WACE Year 11 Mathematics Essential practice exams with worked answers

A calculation begins with the question, not the calculator. Identify what must be found, list the quantities that affect it, and attach units. Decide whether the situation needs an exact count, a money amount, or only an approximate comparison. Information such as a product colour may be irrelevant to cost, whereas pack size is essential. A useful estimate gives you an expected size before a detailed calculation.

Leading digits are the first significant digits of a number: replacing 398 by 400 makes multiplication much easier while preserving its approximate magnitude.

Check results in more than one way. Repeat a calculation using a different method, reverse an operation, or compare with sensible bounds. Dividing $2388 by six returns $398 per chair. An estimate detects a misplaced decimal point but may not detect a small entry error, so it does not replace checking the actual inputs. Written working also makes it easier to trace an error to a particular operation.

Rounding to the nearest decimal place depends on the next digit. For two decimal places, inspect the third decimal digit. Keep trailing zeros when they indicate money precision. Practical rounding can require a direction instead: if 47 people travel in vehicles holding eight people, 47 ÷ 8 = 5.875, so six vehicles are required. Five vehicles leave people behind. If each complete kit requires eight pieces and only 47 pieces are available, only five complete kits can be made.

Choose approximation to match the decision. A quick leading-digit estimate is suitable for checking a bill's size. A close budget decision requires accurate arithmetic before rounding to cents. Avoid rounding every intermediate value because errors can accumulate. Explain the final rounding choice in words: enough containers means round upwards; complete groups available means round downwards. Precision alone does not make an answer useful unless it fits the situation.