Mathematics: Number Work, Fractions, and Word Problems
What the paper actually tests
Cadet College mathematics questions reward clean, fast calculation rather than long algebra. Expect place value and rounding, the four operations on whole numbers and decimals, fractions and their links to percentages, ratio and proportion, average, simple interest, area and perimeter of rectangles and triangles, and unit conversion (metres to centimetres, minutes to hours).
Traps to watch
- Order of operations: brackets, then powers, then multiplication/division left to right, then addition/subtraction. A question like 8 + 4 × 3 is 20, not 36.
- Mixed units: convert before computing. Adding 2 m 45 cm to 130 cm requires one unit first.
- Fraction of a quantity: "two-thirds of 45" means 45 ÷ 3 × 2 = 30. Do not subtract the fraction.
- Percentage increase vs decrease: a 20% rise then a 20% fall does not return to the start.
- Average: total ÷ count. If the average of 5 numbers is 12, the total is 60 - many candidates forget to multiply back.
Rule of thumb
For any word problem, write down what is given, what is asked, and the unit of the answer before calculating. Label the answer with its unit; an unlabelled number is a common source of lost marks.
Worked example
A rectangle is 12 cm long and 8 cm wide. Its length is increased by 25%. What is the new area? New length = 12 × 1.25 = 15 cm. Area = 15 × 8 = 120 cm². Note the width is untouched - do not scale both sides unless the question says so.
Practice habit
Do ten mental-arithmetic items daily (tables to 20, squares to 20, and simple percentages). Speed with accuracy is what separates a good score from a great one.