Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Number Systems — Real Numbers
| Exercise Type | Approach |
|---|---|
| Identify rational/irrational | Rational = p/q form (q≠0); Irrational = non-terminating, non-repeating |
| Represent on number line | Use nested intervals method for irrationals like √2, √3 |
| Operations on irrationals | Rationalise the denominator; use identities (a+b)(a-b) = a²-b² |
| Decimal expansion | Long division for converting fractions to decimals |
Set Language
| Exercise Type | Approach |
|---|---|
| Identify set type | Finite, Infinite, Empty, Singleton, Universal |
| Venn diagrams | Draw overlapping circles; label A, B, U; shade required region |
| Set operations | A∪B (all in A or B); A∩B (only in both); A' (everything NOT in A) |
| De Morgan's Laws | (A∪B)' = A'∩B'; (A∩B)' = A'∪B' |
| Word problems | Translate: "both A and B" = A∩B; "only A" = A-B; "neither" = (A∪B)' |
Algebra
| Exercise Type | Approach |
|---|---|
| Polynomial identification | Degree, coefficients, types (monomial/binomial/trinomial) |
| Remainder Theorem | f(a) = remainder when f(x) divided by (x-a) |
| Factor Theorem | (x-a) is a factor iff f(a) = 0 |
| Factorisation | Try: common factors → grouping → identities → middle term split |
| Algebraic identities | (a+b)² = a²+2ab+b²; (a-b)² = a²-2ab+b²; a²-b² = (a+b)(a-b) |
Coordinate Geometry
| Exercise Type | Approach |
|---|---|
| Plot points | Identify quadrant: (+,+)=I; (-,+)=II; (-,-)=III; (+,-)=IV |
| Distance formula | d = √[(x₂-x₁)² + (y₂-y₁)²] |
| Midpoint formula | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Section formula | P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) |
| Line graphing | Find two points (x=0 and y=0), join them |
Geometry
Lines and Angles
| Exercise Type | Approach |
|---|---|
| Angle pairs | Identify: supplementary, complementary, vertically opposite, alternate, corresponding |
| Parallel lines | Use: corresponding angles equal; alternate angles equal; co-interior angles supplementary |
| Proofs | Start from given → apply theorem → reach conclusion step by step |
Triangles
| Exercise Type | Approach |
|---|---|
| Congruence | List which criterion applies: SSS, SAS, ASA, AAS, RHS |
| Triangle properties | Exterior angle = sum of non-adjacent interior angles |
| Similarity | AA, SAS, SSS similarity criteria |
| Pythagoras | a² + b² = c² (apply and verify; know converse too) |
Mensuration
| Shape | Area Formula | Volume Formula |
|---|---|---|
| Rectangle | l × b | — |
| Triangle | ½ × b × h | — |
| Circle | πr² | — |
| Cuboid | 2(lb + bh + lh) [surface area] | l × b × h |
| Cube | 6a² [surface area] | a³ |
| Cylinder | 2πr(r+h) [total surface area] | πr²h |
| Cone | πr(r+l) [total surface area] | ⅓πr²h |
| Sphere | 4πr² | (4/3)πr³ |
Statistics and Probability
| Exercise Type | Approach |
|---|---|
| Mean | Sum of all values / number of values |
| Median | Middle value (odd n) or average of two middle values (even n) after arranging in order |
| Mode | Most frequently occurring value |
| Frequency table | Tally marks → frequency → cumulative frequency |
| Bar graph | Bars of equal width; height = frequency |
| Probability | P(event) = favourable outcomes / total outcomes (always between 0 and 1) |
Trigonometry
| Exercise Type | Approach |
|---|---|
| Find ratios | sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent |
| Standard angles | Memorise values for 0°, 30°, 45°, 60°, 90° |
| Prove identities | Start from one side only; use identities sin²θ + cos²θ = 1 |
| Applications | Draw diagram first; identify angle of elevation/depression; use tan = opposite/adjacent |
Frequently Asked Questions
Official solutions are available at tnschools.gov.in and in Samacheer Kalvi guide books. This map shows the correct approach for each exercise type.