Algebra Merit

Simplify

Simplify by factorising

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

Make W the subject

Solve for x and y

A square warehouse is extended by 10 metres at one end. The area of the extended warehouse is 375m 2 Find the original area of the warehouse.

Area = 15 2 =225 m 2 A square warehouse is extended by 10 metres at one end. The area of the extended warehouse is 375m 2 Find the original area of the warehouse.

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 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

One of the solutions of 4x 2 + 8x + 3 = 0 is x = -1.5 Use this solution to find the second solution of the equation.

One of the solutions of 4x 2 + 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 4x 2 + 8x + 3 = 0 is x = -1.5 Use this solution to find the second solution of the equation. We need 2x to make 4x 2 We need +1 to make ‘3’

One of the solutions of 4x 2 + 8x + 3 = 0 is x = -1.5 Use this solution to find the second solution of the equation. We need 2x to make 4x 2 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 cm 3

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.

Simplify

Factorise

Express as a single fraction

Solve the equation

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 m 2. The area of the path can be written as 4x+3x 2 +(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 m 2. The width of the path is x metres.