RBSE Secondary Mathematics study plan

Derive and memorise the six trigonometric ratios for 0°, 30°, 45°, 60° and 90°, and state them from memory without a table

Apply the Pythagorean identities sin²θ + cos²θ = 1 and their two variants to simplify at least ten expressions

Prove and use the basic similarity criteria (AA, SSS, SAS) to solve for unknown sides in two-triangle configurations

Solve 15 mixed problems combining angle of elevation and angle of depression with right-triangle similarity reasoning

Convert between the trigonometric ratios of complementary angles and evaluate expressions such as sin(90° − θ) without a calculator

Set up and solve two-step height-and-distance word problems involving a single observer and a single object

Apply the Basic Proportionality Theorem (Thales) and its converse to divide segments and prove lines parallel

Use the ratio-of-areas theorem for similar triangles to find unknown areas or side ratios

Apply the distance formula, section formula and midpoint formula fluently, including points dividing a segment in a given ratio

Compute the area of a triangle from coordinates and use the zero-area condition to test collinearity

Solve pairs of linear equations by substitution, elimination and cross-multiplication, choosing the fastest method per problem

Classify a linear system as consistent, inconsistent or dependent from the ratio of coefficients a₁/a₂, b₁/b₂, c₁/c₂

Translate two-condition word problems (age, speed, digits, fractions) into a pair of equations and solve them

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

Compute the discriminant and use it to determine the nature of roots without solving

Form a quadratic equation from given roots and from a word problem, including the standard upstream/downstream and area cases

Divide polynomials by linear and quadratic divisors and apply the remainder and factor theorems

Find the zeros of a quadratic polynomial and relate their sum and product to the coefficients

Prove that √2, √3 and √5 are irrational by contradiction, writing the argument in full without gaps

Apply Euclid's division lemma and the Fundamental Theorem of Arithmetic to compute HCF and LCM and to prove divisibility results

Identify an arithmetic progression, compute the common difference and generate the nth term using aₙ = a + (n − 1)d

Compute the sum of n terms with and without the last term known, and solve for n when the sum is given

Set up AP word problems involving instalments, savings and equally spaced objects

State and apply the tangent–radius perpendicularity result and the equal-tangent-lengths theorem from an external point

Prove the alternate segment theorem and use it to find unknown angles in a circle configuration

Construct a tangent to a circle from an external point and a triangle similar to a given triangle on a given scale factor, with construction steps written out

Compute the area of a sector, the length of an arc and the area of a segment using θ/360° fractions of πr² and 2πr

Find the area swept by a clock hand or a wheel by modelling it as a sector or a rolling circle

Compute the surface area and volume of combinations of solids such as a cone on a hemisphere or a cylinder with two hemispherical ends

Solve problems involving melting and recasting one solid into another by equating volumes

Handle problems on a frustum of a cone, including its slant height, curved surface area and volume

Convert between units (cm, m, litres) correctly and round only at the final step

Solve real-world capacity problems involving pipes, tanks and displaced water

Compute the mean, median and mode for grouped data, including the missing-frequency case

Draw and read a cumulative frequency curve and use it to estimate the median

Compute classical probability for dice, cards and bag problems and apply the complement rule

Re-solve the five weakest problem types identified in the week 4 mock and confirm each is now correct closed-book

Complete two full-length timed papers under exam conditions and review every error