Mathematics
What the section tests
Arithmetic fluency, fractions and percentages, ratio and proportion, basic algebra, geometry and measurement, and data interpretation from tables or simple charts. Concepts to master: order of operations, converting between fractions, decimals and percentages, solving linear equations, rearranging formulas, area and perimeter of rectangles, triangles and circles, angle facts, averages, and reading scales.
Traps to watch
- Order of operations. Multiplication and division before addition and subtraction; brackets first. In 6 + 2 × 5, the answer is 16, not 40.
- Percentage change. A 20% rise then a 20% fall does not return to the start; multiply by 1.2 and then 0.8 to get 0.96, a 4% net loss.
- Units. Convert to one unit before calculating; a rate in km/h with a time in minutes needs the time divided by 60.
- Rounding too early. Keep full precision until the final step.
- Ratio sharing. Add the ratio parts, divide the total by that sum, then multiply.
Rule of thumb
Estimate the answer first with rounded numbers. If your exact answer is far from the estimate, you have made an operation or unit error, not a rounding error.
Worked example
Share 84 in the ratio 3:4. Total parts = 7; one part = 84 ÷ 7 = 12; shares are 36 and 48. Check: 36 + 48 = 84.
Geometry essentials
Angles in a triangle total 180°, on a straight line 180°, around a point 360°. Area of a triangle = ½ × base × height; circumference = πd; area of a circle = πr².