Punjab PSEB Matric Mathematics study plan

State and apply the real number system: prove irrationality of √2 by contradiction, and classify numbers as rational or irrational with justification.

Apply Euclid's division lemma and the Fundamental Theorem of Arithmetic to find HCF and LCM of pairs and triples of numbers, and verify HCF × LCM = product for two numbers.

Derive and use the laws of exponents for real numbers, including rational exponents, and simplify expressions such as a^(m/n) · a^(p/q).

Solve 15 mixed real-number problems under timed conditions (2 minutes each) and log every error with its cause.

Form polynomials from given zeros and verify the relationship between zeros and coefficients for quadratic polynomials.

Divide polynomials using the long-division algorithm and express dividend = divisor × quotient + remainder.

Solve problems involving sum and product of zeros, including finding a quadratic polynomial with prescribed zero conditions.

Complete 20 polynomial problems spanning construction, division, and coefficient relationships.

Solve pairs of linear equations in two variables by substitution, elimination, and cross-multiplication, and state the condition for consistency from coefficient ratios.

Set up and solve at least 6 word problems (age, work, speed-distance, fractions, geometry) by translating them into two-variable systems.

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

Determine the nature of roots using the discriminant and solve problems that require finding an unknown coefficient from a given root condition.

State and apply the nth term and sum formulas for arithmetic progressions, including problems that require finding n, a, or d from given conditions.

Solve AP word problems involving real contexts (savings, seating rows, multiples of a number within a range) and identify when a sequence is not an AP.

Apply the similarity criteria (AA, SSS, SAS) to prove triangles similar and use the basic proportionality theorem to find unknown lengths.

Solve problems using the ratio-of-areas theorem for similar triangles.

Apply Pythagoras' theorem and its converse to solve right-triangle problems, including proofs of standard results.

Use trigonometric ratios of 0°, 30°, 45°, 60°, and 90° to evaluate expressions without a calculator.

Prove standard trigonometric identities and simplify expressions using sin²θ + cos²θ = 1 and its derived forms.

Solve height-and-distance problems by drawing correct diagrams and choosing the right ratio for single- and two-observer cases.

Compute the mean, median, and mode for grouped data and handle missing-frequency problems by setting up equations.

Draw and interpret cumulative frequency curves (ogive) and read the median from a graph.

Apply the tangent-radius theorem, equal-tangent theorem, and angle-in-alternate-segment theorem to prove circle results.

Construct tangents to a circle from an external point and justify each construction step.

Compute surface areas and volumes of combinations of solids (cone, cylinder, hemisphere, sphere, frustum) and solve melting/recasting problems by equating volumes.

Solve problems on sectors, segments, and areas of shaded regions by subtracting and adding standard areas.

Use the distance formula, section formula, and midpoint formula to solve coordinate geometry problems, including collinearity checks.

Solve 10 mensuration problems in which units must be converted before calculation.

Complete two full-length timed mock papers under exam conditions and score them strictly against the official marking pattern.

Re-solve every question missed across weeks 1–7 and classify each error as conceptual, procedural, or careless.

Memorise and self-test the complete formula sheet covering all units, writing formulas from memory in under 15 minutes.

Practise exam technique: allocating time per section, showing construction marks, and presenting proofs with correct reasons.