Quantitative Aptitude
Quantitative Aptitude tests numerical reasoning through arithmetic, algebra, geometry, mensuration, trigonometry and data interpretation. IB ACIO questions are usually short but trap-heavy; the mark comes from setting up the equation correctly, not from long calculation.
Core rules
- Percentage: successive change = a + b + ab/100; reverse percentage needs the original base.
- Ratio: convert to parts; partnership profit is proportional to capital × time.
- Time-work: combined rate = 1/A + 1/B; use LCM units to avoid fractions.
- Speed: relative speed adds for opposite directions and subtracts for the same direction; boats use still-water speed ± current.
- Interest: SI = PRT/100; CI = P(1+r)^n − P.
- Mensuration: circle area πr²; sphere volume 4/3πr³; cylinder πr²h.
Worked example
A can finish a job in 12 days and B in 18. They work together for 3 days, then A leaves. How long does B take to finish? Take total work = LCM(12,18) = 36 units. A does 3 units/day, B does 2. Together they do 5/day. In 3 days they complete 15; remaining work is 21. B alone takes 21/2 = 10.5 days. The LCM method avoids fractions and shows why remaining work must be divided by B's rate only.
Traps
Using the wrong base in percentage; adding times instead of rates; treating CI as SI for multi-year problems; forgetting unit conversion such as km/h to m/s; in DI, reading the wrong year or confusing 'percent of total' with percentage points.