Transcript
Page 1: Algebra Merit. Simplify Simplify by factorising

Algebra

Merit

Page 2: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 3: Algebra Merit. Simplify Simplify by factorising

Simplify by factorising

Page 4: Algebra Merit. Simplify Simplify by factorising

Simplify by taking out the common factor (2x) out of everything

Page 5: Algebra Merit. Simplify Simplify by factorising

Make W the subject

Page 6: Algebra Merit. Simplify Simplify by factorising

Make W the subject

Page 7: Algebra Merit. Simplify Simplify by factorising

Solve for x and y

Page 8: Algebra Merit. Simplify Simplify by factorising

Solve for x and y

Page 9: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 10: Algebra Merit. Simplify Simplify by factorising

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.

Page 11: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 12: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 13: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 14: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 15: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 16: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 17: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 18: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 19: Algebra Merit. Simplify Simplify by factorising

One of the solutions of 4x2 + 8x + 3 = 0 is x = -1.5

• Use this solution to find the second solution of the equation.

Page 20: Algebra Merit. Simplify Simplify by factorising

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

Page 21: Algebra Merit. Simplify Simplify by factorising

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’

Page 22: Algebra Merit. Simplify Simplify by factorising

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’

Page 23: Algebra Merit. Simplify Simplify by factorising

The volume of the box shown is 60 litres. Find the dimensions of the box.

Page 24: Algebra Merit. Simplify Simplify by factorising

60 litres = 60, 000 cm3

Page 25: Algebra Merit. Simplify Simplify by factorising

60 litres = 60, 000 cm3

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Dimensions are 50cm:30cm:40cm

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• 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.

Page 28: Algebra Merit. Simplify Simplify by factorising

• 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.

Page 29: Algebra Merit. Simplify Simplify by factorising

Simplify

Page 30: Algebra Merit. Simplify Simplify by factorising

Factorise

Page 31: Algebra Merit. Simplify Simplify by factorising

Express as a single fraction

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Express as a single fraction

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Solve the equation

Page 34: Algebra Merit. Simplify Simplify by factorising

Solve the equation

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Simplify

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Simplify

Page 37: Algebra Merit. Simplify Simplify by factorising

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.

Page 38: Algebra Merit. Simplify Simplify by factorising

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.

Page 39: Algebra Merit. Simplify Simplify by factorising

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.

Page 40: Algebra Merit. Simplify Simplify by factorising

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.

Page 41: Algebra Merit. Simplify Simplify by factorising

Graeme is designing a path around the front of his garden. His design is shown below.

The width of the path is x metres.

Page 42: Algebra Merit. Simplify Simplify by factorising

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.

Page 43: Algebra Merit. Simplify Simplify by factorising

Graeme has sufficient paving to make a path with a total area of 22 m2.

The width of the path is x metres.


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