Tamil Nadu Class 9 Maths Practice Drill — Samacheer Kalvi

Section 1: Real Numbers — Quick Drill (10 questions)

1. Classify: 2/3, √2, 0, −5, π, 0.333..., √9, √8 (rational or irrational) 2. Between which two integers does √17 lie? 3. Write 0.252525... as a fraction. [25/99] 4. Simplify: √12 + √48 [= 2√3 + 4√3 = 6√3] 5. Rationalise: 1/(√5 + √3) [= (√5−√3)/2] 6. Find: (√5 + √3)(√5 − √3) [= 5 − 3 = 2] 7. Is 0 a rational number? [Yes — 0 = 0/1] 8. Write √8 in simplest radical form. [2√2] 9. Find: (2√3)² [= 12] 10. Is π rational or irrational? [Irrational — non-terminating, non-repeating]

Section 2: Set Language — Quick Drill (10 questions)

1. If A = {1,2,3} and B = {2,3,4}, find A∩B. [{2,3}] 2. Find A∪B for the same sets. [{1,2,3,4}] 3. Find A-B. [{1}] 4. Find B-A. [{4}] 5. If U = {1,2,3,4,5} and A = {1,3,5}, find A'. [{2,4}] 6. State De Morgan's first law. [(A∪B)' = A'∩B'] 7. If n(A) = 15, n(B) = 12, n(A∩B) = 5, find n(A∪B). [22] 8. What is a power set of {a,b}? [{∅, {a}, {b}, {a,b}}] 9. If A ⊆ B, what is A∩B? [A] 10. If A ⊆ B, what is A∪B? [B]

Section 3: Algebra — Quick Drill (10 questions)

1. Evaluate f(2) if f(x) = x² − 3x + 2. [0] 2. Find the remainder when x³ − 2x + 1 is divided by (x−1). [0] 3. Is (x+1) a factor of x³ + 2x² − x − 2? Check: f(−1) [= −1+2+1−2 = 0 → Yes] 4. Expand: (a−b)² [= a²−2ab+b²] 5. Factorise: x²−16 [= (x+4)(x−4)] 6. Expand: (x+1)(x−1) [= x²−1] 7. Factorise: 2x²+5x+3 [= (2x+3)(x+1)] 8. Find the degree of 5x³ − 2x + 7. [3] 9. Factorise: x³ − 8 [= (x−2)(x²+2x+4)] 10. If f(x) = x³, find f(−2). [−8]

Section 4: Coordinate Geometry — Quick Drill (10 questions)

1. Plot (−2, 3) — which quadrant? [Quadrant II] 2. Distance between (0,0) and (5,12)? [13] 3. Midpoint of (2,4) and (8,10)? [(5,7)] 4. Distance between (1,1) and (4,5)? [5] 5. What is the x-axis in coordinate terms? [y = 0] 6. Is (0,5) on the x-axis or y-axis? [y-axis] 7. Distance between (3,0) and (0,4)? [5] 8. Midpoint of (0,0) and (6,8)? [(3,4)] 9. In which quadrant is (−5, −3)? [Quadrant III] 10. Plot (2, −4) — which quadrant? [Quadrant IV]

Section 5: Trigonometry — Quick Drill (10 questions)

1. sin 90° = ? [1] 2. cos 0° = ? [1] 3. tan 45° = ? [1] 4. sin 30° + cos 60° = ? [1/2 + 1/2 = 1] 5. If sin θ = 5/13, find cos θ. [12/13] 6. sin²45° + cos²45° = ? [1] 7. tan 60° = ? [√3] 8. sec²θ − tan²θ = ? [1] 9. If cos θ = 1/2, what is θ? [60°] 10. sin 0° = ? [0]

Section 6: Statistics and Probability — Quick Drill (10 questions)

1. Mean of 4, 7, 9, 11, 14 = ? [9] 2. Median of 3, 5, 7, 9, 11 = ? [7] 3. Mode of 2, 3, 3, 4, 5, 3, 2 = ? [3] 4. P(head) when a coin is tossed = ? [1/2] 5. P(rolling a 3 on a die) = ? [1/6] 6. P(red ball) from bag of 3 red, 7 blue = ? [3/10] 7. What is the sum of all probabilities in sample space? [1] 8. Median of 2, 4, 6, 8, 10, 12 = ? [(6+8)/2 = 7] 9. P(impossible event) = ? [0] 10. P(certain event) = ? [1]

Section 7: Mensuration — Quick Drill (10 questions)

1. Area of rectangle: l=8, b=5 = ? [40 sq units] 2. Area of circle with r=7 = ? [154 sq units, π=22/7] 3. Volume of cube with side 3 cm = ? [27 cm³] 4. CSA of cylinder: r=2, h=5 = ? [2πrh = 20π cm²] 5. Volume of cylinder: r=3, h=4 = ? [36π cm³] 6. Surface area of sphere: r=7 = ? [616 cm²] 7. Volume of sphere: r=3 = ? [36π cm³] 8. Area of triangle: b=10, h=6 = ? [30 sq units] 9. Volume of cone: r=3, h=4 = ? [12π cm³] 10. TSA of cube with side 5 cm = ? [150 cm²]