# Algebra CAT 2012. Solve Factorise Solve Simplify.

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Algebra CAT 2012

Solve

Factorise

Solve

Simplify

Show that x = 12 is the only real solution to

Where a is a positive number. The difference between the solutions to the equation is 10. Find the value of a.

A square room and a hallway are to have carpet laid on the floor. 123m 2 of carpet is required to cover both the hallway and the room. The width of the hallway is 6m less than the length of the room. The hallway is 5m longer the the length of the room. Write an equation showing this relationship and solve this equation to find the length of the room.

A square room and a hallway are to have carpet laid on the floor. 123m 2 of carpet is required to cover both the hallway and the room. The width of the hallway is 6m less than the length of the room. The hallway is 5m longer the the length of the room. Write an equation showing this relationship and solve this equation to find the length of the room. x X + 5 X-6 x

Question 2

Simplify fully

Factorise fully the following expression and write in its simplest form

Expand and simplify

Simplify

Solve

The formula for the volume of a cylinder is Where r is the radius and h is the height of the cylinder. Write the formula for the radius, r, of the cylinder in terms of V, h and π

The formula for the volume of a cylinder is Where r is the radius and h is the height of the cylinder. Write the formula for the radius, r, of the cylinder in terms of V, h and π

The length of a straight straw that will just fit in a cylindrical can with a height of 8 cm is given by: Where r is the radius of the can. A straight straw that is 3 times as long (3L) just fits in a larger can that has the same height. Write an expression for the radius of the larger can R in terms of r.

The length of a straight straw that will just fit in a cylindrical can with a height of 8 cm is given by: Where r is the radius of the can. A straight straw that is 3 times as long (3L) just fits in a larger can that has the same height. Write an expression for the radius of the larger can R in terms of r.

Question 3 Simplify fully

Question 3 Simplify fully

Solve

Sarah borrows her friend’s car for a holiday. She agrees to pay \$7 a day and \$1 per kilometre that she travels. Write an equation for the amount P Sarah agrees to pay.

Sarah borrows her friend’s car for a holiday. She agrees to pay \$7 a day and \$1 per kilometre that she travels. Write an equation for the amount P Sarah agrees to pay.

Sarah travelled 185 km and should pay her friend \$213. Use your equation to find the number of days Sarah borrowed the car for.

Sarah travelled 185 km and should pay her friend \$213. Use your equation to find the number of days Sarah borrowed the car for.

Emma is 3 times as old as Tara. In another 7 years Emma will be twice as old as Tara will be. Write at least one equation and use algebra to fine Emma’s age now.

Emma is 3 times as old as Tara. In another 7 years Emma will be twice as old as Tara will be. Write at least one equation and use algebra to fine Emma’s age now.

Emma is 3 times as old as Tara. In another 7 years Emma will be twice as old as Tara will be. Write at least one equation and use algebra to fine Emma’s age now.

If Express x in terms of y

If Express x in terms of y