Mathematics and Basic Computation
Mathematics and Basic Computation
This domain tests the arithmetic an Amin uses daily: unit conversion, percentage and ratio, mensuration of plots, triangle solution and coordinate geometry. The exam favours short numerical problems with an exact answer.
Core rules
- Units: 1 m = 100 cm; 1 km = 1000 m; 1 ha = 10,000 m²; 1 acre = 4046.86 m² = 100 decimal; 1 sq km = 100 ha.
- Rectangle area = length × breadth. Triangle area = 1/2 × base × height. Trapezium area = 1/2 × (sum of parallel sides) × perpendicular distance between them. Circle area = πr²; circumference = 2πr.
- Heron's formula: for sides a, b, c, s = (a+b+c)/2 and area = sqrt(s(s-a)(s-b)(s-c)).
- In a right triangle, tan θ = opposite/adjacent; sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse. Bearings use clockwise angles from north.
- Percentage change = (new - old)/old × 100. A scale ratio must be applied to both dimensions for area.
Worked example
A field is a trapezium with parallel sides 30 m and 50 m, and the perpendicular distance between them is 20 m. Area = 1/2 × (30 + 50) × 20 = 1/2 × 80 × 20 = 800 m². In hectares: 800 / 10,000 = 0.08 ha. In acres: 800 / 4046.86 = 0.1977 acre, about 19.77 decimal. The slant side is not used as the height.
Traps
Do not use a sloping side as the perpendicular height of a trapezium. Do not forget to halve the sum of parallel sides. Do not convert square metres to hectares by dividing by 1000. Do not round intermediate values so heavily that the final option is missed.