Number and Algebra: precision, finance and sequences
This domain tests whether you can handle quantities and money without losing accuracy: standard form and significant figures, percentage error, currency conversion, compound interest and depreciation, annuities and amortisation, arithmetic and geometric sequences and series, laws of exponents and logarithms, and small linear systems solved on the GDC.
Core rules
- Arithmetic: uₙ = u₁ + (n−1)d and Sₙ = n/2 (2u₁ + (n−1)d).
- Geometric: uₙ = u₁r^(n−1) and Sₙ = u₁(1−rⁿ)/(1−r), r ≠ 1.
- Compound interest: FV = PV(1 + i)ⁿ, where i is the rate per compounding period as a decimal and n is the number of periods.
- Depreciation: FV = PV(1 − i)ⁿ.
- Percentage error = |approximation − exact| / |exact| × 100%.
- Solve aˣ = b with logs: x = log b / log a.
- Annuities and amortisation belong in the GDC finance app (PV, FV, n, I%, PMT), with consistent signs for money in and money out.
Worked example
$4500 is invested at 3.6% per year compounded monthly for 5 years. Convert the rate and the time to months: i = 0.036/12 = 0.003 and n = 5 × 12 = 60. Then FV = 4500(1.003)^60. Since (1.003)^60 ≈ 1.19687, FV ≈ $5385.9, about $5386. Using 4500(1.036)^5 gives $5374: close, but wrong, because it ignores monthly compounding.
Traps that cost marks
Pairing an annual rate with a monthly period count; counting years instead of periods; giving PMT the wrong sign in the finance app; rounding intermediate values instead of keeping full GDC precision until the final answer (usually 3 s.f.); confusing arithmetic with geometric models; forgetting that a geometric sum formula needs r ≠ 1.