KCSE cheat sheet
KCSE · Keep the key ideas within reach.
Group 4: Technical and Applied Subjects - Core Facts and Rules
Technical drawing conventions: first-angle projection places the front view above the plan and the left view to the right of the front view; third-angle projection places the plan above the front view and the right view to the right.
In first-angle projection the symbol is a truncated cone with the small end pointing towards the observer's left; in third-angle the small end points right.
Scale drawing: scale = drawing length / actual length; a scale of 1:50 means 1 cm on paper represents 50 cm (0.5 m) in reality.
Area of a triangle = ½ × base × perpendicular height; area of a trapezium = ½ × (sum of parallel sides) × height - both used in site and material estimates.
Volume of a cylinder = πr²h; volume of a cone = ⅓πr²h; volume of a prism = cross-sectional area × length.
Ohm's law: V = IR; electrical power P = VI = I²R = V²/R; energy consumed in kWh = power (kW) × time (hours).
Woodwork joints: a mortise-and-tenon resists tension and compression along the rail; a dovetail resists pulling apart at right angles to the joint face; a halving joint suits light frames.
Metalwork: annealing softens metal by heating then slow cooling; hardening heats then quenches rapidly; tempering reheats hardened steel to reduce brittleness.
Agriculture practical rule: seed rate (kg/ha) = (target plant population per m² × 1000-grain weight in g) ÷ (germination % × field establishment %), adjusted for row spacing.
Group 5: Business and Applied Subjects - Core Facts and Rules
Accounting equation: Assets = Capital + Liabilities; every transaction keeps this equation balanced (double entry).
Gross profit = Sales − Cost of sales; net profit = Gross profit + other income − expenses; mark-up = gross profit as % of cost; margin = gross profit as % of selling price.
Depreciation: straight-line = (cost − scrap value) ÷ useful life; reducing balance = fixed % applied to the book value each year.
Working capital = current assets − current liabilities; current ratio = current assets ÷ current liabilities; acid-test ratio = (current assets − stock) ÷ current liabilities.
Break-even output (units) = fixed costs ÷ (selling price per unit − variable cost per unit); margin of safety = actual sales − break-even sales.
Demand and supply: a rise in price normally reduces quantity demanded and raises quantity supplied; equilibrium occurs where the demand and supply curves intersect.
Business structures: a sole trader has unlimited liability; a limited company has separate legal personality and limited liability for shareholders.
National income: GDP = C + I + G + (X − M); inflation erodes purchasing power, while deflation raises the real value of debt.
Kenyan business environment: the Capital Markets Authority regulates securities, the Central Bank of Kenya sets the base rate, and VAT is a consumption tax levied on taxable supplies.