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Algebra CAT. 2012. Solve. Solve. Factorise. Factorise. Solve. Solve. Simplify. Simplify. Show that x = 12 is the only real solution to. 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.
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Algebra CAT 2012
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. • 123m2 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. • 123m2 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 + 5 x X-6 x
Factorise fully the following expression and write in its simplest form
Factorise fully the following expression and write in its simplest form
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
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 xin terms of y