ORT Mathematics study plan

Translate word problems into algebraic expressions and equations, and define each variable in writing before solving.

Solve linear equations and inequalities in one variable, including ones with fractions and nested parentheses, and verify every solution by substitution.

Apply the four-step modelling cycle (formulate, solve, interpret, validate) to short real-world scenarios and state the assumption behind each model.

Graph linear relations from a table, an equation, and two points, and read slope and intercept as rate of change and starting value.

Classify relations as functions or not, and determine domain and range from equations, tables, and graphs.

Evaluate, compose, and invert simple functions, and explain what f(g(x)) means inside a stated context.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and interpret the discriminant before solving.

Build quadratic models for area, revenue, and projectile situations, and justify whether the vertex or a root answers the question asked.

Solve 2x2 and simple 3x3 systems by substitution and elimination, and interpret the solution as an intersection or break-even point.

Apply exponent laws and solve exponential growth and decay equations, including compound interest, using logarithms where required.

Decompose multi-step modelling problems into ordered sub-goals, recording units and assumptions at each stage.

Critique worked solutions for unit errors, extraneous roots, and unjustified assumptions, and state the correction.

Compute perimeter, area, surface area, and volume of composite 2D and 3D figures, keeping units consistent throughout.

Apply the Pythagorean theorem and distance and midpoint formulas, and solve right-triangle problems with sine, cosine, and tangent.

Use similarity and congruence criteria to find unknown lengths, and justify each proportion you set up.

Convert within and between metric and imperial units in measurement contexts, and round to an appropriate number of significant figures.

Solve coordinate-geometry problems involving slope, parallel and perpendicular lines, circle equations, and line-circle intersections.

Compute fluently with fractions, decimals, percentages, ratios, and proportions, and choose the representation that shortens the work.

Apply divisibility, primes, LCM and GCD, absolute value, and order of operations to simplify expressions without a calculator.

Estimate an answer before computing and use the estimate to catch magnitude and unit errors.

Convert between scientific notation, radicals, and rational exponents, and simplify expressions in each form.

Compute and interpret mean, median, mode, range, standard deviation, and quartiles, and explain what each measure does and does not reveal.

Construct and read histograms, box plots, and scatterplots, and describe shape, center, spread, and outliers.

Compute probabilities for simple, compound, and conditional events using two-way tables and tree diagrams.

Distinguish correlation from causation and judge a regression line's fit using residuals, interpolation, and extrapolation.

Solve counting problems with the multiplication principle, permutations, and combinations, choosing the correct tool for the wording.

Design a small model or survey, state its assumptions and limitations, and describe two ways the conclusion could fail.

Interpret statistical claims in short passages and identify sampling, wording, and representation bias.

Complete two full-length timed practice exams under exam conditions and mark them with a domain-by-domain error tally.

Re-teach the three weakest topics named by the error tally, working five fresh problems in each until they are correct unaided.

Reconstruct a one-page formula and strategy sheet from memory, then verify every entry against source material.

Practise pacing by setting a per-item time budget and skipping then returning to items that overrun it.