BSEB Matric Adv Math (Opt) study plan

Classify real numbers into rational and irrational subsets and prove the irrationality of numbers such as the square root of 2 by contradiction

Solve quadratic equations by all four routes: factorisation, completing the square, the quadratic formula, and the discriminant test for the nature of roots

Form a quadratic equation from given roots and from a sum-and-product relationship, and verify the result by substitution

Relate the coefficients of a quadratic to the sum and product of its roots and use that relation to find unknown coefficients

Apply the remainder theorem and factor theorem to test candidate factors of a polynomial and to find unknown coefficients

Carry out polynomial division and express the result as quotient plus remainder over divisor

Factorise cubic polynomials by finding one rational root and then splitting the remaining quadratic

Solve word problems that reduce to quadratic equations, such as age, speed-distance-time and area problems, by defining the variable explicitly

Derive and recall the exact values of the six trigonometric ratios at 0, 30, 45, 60 and 90 degrees without consulting a table

Prove standard identities involving sine, cosine, tangent, cotangent, secant and cosecant, and simplify expressions using the Pythagorean identities

Convert between degree and radian measure and evaluate expressions combining complementary angles

Set up and solve heights-and-distances problems involving one observer and a single angle of elevation or depression, drawing the diagram first

Solve two-observer problems where the distance between observers is given and two angles of elevation are known, including cases where the observers are on opposite sides

Solve problems involving a moving object, such as a plane or boat, where the angle changes over time and the distance travelled is required

State and apply the basic proportionality theorem and its converse to find unknown lengths in triangles

Apply the criteria for similar triangles to prove two triangles similar and then use the ratio of corresponding sides

Prove and apply the tangent-radius perpendicularity result, the equal-tangent result from an external point, and the alternate segment theorem

Solve circle problems involving chords, cyclic quadrilaterals and the angle in a semicircle

Construct a triangle similar to a given triangle on a stated scale factor and justify each construction step in writing

Construct tangents to a circle from an external point and from a point on the circle, leaving construction arcs visible

Compute the area and perimeter of sectors, segments and combinations of plane figures, choosing the correct formula before substituting

Compute surface area and volume of cylinders, cones, spheres, hemispheres and their combinations, including solids formed by joining a cone to a cylinder

Find the distance between two points, the midpoint, and the point dividing a segment in a given ratio using section formula

Derive the equation of a line in slope-intercept and two-point form, and find the slope of parallel and perpendicular lines

Find the nth term and the sum of the first n terms of an arithmetic progression and use them to solve for an unknown term, common difference or number of terms

Solve problems where a term or sum is given and the progression must be reconstructed, including three-term and four-term symmetric setups

Compute mean, median and mode for grouped data using the assumed-mean and step-deviation methods and interpret the results

Compute the probability of simple events using the classical definition, including problems with cards, dice and balls drawn from a bag

Solve reasoning items on number series, coding-decoding, direction sense and blood relations by identifying the pattern before computing

Work through one full-length timed paper under exam conditions without notes, then classify every error as conceptual, procedural or careless

Revisit the week 2 error log and week 4 mock and re-solve every item previously marked wrong

Memorise and reproduce from memory the complete formula sheet covering all nine domains