AP SSC Mathematics study plan

State and prove the Basic Proportionality Theorem (Thales theorem) and its converse from memory, with a labelled diagram for each.

Prove the AA, SSS and SAS similarity criteria and use them to decide similarity in at least 10 paired-triangle figures.

Prove the Pythagoras theorem and its converse, and apply the altitude-on-hypotenuse relation (BD² = AD·DC type results) to 6 numerical problems.

State and apply circle tangent results - radius perpendicular to tangent at the point of contact, equal tangents from an external point, and the alternate segment theorem - to 8 problems.

Construct a triangle similar to a given triangle for a given scale factor, and construct a pair of tangents to a circle from an external point, writing the construction steps.

Set up and solve 5 two-part riders that combine a similarity result with a circle property.

Derive and write out the curved surface area, total surface area and volume formulas for cylinder, cone, sphere, hemisphere and frustum without consulting notes.

Compute surface area and volume of at least 6 combination solids (cylinder + hemisphere, cone + cylinder, frustum + hemisphere) by splitting each into its component parts before calculating.

Find arc length, area of a sector and area of a minor/major segment, using the degree-measure formulas and the triangle-subtraction method for segments.

Convert between cm, m, litres and cubic metres inside word problems, and solve 4 costing problems (painting, plastering, capacity) that require unit conversion before applying a formula.

Solve 4 melting/recasting and pipe-flow problems by equating volumes rather than by formula-guessing.

Reproduce the trigonometric ratio table for 0°, 30°, 45°, 60° and 90° from memory and use it to evaluate 12 expressions without a calculator.

Prove at least 6 standard identities, including sin²θ + cos²θ = 1 and its two derived forms, and use them to simplify compound fractional expressions.

Eliminate a variable from a pair of trigonometric equations to obtain a required relation, on 5 problems.

Draw an accurate diagram for every heights-and-distances problem before writing any equation, marking the angle of elevation or depression at the correct vertex.

Solve 10 heights-and-distances problems covering single-triangle, two-triangle and moving-object cases, stating the answer with correct units and reasonable rounding.

Write the nth term, the sum of the first n terms, and the arithmetic-mean relation for an AP, then solve 8 problems that require finding a, d or n from two given conditions.

Solve 4 AP word problems (instalments, savings, seating rows, multiples in a range) by first identifying a and d, then choosing the term or sum formula.

Use Euclid's division algorithm to find the HCF of two and three numbers, and use the Fundamental Theorem of Arithmetic to find HCF and LCM by prime factorisation.

Prove that √2, √3 and √5 are irrational by contradiction, writing each proof in full sentences.

Apply the relation HCF × LCM = product of two numbers, and decide when a terminating decimal expansion occurs from the denominator's prime factorisation.

Apply the distance formula, section formula (internal and midpoint) and area-of-triangle formula to 12 coordinate problems, including 3 that prove collinearity or a named quadrilateral.

Sketch 4 pairs of linear equations on graph paper using intercepts, and read off whether the system is consistent, inconsistent or dependent from the lines.

Solve the same pair of equations by substitution, elimination and cross-multiplication, and verify that all three give the same solution.

Classify 12 systems as consistent/inconsistent/dependent by comparing a₁/a₂, b₁/b₂ and c₁/c₂ before solving them.

Solve 4 word problems (age, work, boat-and-stream, two-digit number) by forming a pair of equations and stating the answer in the original context.

Read the number of zeroes and their signs from a sketched polynomial graph, and verify zeroes against the coefficients using sum = −b/a and product = c/a.

Find the remaining zeroes of a cubic or quadratic when some zeroes are given, using the division algorithm and factorisation.

Perform union, intersection, difference and complement on given sets written in roster and set-builder form, and shade the result on a Venn diagram.

Apply the cardinality formulas n(A∪B) = n(A) + n(B) − n(A∩B) and its three-set counterpart to 8 survey-type word problems.

Distinguish subsets, proper subsets and the power set, and count subsets of a set with n elements.

Compute the mean of a grouped frequency distribution by the direct, assumed-mean and step-deviation methods on the same data set, and confirm all three give the same answer.

Compute the median and mode of grouped data, and identify the modal and median classes before substituting into the formulas.

Draw a less-than ogive and a more-than ogive on the same axes and read the median from their point of intersection.

Apply the classical definition of probability to dice, coins, cards and bag-of-balls experiments, using complementary events to shortcut at least 3 problems.

State why an empirical probability approaches the theoretical value as trials increase, and check that every computed probability lies between 0 and 1.

Complete two full-length timed mock papers (one mid-week, one at the weekend) under exam conditions, with no notes and strict timing.

Re-work every question missed across the previous seven weeks' error logs and confirm each is now solvable closed-book.

Run a 30-minute formula-recall sprint covering mensuration, trigonometry, coordinate geometry, progressions and statistics, writing each formula from memory.

Target the two lowest-scoring domains from the first mock with a focused 25-question set each before sitting the second mock.

Practise answer presentation: correct units, diagrams for geometry and heights-and-distances, and one-line justification before each theorem use.