Mathematics
What the Mathematics paper tests
The PSEB Matric Mathematics paper (Class 10) samples the full syllabus: real numbers, polynomials, linear equations, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry and its applications, circles, constructions, areas related to circles, surface areas and volumes, statistics and probability. Questions range from one-mark objective items to short and long answers, so a correct final value alone is not enough - formula, substitution and statement earn method marks.
Rules and formulas to hold
- Real numbers: Euclid's division lemma is a = bq + r with 0 ≤ r < b. For two positive integers, HCF × LCM = product of the numbers.
- Quadratics: For ax² + bx + c = 0, D = b² − 4ac. D > 0 gives two distinct real roots, D = 0 equal roots, D < 0 no real roots. Roots are x = (−b ± √D)/(2a); sum = −b/a, product = c/a.
- AP: aₙ = a + (n − 1)d and Sₙ = n/2[2a + (n − 1)d].
- Coordinate geometry: distance = √[(x₂ − x₁)² + (y₂ − y₁)²]; section formula gives ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).
- Circles: a tangent is perpendicular to the radius at the point of contact.
- Trigonometry: sin²θ + cos²θ = 1; angles of elevation and depression are measured from the horizontal.
- Statistics: use class marks for grouped mean; median uses n/2 and cumulative frequency; mode uses the modal class.
Worked example
Solve x² − 5x + 6 = 0. Factorise: two numbers with product 6 and sum −5 are −2 and −3, so (x − 2)(x − 3) = 0, giving x = 2 or x = 3. Check with D = 25 − 24 = 1 > 0, so two distinct real roots are expected. Substituting x = 2: 4 − 10 + 6 = 0.
Traps that cost marks
Do not drop the negative sign in the quadratic formula; do not mix class limits with class boundaries in the median; convert a depression angle to the correct triangle; state units (cm, cm², cm³); and show construction arcs and steps rather than only the final figure.