Stage 8 - Q1 - 2 marks
A rectangle has sides \(x+9\) and 6. Find its perimeter.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q2 - 2 marks
A rectangle has sides \(x+7\) and 8. Find its perimeter.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q3 - 3 marks
A rectangle has sides \(x+5\) and 9. Find its area.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q4 - 3 marks
A rectangle has sides \(x+3\) and 11. Find its area.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q5 - 4 marks
A club charges 1 dollars per visit and a membership fee of 12 dollars. Write a cost expression for n visits, then calculate the cost of 7 visits.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q6 - 4 marks
A club charges 12 dollars per visit and a membership fee of 3 dollars. Write a cost expression for n visits, then calculate the cost of 7 visits.
Hint
Define the variable and identify whether quantities are added or multiplied.
Stage 8 - Q7 - 5 marks
A club sells adult tickets for a dollars and child tickets for c dollars. A family buys 3 adult and 4 child tickets, then receives a discount of d dollars on the total. Write an expression and explain why the discount is subtracted once.
Hint
Which quantities depend on the number of tickets?
Stage 8 - Q8 - 5 marks
A rectangle has perimeter \(6x+10\) cm and one side \(x+1\) cm. Find an expression for the adjacent side.
Hint
Halve the perimeter before subtracting a side.
Stage 8 - Q9 - 5 marks
One square has side \(x+2\) and another has side x. Find the difference in their areas without expanding a double bracket. Explain using strips.
Hint
Divide the added region into two rectangles and a small square.
Stage 8 - Q10 - 5 marks
A rectangular garden is twice as long as it is wide. A 1 m path lies inside all four edges. Let the outer width be x metres. Find the path area as a simplified expression and state the allowed values of x.
Hint
Subtract the inner rectangle from the outer rectangle. A path removes width from both ends.