b) 2 (3 + 4) + 3 (1 − 3 ) − 6 + 1
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)
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?
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=…)
6.a)Solve the following equations simultaneously: 








2 + =7 

3 + 2 = 10 


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?
b) Find the yintercept of the line that runs perpendicular to the line in parta) 

and passes through the point (1,7) 

d) 
1 


Find the equation of the line that passes through the points ( 
2 
, −8) and 


(−5,14) 



Solve the following equations:
Answers should be given as integers or simplified fractions (do NOT use decimals).
c) 
2(2 + 4) = − 
(3 + 6) 




4 









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.
6 following equations simultaneously:








2 + =7 

3 + 2 = 10 


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?
b) Find the yintercept of the line that runs perpendicular to the line in part a) 

and passes through the point (1,7) 

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




Find the equation of the line that passes through the points ( 
2 
, −8) and 


(−5,14) 



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