − 2) − 5           

1. b) 2 (3   + 4) + 3  (1 − 3  ) − 6   + 1      

 Solve the following equations:

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

1. a) 7 − 8 = −120        

1. b) 5(3 − 2 ) = 4   − 1         

3. 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.       

 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.

4. a) A mobile phone plan costs $50 per month plus 7 cents per text message.  (2 marks)

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

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

• 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.

• Combine your equations and solve to find the length of the River Tamar.

5. 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!

6 following equations simultaneously:

b) A café owner blends two brands of coffee together to save money. Brand A coffee costs $7 per kilogram, and brand B costs $11 per kilogram. The total weight of the blended coffee is 15 kilograms and the total cost is $129. How many kilograms of each brand did the owner use?

7. a) Consider the equation1=₁₀  −5

• What is the gradient of the line described by this equation? Sketch the direction of the slope of this line.

• What are the coordinates of the y-intercept of this line?

 c) Find the gradient of the line that passes through the points (-7, 8) and (-3, 18) (3 marks)