Class 9 Maths — Term 1 Unit Test
Time: 2.5 Hours | Marks: 60
Section A — 1 Mark (1 × 10 = 10)
1. Define a rational number. 2. Is √3 rational or irrational? 3. What is the decimal expansion of 1/3? 4. What is the cardinality of the set {1, 2, 3, 4, 5}? 5. What is an empty set? 6. Define a polynomial. 7. What is the degree of the polynomial 3x⁴ − 2x² + 5? 8. State the Remainder Theorem. 9. State the Factor Theorem. 10. Simplify: (a + b)²
Section B — 3 Mark (3 × 6 = 18)
(Choose 6 of 7)
1. Show that √5 is irrational. 2. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A∪B, A∩B, and A−B. 3. Draw a Venn diagram for two sets A and B where A∩B ≠ ∅. Shade A∩B. 4. If f(x) = x³ − 6x² + 11x − 6, find f(1), f(2), and f(3). 5. Factorise: x² − 5x + 6 6. Expand: (2a + 3b)² 7. Using the Factor Theorem, determine if (x − 2) is a factor of x³ − 3x + 2.
Section C — 5 Mark (5 × 4 = 20)
(Choose 4 of 5)
1. Prove that √2 is irrational. 2. In a class of 40 students, 25 play cricket, 18 play football, and 10 play both. Find how many play (a) only cricket, (b) only football, (c) neither. 3. Factorise completely: x³ − 6x² + 11x − 6. [Hint: x = 1 is a root] 4. Expand (a + b + c)² and verify with a = 1, b = 2, c = 3. 5. If p(x) = x³ − 3x² + 3x − 1, find p(0), p(1), p(−1), and p(2). What do you notice?
Section D — Application (1 × 12 = 12)
D1. Set Language Word Problem (6 marks): In a survey of 100 people: 65 like tea, 45 like coffee, and 20 like both. Using a Venn diagram, find: (a) How many like tea only? [45] (b) How many like coffee only? [25] (c) How many like neither? [10] (d) How many like at least one? [90] (e) How many like tea or coffee? [90] (f) How many like exactly one? [70]
D2. Factorisation (6 marks, 2 each): Factorise: 1. x² − 9 [= (x+3)(x−3)] 2. 4x² − 12x + 9 [= (2x−3)²] 3. x³ + 8 [= (x+2)(x²−2x+4)]
End of Term 1 Unit Test