1. 1
   A factory records daily production numbers and needs to round and estimate values for a summary report.

   (a)

   Round 4,872 to the nearest hundred.

   [1 mark]

   • A$4900$
   • B$4800$
   • C$4870$
   • D$5000$

   (b)

   Round $6.2384$ to 2 significant figures.

   [1 mark]

   • A$6.3$
   • B$6.24$
   • C$6.2$
   • D$6.238$

   (c)

   Estimate the value of $\frac{198 \times 5.1}{9.8}$ by rounding each number to 1 significant figure.

   [1 mark]

   • A$20$
   • B$200$
   • C$1000$
   • D$100$

   Total for question 1: 3 marks

2. 2
   A carpenter measures the side lengths of a rectangular table top, each given to the nearest centimetre, and needs to find bounds for calculated quantities such as perimeter.

   (a)

   A length is measured as $12$ cm, correct to the nearest centimetre. Write down the upper and lower bounds of this length.

   [2 marks]

   (b)

   The table top has a width measured as $8$ cm, correct to the nearest centimetre. Using your bounds for the length (part (a)) and appropriate bounds for the width, calculate the upper bound for the perimeter of the table top.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A land surveyor is measuring a rectangular field and needs upper and lower bounds for calculated areas, then estimating the true value using rounding to check for errors.

   (a)

   A rectangular field has a length of $85$ m and a width of $42$ m, both measured to the nearest metre. Calculate the upper and lower bounds for the area of the field.

   [3 marks]

   (b)

   The length of the field is 85 m and the width is 42 m, each measured to the nearest metre, so the area lies between the bounds $3506.75\ \text{m}^2$ and $3633.75\ \text{m}^2$. Using estimation (rounding the length and width each to 1 significant figure before multiplying), estimate the area of the field, and comment on whether your estimate lies between these bounds.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A sports scientist is calculating a cyclist's average speed from distance and time measurements given to certain degrees of accuracy, and needs to find bounds on the calculated speed.

   (a)

   A cyclist travels a distance of $d = 45$ km, given to the nearest kilometre, in a time of $t = 2.5$ hours, given to the nearest 0.1 hour. Write down the upper and lower bounds for both $d$ and $t$.

   [4 marks]

   (b)

   Using average speed $= \dfrac{\text{distance}}{\text{time}}$, calculate the upper bound for the cyclist's average speed, using the bounds found in part (a).

   [4 marks]

   (c)

   Calculate the lower bound for the cyclist's average speed, then find the difference between the upper and lower bounds of speed (using your answer to part (b)), giving your final answer correct to 2 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions