Bihar BSEB Matric Mathematics study plan

State and apply the Fundamental Theorem of Arithmetic to factor composite numbers up to 1000 into primes without a calculator

Prove that the square root of 2, 3 and 5 are irrational using the contradiction method and write the proof in full sentences

Compute HCF and LCM of two or three numbers by both the prime factorisation method and Euclid's division algorithm, then verify HCF × LCM = product of the two numbers

Convert terminating and non-terminating recurring decimals into p/q form and classify numbers as rational or irrational

Build a one-page formula and definition sheet for real numbers that you will reuse in later revision

Find the zeroes of a quadratic polynomial by factorisation and by the quadratic formula, and verify the relationship between zeroes and coefficients

Form a quadratic polynomial when the sum and product of its zeroes are given

Solve a pair of linear equations by substitution, elimination and cross-multiplication, and check which method is fastest for a given pair

Identify from the ratio of coefficients whether a pair of linear equations is consistent, inconsistent or dependent, and draw the corresponding pair of lines

Translate three age, two fraction and two work-related word problems into a pair of equations and solve them

Solve quadratic equations by factorisation, completing the square and the quadratic formula, and compute the discriminant to state the nature of roots

Solve at least four application problems on speed-time, area and number puzzles that reduce to quadratic equations

Find the nth term and the sum of the first n terms of an AP using the standard formulas, including for APs given only by their first two terms

Insert a given number of arithmetic means between two numbers and find the common difference

Solve three real-life AP problems such as savings growth, ladder rungs and prize distribution

State and apply the Basic Proportionality Theorem (Thales theorem) and its converse to find unknown lengths in triangles

Prove the AA, SSS and SAS similarity criteria and use them to establish the ratio of areas of similar triangles

Apply the Pythagoras theorem and its converse, and use the ratio of areas theorem to solve at least six numerical problems

Compute all six trigonometric ratios for the standard angles 0, 30, 45, 60 and 90 degrees from memory without a table

Prove the standard trigonometric identities such as sin squared plus cos squared equals one, and simplify expressions using them

Solve height-and-distance problems involving one or two right triangles with angles of elevation and depression, drawing the figure each time

Use the distance formula to find lengths, and use the section formula to find the point dividing a segment in a given ratio, including the midpoint case

Find the coordinates of a point using the area of a triangle formula and test whether three given points are collinear

State the three conditions for a tangent to a circle and prove that the tangent at any point of a circle is perpendicular to the radius through the point

Prove that lengths of tangents drawn from an external point to a circle are equal and apply this to numerical problems

Perform the standard constructions: divide a line segment in a given ratio, construct a triangle similar to a given triangle with a given scale factor, and draw tangents to a circle from an external point

Compute the area of a sector and the length of an arc using the angle-based formulas, and convert between degrees and radians where needed

Find the area of the segment of a circle by subtracting the area of the triangle from the area of the sector

Compute the surface area and volume of a combination solid such as a cylinder with two hemispherical ends or a cone on a cylinder

Solve conversion problems involving melting or recasting one solid into another while conserving volume

Solve at least four practical problems on cost of painting, capacity of vessels and water flow through pipes

Construct a grouped frequency distribution and compute the mean by the direct, assumed-mean and step-deviation methods

Find the median and mode of grouped data and interpret what each measure tells you about the distribution

Draw and read a cumulative frequency curve (ogive) to estimate the median graphically

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

Apply the complementary event rule, probability of sure and impossible events, and solve at least five two-step probability problems

Revise every formula card and error log, rewriting any problem you previously got wrong from scratch

Attempt two full-length mock papers of 100 marks under the real 3 hour 15 minute timing and mark them strictly

Classify your remaining mistakes by domain and redo the two weakest domains using targeted practice

Practise showing construction steps, proof structure and units clearly so that method marks are not lost

Memorise the standard angle table, mensuration formulas and algebraic identities for instant recall