Algebra Merit. Simplify Simplify by factorising.
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Transcript of Algebra Merit. Simplify Simplify by factorising.
Algebra
Merit
Simplify
Simplify by factorising
Simplify by taking out the common factor (2x) out of everything
Make W the subject
Make W the subject
Solve for x and y
Solve for x and y
• A square warehouse is extended by 10 metres at one end. The area of the extended warehouse is 375m2 Find the original area of the warehouse.
Area = 152 =225 m2
• A square warehouse is extended by 10 metres at one end. The area of the extended warehouse is 375m2 Find the original area of the warehouse.
Simplify
Simplify
• Elton has more than twice as many CDs as Robbie. Altogether they have 56 CDs. Write a relevant equation and use it find the least number of CDs that Elton could have.
• Elton has more than twice as many CDs as Robbie. Altogether they have 56 CDs. Write a relevant equation and use it find the least number of CDs that Elton could have.
• Elton purchases some DVDs from the mall. He buys four times as many music DVDs as movie DVDs. The music DVDs are $2.50 each. The movie DVDs are $1.50 each. Altogether he spends $92.Solve the equations to find out how many music DVDs that he purchased.
• Elton purchases some DVDs from the mall. He buys four times as many music DVDs as movie DVDs. The music DVDs are $2.50 each. The movie DVDs are $1.50 each. Altogether he spends $92.Solve the equations to find out how many music DVDs that he purchased.
Simplify
Simplify
One of the solutions of 4x2 + 8x + 3 = 0 is x = -1.5
• Use this solution to find the second solution of the equation.
One of the solutions of 4x2 + 8x + 3 = 0 is x = -1.5
• Use this solution to find the second solution of the equation.
• Must be one of the brackets
One of the solutions of 4x2 + 8x + 3 = 0 is x = -1.5
• Use this solution to find the second solution of the equation.
• We need 2x to make 4x2
• We need +1 to make ‘3’
One of the solutions of 4x2 + 8x + 3 = 0 is x = -1.5
• Use this solution to find the second solution of the equation.
• We need 2x to make 4x2
• We need +1 to make ‘3’
The volume of the box shown is 60 litres. Find the dimensions of the box.
60 litres = 60, 000 cm3
60 litres = 60, 000 cm3
Dimensions are 50cm:30cm:40cm
• The triangle drawn below is equilateral. The perimeter is 30 cm. Write down two equations and solve them simultaneously to find the values of x and y.
• The triangle drawn below is equilateral. The perimeter is 30 cm. Write down two equations and solve them simultaneously to find the values of x and y.
Simplify
Factorise
Express as a single fraction
Express as a single fraction
Solve the equation
Solve the equation
Simplify
Simplify
There are V litres in Claudia’s water tank. There are d “drippers” on the irrigation hose from the tank to the garden. Each dripper
uses x litres of water per day.
• Write an expression to show the total amount of water, T, left in the tank after one day.
There are V litres in Claudia’s water tank. There are d “drippers” on the irrigation hose from the tank to the garden. Each dripper
uses x litres of water per day.
• Write an expression to show the total amount of water, T, left in the tank after one day.
There are V litres in Claudia’s water tank. There are d “drippers” on the irrigation hose from the tank to the garden. Each dripper
uses x litres of water per day.
• At the end of the day on the 1st of April there were 150 litres of water in the tank. The next day, 4 drippers were used to irrigate the garden and at the end of the day there were 60 litres of water left.
• Use the expression you gave above to show how much water each dripper used on that day.
There are V litres in Claudia’s water tank. There are d “drippers” on the irrigation hose from the tank to the garden. Each dripper
uses x litres of water per day.
• At the end of the day on the 1st of April there were 150 litres of water in the tank. The next day, 4 drippers were used to irrigate the garden and at the end of the day there were 60 litres of water left.
• Use the expression you gave above to show how much water each dripper used on that day.
Graeme is designing a path around the front of his garden. His design is shown below.
The width of the path is x metres.
Graeme has sufficient paving to make a path with a total area of 22 m2.
• The area of the path can be written as
• 4x+3x2 +(5-2x)x=22. • Rewrite the equation
and then solve to find the width of the path around the front of the garden.
The width of the path is x metres.
Graeme has sufficient paving to make a path with a total area of 22 m2.
The width of the path is x metres.