Maths U1 and U2

Grade 9 Mathematics — Unit 1 & Unit 2

Knowt Practice Question Bank

🟢 UNIT 1 — Real Numbers, Intervals & Absolute Value

1. Write the set of real numbers between −3 and 8, including both endpoints, in interval notation.

2. Write the set of real numbers between 4 and 6, excluding both endpoints, in interval notation.

3. Write (x\geq -1) in interval notation.

4. Write ((-∞,-5]) as an inequality.

5. Represent ([1,3)) on a number line.

6. Represent ((-2,4)\cup[5,∞)) on a number line.

7. Find:
   [
   |−12|
   ]

8. Find:
   [
   |0|
   ]

9. Find:
   [
   |−\sqrt2|
   ]

10. Find:
    [
    |2-\sqrt8|
    ]

11. Find the distance between −7 and 5.

12. Find the distance between −20 and −8.

13. Solve:
    [
    |x|=8
    ]

14. Solve:
    [
    |x|=0
    ]

15. Solve:
    [
    |x|=-4
    ]

16. Solve:
    [
    |x|+3=14
    ]

17. Solve:
    [
    |x|-3=-2
    ]

18. True or False:
    [
    |a-b|=|b-a|
    ]

19. Explain why an absolute value can never be negative.

20. If two points on a number line are (a=-3) and (b=4), find (|a-b|).

🔵 UNIT 1 — Exponents & Radicals

21. Evaluate:
    [
    3^4
    ]

22. Evaluate:
    [
    (-2)^5
    ]

23. Evaluate:
    [
    (-3)^4
    ]

24. Write (2\times2\times2\times2\times2) using exponential notation.

25. Simplify:
    [
    a^3\cdot a^5
    ]

26. Simplify:
    [
    \frac{a^8}{a^3}
    ]

27. Simplify:
    [
    (a^4)^3
    ]

28. Simplify:
    [
    (ab)^5
    ]

29. Simplify:
    [
    \left(\frac ab\right)^4
    ]

30. Rewrite using positive exponents:
    [
    x^{-6}
    ]

31. Rewrite using negative exponents:
    [
    \frac1{y^4}
    ]

32. Simplify:
    [
    2^3\cdot2^4
    ]

33. Simplify:
    [
    \frac{5^7}{5^2}
    ]

34. Simplify:
    [
    (3^2)^4
    ]

35. Simplify:
    [
    \frac{x^5}{x^8}
    ]

36. Simplify:
    [
    2^{-3}
    ]

37. Simplify:
    [
    \frac{a^m}{a^n}
    ]

38. State the exponent rule used when multiplying powers with the same base.

39. State the exponent rule used when raising a power to another power.

40. State the exponent rule for a negative exponent.

🔴 UNIT 2 — Exponential Equations

41. Solve:
    [
    2^x=8
    ]

42. Solve:
    [
    3^x=27
    ]

43. Solve:
    [
    3^x=\frac1{27}
    ]

44. Solve:
    [
    3^x=81
    ]

45. Solve:
    [
    2^x=\frac18
    ]

46. Solve:
    [
    8^x=16
    ]

47. Solve:
    [
    2^{x+4}=32
    ]

48. Solve:
    [
    9^{x+4}=27
    ]

49. Solve:
    [
    5^{x-1}=125
    ]

50. Solve:
    [
    4^x=64
    ]

51. Solve:
    [
    27^x=9
    ]

52. Solve:
    [
    16^x=8
    ]

53. Solve:
    [
    2^{3x}=16
    ]

54. Solve:
    [
    3^{2x}=81
    ]

55. Solve:
    [
    4^{x+1}=64
    ]

56. Rewrite both sides using the same base and solve:
    [
    8^x=32
    ]

57. Rewrite both sides using the same base and solve:
    [
    27^x=\frac1{9}
    ]

58. Rewrite both sides using the same base and solve:
    [
    16^{x}=2
    ]

59. If
    [
    a^x=a^y,\qquad a>0,
    ]
    what can you conclude about (x) and (y)?

60. Explain the general method for solving an exponential equation when both sides can be written with the same base.

💀 BOSS ROUND — Mixed U1 + U2

61. Solve:
    [
    |2x-3|=7
    ]

62. Solve:
    [
    |3x+2|=5
    ]

63. Simplify completely:
    [
    \frac{2^5\cdot2^{-3}}{2^2}
    ]

64. Simplify completely:
    [
    \frac{(x^3)^2}{x^4}
    ]

65. Solve:
    [
    2^{x+1}=16
    ]

66. Solve:
    [
    3^{2x-1}=27
    ]

67. Solve:
    [
    4^x=\frac1{16}
    ]

68. Solve:
    [
    9^{x}=\frac1{27}
    ]

69. Find the distance between the points represented by (-\sqrt5) and (\sqrt5).

70. Solve:
    [
    |x-4|=9
    ]

71. Write the solution set of (x\leq3) in interval notation.

72. Write the interval ((-∞,2)) as an inequality.

73. Simplify:
    [
    \left(\frac{2^3}{2^5}\right)^2
    ]

74. Solve:
    [
    2^{2x+1}=32
    ]

75. Challenge: Solve
    [
    4^{x+1}=2^{3x-1}
    ]
    by expressing both sides with the same base.

76.