RBSE Praveshika Mathematics study plan
RBSE Praveshika Mathematics · Give each week a clear focus.
8 weeks · About 7 hours per week
Number System and Real Numbers & Surds, Indices and Commercial Mathematics
Classify given numbers as rational, irrational, integer, or natural and justify each classification in one written sentence
Convert repeating decimals into p/q form for at least eight different examples without assistance
Apply the laws of indices to simplify twenty expressions involving negative and fractional exponents
Simplify and rationalise surd denominators in fifteen problems, including binomial denominators using the conjugate
Your checkpoint
A handwritten sheet of 40 solved items (20 indices, 20 surds/rationalisation) with every step shown and errors corrected in a different colour
Number System and Real Numbers & Surds, Indices and Commercial Mathematics
Place rational and irrational numbers on the number line by geometric construction for at least five cases
State and use the rationalisation factor for binomial surds and verify results by substitution
Solve percentage, profit-loss, and simple/compound interest word problems showing the formula used at each step
Compute HCF and LCM of algebraic and numeric expressions and verify the product rule HCF x LCM = product of numbers
Your checkpoint
A 25-question self-made test on real numbers and commercial arithmetic, completed in 60 minutes, scored, with a written list of the three error types made
Polynomials and Factorization & Linear Equations in Two Variables
Find all zeroes of quadratic and cubic polynomials and verify them against the coefficient relationships
Factorise polynomials using splitting the middle term, grouping, and the factor theorem across fifteen examples
Solve systems of two linear equations by substitution, elimination, and cross-multiplication, and check each solution by substitution
Identify inconsistent and dependent systems from the coefficient ratios and sketch what each case looks like
Your checkpoint
A comparison table of 12 linear systems showing the coefficient ratios, the method used, the solution, and whether the system is consistent, inconsistent, or dependent
Euclidean Geometry: Triangles and Circles
Prove and apply the basic proportionality (Thales) theorem and its converse in at least four configurations
Prove triangle similarity by AA, SSS, and SAS criteria and use similarity to compute unknown lengths
Apply the Pythagoras theorem and its converse to compute sides and identify right triangles
State and use circle theorems on chords, tangents, and angles in the same segment, drawing the figure before each proof
Your checkpoint
A geometry proof portfolio of 10 fully written proofs, each with a labelled diagram, given, to prove, construction, and reasons cited line by line
Euclidean Geometry: Triangles and Circles & Coordinate Geometry
Prove the tangent-radius perpendicularity theorem and the equal-tangent-lengths theorem and apply them to find unknown lengths
Solve mixed geometry problems that combine circle theorems with similarity, writing the reason for every equality
Plot points and compute the distance between two points using the distance formula in ten coordinate problems
Find the midpoint and the section-ratio point of a segment and verify results by plotting on graph paper
Your checkpoint
A single timed 90-minute mock section of 12 geometry and coordinate geometry questions, scored, with every lost mark traced to a missing theorem statement or reason
Mensuration: Areas and Volumes & Trigonometry and Its Applications
Compute areas of triangles, quadrilaterals, circles, and sectors by selecting the correct formula and showing unit conversions
Compute surface areas and volumes of cubes, cuboids, cylinders, cones, spheres, and hemispheres, including combined solids
Derive and use the trigonometric ratios for 0, 30, 45, 60, and 90 degrees without a table
Solve height-and-distance problems by drawing the diagram first and labelling the angle of elevation or depression
Your checkpoint
A formula sheet written from memory plus 15 solved mensuration and 10 solved height-and-distance problems with diagrams, all checked against the sheet
Trigonometry and Its Applications & Statistics and Probability
Prove standard trigonometric identities and apply them to simplify at least twelve expressions
Compute mean, median, and mode for grouped data, including a grouped frequency distribution with class intervals
Draw and interpret a cumulative frequency curve and read the median from it
Compute classical probability for single and two-dice experiments and state the sample space explicitly
Your checkpoint
A statistics and probability lab sheet: one grouped-data set fully analysed (mean, median, mode, ogive, and one probability question on the same data) with all working shown
Number System and Real Numbers & Polynomials and Factorization & Linear Equations in Two Variables & Coordinate Geometry & Euclidean Geometry: Triangles and Circles & Mensuration: Areas and Volumes & Trigonometry and Its Applications & Statistics and Probability & Surds, Indices and Commercial Mathematics
Assemble and rank the 20 formulas you forget most often and drill them until each is reproduced from memory
Complete three full-length timed practice papers under exam conditions and score each honestly
Categorise every wrong answer by domain and re-solve those items without notes
Revisit the two weakest domains from the scored papers and rebuild the underlying concept before retesting
Your checkpoint
A three-paper score log with domain-wise accuracy percentages and a one-page correction sheet listing every recurring error and the rule that prevents it
Milestones
Week 2: Score at least 70% on the self-made real numbers and commercial arithmetic test, and correctly rationalise 9 of 10 binomial surd denominators
Week 4: Write the Thales theorem and the tangent-radius theorem from memory with full reasons, and score at least 70% on a 10-question geometry proof set
Week 6: Reproduce the full mensuration and trigonometric ratio formula sheet from memory with no omissions, and solve 8 of 10 height-and-distance problems correctly
Week 8: Average at least 65% across the three timed papers with no domain below 50% accuracy, and show a lower error count in the final paper than the first