1. Solve: $x^2 - 5x + 6 = 0$ - Factorize: $(x-2)(x-3)=0$ - Roots: $x=2,3$ - Answer: B) 2,3 2. Solve: $x^2 + 2x - 15 = 0$ - Factorize: $(x+5)(x-3)=0$ - Roots: $x=-5,3$ - Answer: C) -5,-3 (Check sign: correct roots are -5 and 3, so option B is 5,-3, option C is -5,-3; correct roots are -5 and 3, so none exactly match, but closest is C) 3. Find roots: $x^2 - 9 = 0$ - Factorize: $(x-3)(x+3)=0$ - Roots: $x=\pm 3$ - Answer: A) ±3 4. Solve: $2x^2 - 7x + 3 = 0$ - Use quadratic formula: $x=\frac{7 \pm \sqrt{49 - 24}}{4} = \frac{7 \pm 5}{4}$ - Roots: $x=3$, $x=\frac{1}{2}$ - Answer: B) 1/2,3 5. Solve: $x^2 + x - 12 = 0$ - Factorize: $(x+4)(x-3)=0$ - Roots: $x=-4,3$ - Answer: B) 4,-3 (Check sign: roots are -4 and 3, so option A is 3,-4, option B is 4,-3; correct roots are -4 and 3, so option A) 6. Use quadratic formula: $x^2 - 4x + 1 = 0$ - $x=\frac{4 \pm \sqrt{16 - 4}}{2} = 2 \pm \sqrt{3}$ - Answer: A) 2±√3 7. Solve: $x^2 - 2x - 8 = 0$ - Factorize: $(x-4)(x+2)=0$ - Roots: $x=4,-2$ - Answer: D) 2,4 (Check sign: roots are 4 and -2, so option A is -2,4, option D is 2,4; correct roots are 4 and -2, so option A) 8. Solve: $3x^2 - 12 = 0$ - $3x^2=12 \Rightarrow x^2=4 \Rightarrow x=\pm 2$ - Answer: A) ±2 9. Solve: $x^2 + 6x + 9 = 0$ - Factorize: $(x+3)^2=0$ - Root: $x=-3$ - Answer: A) -3 10. Solve: $5x^2 - 20x = 0$ - Factorize: $5x(x-4)=0$ - Roots: $x=0,4$ - Answer: A) 0,4 11. Solve: $x^2 - 16 = 0$ - Factorize: $(x-4)(x+4)=0$ - Roots: $x=\pm 4$ - Answer: A) ±4 12. Solve: $4x^2 + 4x + 1 = 0$ - Factorize: $(2x+1)^2=0$ - Root: $x=-\frac{1}{2}$ - Answer: A) -1/2 13. Solve: $x^2 + 10x + 25 = 0$ - Factorize: $(x+5)^2=0$ - Root: $x=-5$ - Answer: A) -5 14. Solve: $x^2 - x - 2 = 0$ - Factorize: $(x-2)(x+1)=0$ - Roots: $x=2,-1$ - Answer: A) 2,-1 15. Solve: $2x^2 + x - 3 = 0$ - Use quadratic formula: $x=\frac{-1 \pm \sqrt{1 + 24}}{4} = \frac{-1 \pm 5}{4}$ - Roots: $x=1, -\frac{3}{2}$ - Answer: A) 1,-3/2 16. Solve system: $2x + y = 7$, $x - y = 1$ - Add: $3x = 8 \Rightarrow x=\frac{8}{3}$ - Substitute: $2(\frac{8}{3}) + y = 7 \Rightarrow y = 7 - \frac{16}{3} = \frac{5}{3}$ - None of options match exactly; closest integer option is A) (2,3) 17. Solve system: $x + y = 6$, $x - y = 2$ - Add: $2x=8 \Rightarrow x=4$ - Substitute: $4 + y=6 \Rightarrow y=2$ - Answer: A) (4,2) 18. Solve system: $3x - y = 5$, $x + y = 7$ - Add: $4x=12 \Rightarrow x=3$ - Substitute: $3 + y=7 \Rightarrow y=4$ - Answer: A) (3,4) 19. Solve system: $4x + 2y = 10$, $2x - y = 1$ - Multiply second by 2: $4x - 2y = 2$ - Add: $8x = 12 \Rightarrow x=\frac{3}{2}$ - Substitute: $2(\frac{3}{2}) - y = 1 \Rightarrow 3 - y = 1 \Rightarrow y=2$ - None of options match exactly; closest is C) (3,2) 20. Solve system: $x - 3y = 4$, $2x + y = 7$ - Multiply second by 3: $6x + 3y = 21$ - Add to first: $7x = 25 \Rightarrow x=\frac{25}{7}$ - Substitute: $\frac{25}{7} - 3y = 4 \Rightarrow y=\frac{3}{7}$ - None of options match exactly; closest is A) (2,-1) 21. Solve system: $5x + y = 11$, $x - y = 1$ - Add: $6x = 12 \Rightarrow x=2$ - Substitute: $5(2) + y = 11 \Rightarrow y=1$ - Answer: A) (2,1) 22. Solve system: $2x + 3y = 12$, $4x - 3y = 6$ - Add: $6x = 18 \Rightarrow x=3$ - Substitute: $2(3) + 3y = 12 \Rightarrow 6 + 3y = 12 \Rightarrow y=2$ - Answer: A) (3,2) 23. Solve system: $x + 4y = 9$, $x - y = 4$ - Subtract second from first: $5y = 5 \Rightarrow y=1$ - Substitute: $x - 1 = 4 \Rightarrow x=5$ - Answer: A) (5,1) 24. Solve system: $6x - y = 11$, $2x + y = 7$ - Add: $8x = 18 \Rightarrow x=\frac{9}{4}$ - Substitute: $2(\frac{9}{4}) + y = 7 \Rightarrow \frac{9}{2} + y = 7 \Rightarrow y=\frac{5}{2}$ - None of options match exactly; closest is A) (2,3) 25. Solve system: $x + y = 10$, $x - 2y = 1$ - Multiply first by 2: $2x + 2y = 20$ - Add to second: $3x = 21 \Rightarrow x=7$ - Substitute: $7 + y = 10 \Rightarrow y=3$ - Answer: A) (7,3) 26. Solve system: $3x + 2y = 12$, $x - y = 1$ - Multiply second by 2: $2x - 2y = 2$ - Subtract from first: $(3x + 2y) - (2x - 2y) = 12 - 2 \Rightarrow x + 4y = 10$ - Substitute $x = y + 1$ from second: $(y + 1) + 4y = 10 \Rightarrow 5y = 9 \Rightarrow y=\frac{9}{5}$ - Substitute back: $x = \frac{9}{5} + 1 = \frac{14}{5}$ - None of options match exactly; closest is B) (3,2) 27. Solve system: $7x - y = 20$, $x + y = 8$ - Add: $8x = 28 \Rightarrow x=3.5$ - Substitute: $3.5 + y = 8 \Rightarrow y=4.5$ - None of options match exactly; closest is A) (3,5) 28. Solve system: $9x + y = 28$, $x - y = 2$ - Add: $10x = 30 \Rightarrow x=3$ - Substitute: $9(3) + y = 28 \Rightarrow 27 + y = 28 \Rightarrow y=1$ - Answer: A) (3,1) 29. Solve system: $x + 2y = 4$, $2x - y = 5$ - Multiply first by 1: $x + 2y = 4$ - Multiply second by 2: $4x - 2y = 10$ - Add: $5x = 14 \Rightarrow x=\frac{14}{5}$ - Substitute: $\frac{14}{5} + 2y = 4 \Rightarrow 2y = 4 - \frac{14}{5} = \frac{6}{5} \Rightarrow y=\frac{3}{5}$ - None of options match exactly; closest is A) (2,1) 30. Solve system: $5x + 3y = 19$, $x - y = 1$ - Multiply second by 3: $3x - 3y = 3$ - Add: $8x = 22 \Rightarrow x=\frac{11}{4}$ - Substitute: $\frac{11}{4} - y = 1 \Rightarrow y=\frac{7}{4}$ - None of options match exactly; closest is B) (3,2) 31. Expand: $(x+2)(x+3)$ - $x^2 + 3x + 2x + 6 = x^2 + 5x + 6$ - Answer: A) x²+5x+6 32. Factorise: $x^2 + 7x + 12$ - Factors of 12 that sum to 7: 3 and 4 - $(x+3)(x+4)$ - Answer: A) (x+3)(x+4) 33. Expand: $(2x - 3)(x + 4)$ - $2x^2 + 8x - 3x - 12 = 2x^2 + 5x - 12$ - Answer: A) 2x²+5x-12 34. Factorise: $x^2 - 6x + 9$ - Perfect square: $(x - 3)^2$ - Answer: A) (x-3)² 35. Divide: $(x^3 + 3x^2 + 2x) ÷ x$ - $x^2 + 3x + 2$ - Answer: A) x²+3x+2 36. Expand: $(x - 5)(x - 1)$ - $x^2 - x - 5x + 5 = x^2 - 6x + 5$ - Answer: A) x²-6x+5 37. Factorise: $x^2 - 2x - 15$ - Factors of -15 that sum to -2: -5 and 3 - $(x - 5)(x + 3)$ - Answer: A) (x-5)(x+3) 38. Expand: $(3x + 1)(x - 4)$ - $3x^2 - 12x + x - 4 = 3x^2 - 11x - 4$ - Answer: A) 3x²-11x-4 39. Expand: $(2x + 5)^2$ - $4x^2 + 20x + 25$ - Answer: A) 4x²+20x+25 40. Factorise: $x^3 - x$ - $x(x^2 - 1) = x(x - 1)(x + 1)$ - Answer: A) x(x-1)(x+1) 41. Expand: $(x + 7)(x - 2)$ - $x^2 - 2x + 7x - 14 = x^2 + 5x - 14$ - Answer: A) x²+5x-14 42. Factorise: $x^2 - 25$ - Difference of squares: $(x - 5)(x + 5)$ - Answer: A) (x-5)(x+5) 43. Expand: $(x - 4)(2x - 3)$ - $2x^2 - 3x - 8x + 12 = 2x^2 - 11x + 12$ - Answer: A) 2x²-11x+12 44. Expand: $3x(x + 5)$ - $3x^2 + 15x$ - Answer: A) 3x²+15x 45. Factorise: $x^3 + 2x^2 - x - 2$ - Group: $x^2(x + 2) - 1(x + 2) = (x + 2)(x^2 - 1) = (x + 2)(x - 1)(x + 1)$ - Answer: A) (x+2)(x²-1) 46. A die is thrown. $P(4) = \frac{1}{6}$ - Answer: A) 1/6 47. Toss a coin. $P(head) = \frac{1}{2}$ - Answer: A) 1/2 48. Bag: 3 red, 2 blue. $P(red) = \frac{3}{5}$ - Answer: C) 3/5 49. Pick a letter from 'MATH'. Vowels: A - $P(vowel) = \frac{1}{4}$ - Answer: C) 1/4 50. Cards numbered 1–10. Even numbers: 2,4,6,8,10 (5 cards) - $P(even) = \frac{5}{10} = \frac{1}{2}$ - Answer: A) 1/2 51. Toss 2 coins. $P(2 heads) = \frac{1}{4}$ - Answer: B) 1/4 52. A die rolled. Odd numbers: 1,3,5 (3 numbers) - $P(odd) = \frac{3}{6} = \frac{1}{2}$ - Answer: A) 1/2 53. Bag: 5 red, 5 blue. $P(blue) = \frac{5}{10} = \frac{1}{2}$ - Answer: A) 1/2 54. Box: 8 pens, 2 bad. Good pens = 8 - Total = 10 - $P(good) = \frac{8}{10} = \frac{4}{5}$ - Answer: A) 4/5 55. Bag: 2 white, 3 black. $P(white) = \frac{2}{5}$ - Answer: D) 2/5 56. Pick 1–20. Multiples of 5: 5,10,15,20 (4 numbers) - $P = \frac{4}{20} = \frac{1}{5}$ - Answer: B) 1/5 57. Box: 6 green, 4 yellow. $P(green) = \frac{6}{10} = \frac{3}{5}$ - Answer: C) 3/5 58. Toss 3 coins. $P(3 heads) = \frac{1}{8}$ - Answer: A) 1/8 59. Pick from 'PROBABILITY'. Letters: 11 total, P appears once - $P(P) = \frac{1}{11}$ - Answer: B) 1/11 60. Pick 1–6. Numbers >4: 5,6 (2 numbers) - $P = \frac{2}{6} = \frac{1}{3}$ - Answer: A) 1/3