ASSEB HSLC General Mathematics study plan

Classify numbers into rational, irrational, integer, and real categories and justify each classification with a one-line reason

Simplify surds by extracting perfect-square factors, rationalise denominators with single and binomial surds, and combine like surds in sums

Factorise quadratic expressions by splitting the middle term and by completing the square, choosing the faster method for each example

Solve quadratic equations by factorisation, completing the square, and the quadratic formula, and verify roots by substitution

Solve pairs of linear equations in two variables by substitution and elimination, including one word problem per method

State and prove the key triangle theorems (angle sum, exterior angle, congruence criteria, and the basic proportionality theorem) from memory without notes

Apply circle theorems on angles in the same segment, angle in a semicircle, tangent-radius perpendicularity, and cyclic quadrilaterals to find unknown angles in multi-step figures

Derive and apply the sine, cosine, and tangent ratios for standard angles 0, 30, 45, 60, and 90 degrees without a table

Solve right-triangle problems involving angles of elevation and depression, drawing a labelled diagram before calculating

Prove two triangles similar or congruent and use the result to find a missing length or ratio

Divide polynomials by linear and quadratic divisors using long division and the remainder and factor theorems, stating the remainder before dividing

Find the value of an unknown coefficient given a factor or remainder condition, and verify the result

Translate a word problem into an equation or system, define the variable in words, and check the answer against the original wording

Solve problems on ages, work-rate, speed-distance-time, and mixtures by setting up linear or quadratic models

Identify and correct common errors in worked solutions such as sign slips, unverified roots, and rejected negative lengths

Plot points and compute distance, midpoint, and section-ratio results on the Cartesian plane without a graph for simple cases

Derive and use the slope of a line from two points, and write equations of lines in slope-intercept, point-slope, and two-point forms

Determine whether two lines are parallel, perpendicular, or intersecting from their equations, and find the intersection point

Generate the nth term and sum of an arithmetic progression, and solve for n, a, or d given conditions

Insert arithmetic means between two numbers and apply APs to simple real-life sequence problems

Compute perimeter and area of triangles, quadrilaterals, circles, and sectors, including composite figures, choosing the correct formula each time

Calculate surface area and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres, and convert between units correctly

Solve problems on melting, recasting, and displacement that conserve volume, setting up the equality before computing

Apply trigonometric ratios to find heights and distances in two-observer and two-angle problems

State the exact values of trigonometric ratios at standard angles and simplify expressions using identities such as sin squared plus cos squared equals one

Compute mean, median, and mode for grouped and ungrouped data, and interpret which measure best describes a given distribution

Draw and read histograms, frequency polygons, and cumulative frequency curves, and estimate the median from an ogive

Calculate the probability of simple and compound events using equally likely outcomes, and apply the complement rule

Use set notation to find unions, intersections, and complements, and represent them on a Venn diagram

Distinguish a relation from a function, test whether a relation is a function, and evaluate function values at given inputs

Solve multi-step reasoning problems by restating the given information, identifying the unknown, and selecting a strategy before calculating

Write complete geometric proofs with numbered statements and reasons, including at least one construction

Solve problems combining geometry with mensuration, such as finding the area of a shaded region bounded by circle arcs

Work through pattern and sequence reasoning questions, stating the general rule in words and symbols

Check answers for plausibility, rejecting impossible results such as negative lengths or probabilities above one

Re-solve every question missed in the week 7 mock without notes, then compare against the model solution

Recall all key formulas and theorems across the ten domains in a single written brain dump within 30 minutes

Complete two timed half-papers focused on the weakest three topics identified in the mock

Reduce the error log to zero repeat mistakes by re-testing each logged error type once

Finalise an exam-day plan covering question order, time allocation per section, and a check routine for units and signs