Mathematics: Arithmetic, Algebra and Geometry
What is tested
Arithmetic covers fractions, decimals, percentages, ratio and proportion, averages, HCF and LCM, profit and loss, simple interest, and speed–time–distance. Algebra covers simplification, linear equations, and exponents. Geometry covers angle facts, triangle properties, Pythagoras' theorem, circle basics, perimeter and area, and the volume of a cuboid or cylinder. Word problems dominate, so translation from words to an equation is a core skill.
Core rules
- Follow BODMAS: brackets, orders, division/multiplication, addition/subtraction.
- Percentage change = (change ÷ original) × 100.
- Profit percentage is calculated on cost price unless stated otherwise; discount percentage is calculated on marked price.
- Average = total ÷ count; to combine averages, work with totals, not the averages themselves.
- Angles of a triangle sum to 180°; an exterior angle equals the sum of the two opposite interior angles.
- For a right triangle, a² + b² = c², where c is the hypotenuse.
Worked example
A shopkeeper marks an item at Rs 800, gives a 15% discount, and has a cost price of Rs 600. Find the profit percentage. Discount = 15% of 800 = 120, so selling price = 680. Profit = 680 − 600 = 80. Profit% = 80 ÷ 600 × 100 = 13.33%. The trap is calculating profit on the selling price or on the marked price instead of the cost price.
Traps
Confusing percentage points with percent change, forgetting unit conversion (cm to m), using diameter as radius, and assuming a triangle is right-angled without evidence.