Maths

Operations with numbers in the form a × 10k

RUN → Input number in scientific notation → Use ×10^x key → Solve calculations

Arithmetic sequences: nth term

MENU → RUN → Use formula an = a1 + (n-1)d → Input values → SOLVE → Read nth term

Arithmetic sequences: sum of n terms

MENU → RUN → Use formula Sn = n/2(a1 + an) → Input values → SOLVE

Arithmetic sequences: sigma notation

RUN → Evaluate Σ from 1 to n of formula → Input values → SOLVE

Geometric sequences: nth term

MENU → RUN → Use formula an = a·r^(n-1) → Input values → SOLVE

Geometric sequences: sum of n terms

MENU → RUN → Use formula Sn = a(1-r^n)/(1-r) → Input values → SOLVE

Financial applications: compound interest

MENU → FINANCE → Compound Interest → Input P

Financial applications: annual depreciation

MENU → FINANCE → Compound Interest → Use negative rate → Input values → SOLVE

Laws of exponents with integer exponents

RUN → Input using ^ key → Solve → Use negative powers where needed

Logarithms base 10

MENU → MATH → LOG → Input number → SOLVE

Natural logarithms

MENU → MATH → LN → Input number → SOLVE

Decimal places and significant figures

RUN → Set decimal places in SETUP → Solve → Round results

Upper and lower bounds

RUN → Calculate max/min by adjusting value by ± rounding error → Solve

Percentage errors

RUN → Compute |approx - exact| / exact × 100 → SOLVE

Estimation

RUN → Round values appropriately → Perform operations → Check reasonableness

Amortization and annuities

MENU → FINANCE → TVM → Input PMT

Systems of linear equations (up to 3 variables)

MODE → EQN → Simultaneous → Input coefficients → SOLVE

Polynomial equations

MODE → EQN → Polynomial → Degree n → Input coefficients → SOLVE

Linear models: gradient and intercept

MENU → STAT → 2-Variable → Input data → CALC → Regression → y = ax + b

Quadratic models: find vertex

roots

Exponential growth/decay: f(x) = ka^x + c

MENU → GRAPH → Function → CALC → Value → Solve for x or f(x)

Direct/inverse variation: f(x) = ax^n or f(x) = ax^-n

MENU → RUN → Input values → Solve using ^ key

Cubic models: f(x) = ax^3 + bx^2 + cx + d

MENU → GRAPH → Function → CALC → Value → Solve for roots

Sinusoidal models: f(x) = asin(bx)+d or f(x)=acos(bx)+d

MENU → GRAPH → Function → CALC → Value → Solve

Distance between two points

MENU → RUN → Use √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2) → SOLVE

Midpoint between two points

RUN → Average coordinates (x1+x2)/2

Volume of 3D solids

MENU → RUN → Input formula → Solve using known dimensions

Surface area of 3D solids

MENU → RUN → Input formula → Solve using known dimensions

Angles between lines/line-plane

RUN → Use dot product formula for vectors → SOLVE

Right-angled triangles: sin

cos

Sine rule

MENU → RUN → sin A / a = sin B / b → Input knowns → SOLVE unknown angle or side

Cosine rule

MENU → RUN → c^2 = a^2 + b^2 - 2ab cos C → Input knowns → SOLVE

Area of triangle

MENU → RUN → Use 1/2 ab sin C → Input values → SOLVE

Angles of elevation/depression

RUN → Draw triangle → Apply trig → SIN

Circle: length of arc

RUN → θ/360 × 2πr → Input values → SOLVE

Circle: area of sector

RUN → θ/360 × πr^2 → Input values → SOLVE

Perpendicular bisector

RUN → Find midpoint → Compute slope → Use y - y1 = m(x - x1) → SOLVE

Voronoi diagrams

RUN → Plot points → Compute nearest distances manually or with GRAPH → Identify edges/cells → Solve

Nearest neighbour interpolation

RUN → Use distances to find closest data point → Assign value → Solve

Population

sample

Frequency distributions

MENU → STAT → 1-Variable → Input data → CALC → Σx

Histograms/cumulative frequency

MENU → STAT → 1-Variable → Input data → GRAPH → HIST / C.F → Read median

Box-and-whisker diagram

MENU → STAT → 1-Variable → Input data → GRAPH → BOX → Identify min

Linear correlation

MENU → STAT → 2-Variable → Input paired data → CALC → Regression → r → Predict y from x

Probability: relative frequency

tree diagrams

Discrete random variables

MENU → RUN → List outcomes & probabilities → CALC → Expected value E(X) = Σ x·p

Binomial distribution: MENU → PROB → Binomial PD → Input n

p

Binomial distribution cumulative

MENU → PROB → Binomial CD → Input n

Normal distribution: MENU → PROB → Normal → Input mean

SD

Inverse normal

MENU → PROB → Normal → Input P → SOLVE → Find x for given cumulative probability

Spearman’s rank correlation

MENU → STAT → 2-Variable → Input ranks → CALC → Spearman’s r → SOLVE