1. 1
   A number club records these ten numbers: -8, 0, 1, 4, 8, 9, 13, 16, 27, 30.

   (a)

   Which of these numbers is a square number?

   [1 mark]

   • A8
   • B9
   • C13
   • D30

   (b)

   Which of these numbers is a prime number?

   [1 mark]

   • A8
   • B9
   • C13
   • D30

   (c)

   Which of these numbers is a cube number greater than 1?

   [1 mark]

   • A8
   • B9
   • C13
   • D30

   Total for question 1: 3 marks

2. 2
   The temperature in a town was recorded at three points during one winter day. At 6 am the temperature was -7 degrees C. By midday it had risen by 12 degrees C from the 6 am value. By 10 pm it had fallen by 9 degrees C from its midday value.

   (a)

   Work out the temperature at midday.

   [2 marks]

   (b)

   Work out the temperature at 10 pm, and state whether this is higher or lower than the temperature at 6 am.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A jeweller uses square and cube numbers to design pendant sizes. The area of a square pendant face is 121 mm^2. The volume of a cube-shaped charm is 125 mm^3.

   (a)

   Find the side length of the square pendant face, and hence write down its reciprocal as a decimal correct to 3 decimal places.

   [3 marks]

   (b)

   Find the side length of the cube-shaped charm, then calculate the sum of this side length and the side length found in part (a).

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A cafe orders ingredients in mixed numbers and calculates costs using the order of operations. Flour costs 2 dollars per whole bag; a delivery contains $3\frac{1}{2}$ bags of flour that arrived, plus $2\frac{3}{4}$ bags returned as damaged. A separate charge is calculated using brackets: the cafe must pay $3 \times (8-5) + 4^2$ dollars for a bulk discount fee, which is then subtracted from the total flour cost.

   (a)

   Work out the total number of bags of flour remaining after the damaged bags are returned (subtract the mixed numbers), and give your answer as a decimal.

   [4 marks]

   (b)

   Work out the value of the bulk discount fee expression $3 \times (8-5) + 4^2$, applying the correct order of operations.

   [4 marks]

   (c)

   Given the flour costs 2 dollars per bag, calculate the total cost of the remaining flour (from part (a)), then subtract the bulk discount fee (from part (b)) to find the final amount the cafe pays. State whether the final amount is positive or negative.

   [5 marks]

   Total for question 4: 13 marks

End of questions