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Pre-Calculus I — One Question at a Time

Pre-Calculus I — One Question at a Time

Practise 150 Pre-Calculus I multiple-choice questions covering sets, functions, algebraic equations, matrices, trigonometry and complex numbers. Work through one question at a time, check the correct answer with an explanation, and select Next Question to continue. This is self-paced practice without automatic scoring.

Before you practise: Read Pre-Calculus I study material and examples. You can also browse all 1,576 interactive MCQs.

Practice Set 1 · Question 1 of 150

Question 1. Which number is irrational?

  1. 3/7
  2. √2
  3. −4
  4. 0.25
Show Answer and Explanation

Correct answer: B. √2

√2 cannot be expressed as a ratio of two integers.

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Practice Set 1 · Question 2 of 150

Question 2. If A={1,2,3} and B={3,4}, what is A ∩ B?

  1. {1,2,3,4}
  2. {1,2}
  3. {3}
  4. ∅
Show Answer and Explanation

Correct answer: C. {3}

The intersection contains the common elements.

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Practice Set 1 · Question 3 of 150

Question 3. For f(x)=2x+3, find f(4).

  1. 7
  2. 8
  3. 11
  4. 14
Show Answer and Explanation

Correct answer: C. 11

Substitute x=4: 2×4+3=11.

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Practice Set 1 · Question 4 of 150

Question 4. Find the inverse of f(x)=3x−6.

  1. (x+6)/3
  2. 3x+6
  3. (x−6)/3
  4. x/3−6
Show Answer and Explanation

Correct answer: A. (x+6)/3

Solve y=3x−6 for x, obtaining x=(y+6)/3.

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Practice Set 1 · Question 5 of 150

Question 5. Find det([[2,1],[3,4]]).

  1. 11
  2. 5
  3. −5
  4. 8
Show Answer and Explanation

Correct answer: B. 5

For a 2×2 matrix, determinant is ad−bc=8−3=5.

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Practice Set 1 · Question 6 of 150

Question 6. What are the roots of x²−5x+6=0?

  1. −2 and −3
  2. 1 and 6
  3. 2 and 3
  4. −1 and −6
Show Answer and Explanation

Correct answer: C. 2 and 3

Factor as (x−2)(x−3)=0.

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Practice Set 1 · Question 7 of 150

Question 7. What is the remainder of x²+2x+1 divided by x−1?

  1. 0
  2. 2
  3. 3
  4. 4
Show Answer and Explanation

Correct answer: D. 4

The remainder theorem gives p(1)=1+2+1=4.

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Practice Set 1 · Question 8 of 150

Question 8. For x≠0,−1, what equals 1/[x(x+1)]?

  1. 1/x−1/(x+1)
  2. 1/x+1/(x+1)
  3. 1/(x+1)−1/x
  4. 1/x²
Show Answer and Explanation

Correct answer: A. 1/x−1/(x+1)

Combining 1/x−1/(x+1) gives 1/[x(x+1)].

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Practice Set 1 · Question 9 of 150

Question 9. What is the coefficient of x² in (1+x)⁴?

  1. 4
  2. 6
  3. 8
  4. 12
Show Answer and Explanation

Correct answer: B. 6

The coefficient equals C(4,2)=6.

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Practice Set 1 · Question 10 of 150

Question 10. Convert 180 degrees to radians.

  1. π/2
  2. 2π
  3. π
  4. π/4
Show Answer and Explanation

Correct answer: C. π

Multiply 180 by π/180 to obtain π radians.

Continue to Practice Set 2

Practice Set 2 · Question 11 of 150

Question 11. What is i², where i is the imaginary unit?

  1. 1
  2. −1
  3. i
  4. 0
Show Answer and Explanation

Correct answer: B. −1

The imaginary unit satisfies i²=−1.

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Practice Set 2 · Question 12 of 150

Question 12. What is the modulus of 3+4i?

  1. 3
  2. 4
  3. 5
  4. 7
Show Answer and Explanation

Correct answer: C. 5

The modulus is √(3²+4²)=5.

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Practice Set 2 · Question 13 of 150

Question 13. How many subsets does a set with four elements have?

  1. 4
  2. 8
  3. 16
  4. 24
Show Answer and Explanation

Correct answer: C. 16

A set of n elements has 2ⁿ subsets, so 2⁴=16.

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Practice Set 2 · Question 14 of 150

Question 14. What is the rank of [[1,2],[2,4]]?

  1. 0
  2. 1
  3. 2
  4. 4
Show Answer and Explanation

Correct answer: B. 1

The second row is twice the first, so only one row is independent.

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Practice Set 2 · Question 15 of 150

Question 15. Solve x+y=7 and x−y=3. Find x.

  1. 2
  2. 3
  3. 4
  4. 5
Show Answer and Explanation

Correct answer: D. 5

Adding gives 2x=10, so x=5.

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Practice Set 2 · Question 16 of 150

Question 16. If p(x)=x³−2x+1, what is p(−1)?

  1. −2
  2. 0
  3. 2
  4. 4
Show Answer and Explanation

Correct answer: C. 2

p(−1)=−1+2+1=2.

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Practice Set 2 · Question 17 of 150

Question 17. For x≠1,−1, which decomposition equals 2/(x²−1)?

  1. 1/(x−1)−1/(x+1)
  2. 1/(x−1)+1/(x+1)
  3. 2/(x−1)
  4. 2/(x+1)
Show Answer and Explanation

Correct answer: A. 1/(x−1)−1/(x+1)

Subtracting gives [(x+1)−(x−1)]/[(x−1)(x+1)]=2/(x²−1).

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Practice Set 2 · Question 18 of 150

Question 18. Which statement is the inductive step in a proof for all integers n≥1?

  1. Prove only n=1
  2. Assume P(k) and prove P(k+1)
  3. Assume P(k+1) without proof
  4. Check n=1,2,3 only
Show Answer and Explanation

Correct answer: B. Assume P(k) and prove P(k+1)

Induction proves a base case and the implication P(k)⇒P(k+1).

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Practice Set 2 · Question 19 of 150

Question 19. What is sin(π/6)?

  1. 0
  2. 1
  3. 1/2
  4. √3/2
Show Answer and Explanation

Correct answer: C. 1/2

The standard sine value at 30 degrees is 1/2.

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Practice Set 2 · Question 20 of 150

Question 20. What is cos²θ+sin²θ for every real θ?

  1. 0
  2. 1
  3. 2
  4. cos 2θ
Show Answer and Explanation

Correct answer: B. 1

The Pythagorean trigonometric identity equals 1.

Continue to Practice Set 3

Practice Set 3 · Question 21 of 150

Question 21. What is the conjugate of 2−5i?

  1. 2+5i
  2. 2−5i
  3. −2+5i
  4. −2−5i
Show Answer and Explanation

Correct answer: A. 2+5i

The conjugate reverses the sign of the imaginary part.

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Practice Set 3 · Question 22 of 150

Question 22. What is (1+i)(1−i)?

  1. 0
  2. 1
  3. 2
  4. 2i
Show Answer and Explanation

Correct answer: C. 2

By difference of squares, 1−i²=2.

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Practice Set 3 · Question 23 of 150

Question 23. What is the domain of f(x)=1/(x−3)?

  1. All real numbers
  2. All real numbers except 3
  3. Only x>3
  4. Only x≥3
Show Answer and Explanation

Correct answer: B. All real numbers except 3

The denominator must not equal zero.

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Practice Set 3 · Question 24 of 150

Question 24. For A={1,2} and B={2,3}, find A∪B.

  1. {2}
  2. {1,3}
  3. {1,2,2,3}
  4. {1,2,3}
Show Answer and Explanation

Correct answer: D. {1,2,3}

The union contains distinct elements from either set.

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Practice Set 3 · Question 25 of 150

Question 25. For [[1,2],[0,1]] × [[2,0],[3,4]], what is the top-left entry?

  1. 2
  2. 5
  3. 8
  4. 10
Show Answer and Explanation

Correct answer: C. 8

The first row dot first column is 1×2+2×3=8.

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Practice Set 3 · Question 26 of 150

Question 26. Find the discriminant of 2x²−4x+3=0.

  1. −8
  2. 8
  3. 16
  4. −4
Show Answer and Explanation

Correct answer: A. −8

b²−4ac=16−24=−8.

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Practice Set 3 · Question 27 of 150

Question 27. If x+2 divides p(x), which statement holds?

  1. p(2)=0
  2. p(−2)=0
  3. p(0)=2
  4. p'(2)=0
Show Answer and Explanation

Correct answer: B. p(−2)=0

The factor theorem requires p(−2)=0.

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Practice Set 3 · Question 28 of 150

Question 28. Find the coefficient of x³ in (1+x)⁵.

  1. 5
  2. 6
  3. 10
  4. 20
Show Answer and Explanation

Correct answer: C. 10

C(5,3)=10.

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Practice Set 3 · Question 29 of 150

Question 29. What is tan(π/4)?

  1. 0
  2. 1/2
  3. √3
  4. 1
Show Answer and Explanation

Correct answer: D. 1

The tangent at 45° is 1.

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Practice Set 3 · Question 30 of 150

Question 30. To prove P(n) for all n≥1 by induction, what base case is needed?

  1. P(1)
  2. P(2) only
  3. P(100)
  4. P(n+2)
Show Answer and Explanation

Correct answer: A. P(1)

The base statement P(1) starts induction.

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Practice Set 4 · Question 31 of 150

Question 31. Evaluate f(1) for f(x)=2x+3.

  1. 4
  2. 8
  3. 5
  4. 6
Show Answer and Explanation

Correct answer: C. 5

Substitute x=1: 2×1+3=5.

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Practice Set 4 · Question 32 of 150

Question 32. Evaluate f(2) for f(x)=3x+4.

  1. 13
  2. 10
  3. 11
  4. 9
Show Answer and Explanation

Correct answer: B. 10

Substitute x=2: 3×2+4=10.

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Practice Set 4 · Question 33 of 150

Question 33. Evaluate f(3) for f(x)=4x+5.

  1. 17
  2. 18
  3. 16
  4. 20
Show Answer and Explanation

Correct answer: A. 17

Substitute x=3: 4×3+5=17.

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Practice Set 4 · Question 34 of 150

Question 34. Evaluate f(4) for f(x)=5x+6.

  1. 27
  2. 25
  3. 29
  4. 26
Show Answer and Explanation

Correct answer: D. 26

Substitute x=4: 5×4+6=26.

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Practice Set 4 · Question 35 of 150

Question 35. Evaluate f(5) for f(x)=6x+7.

  1. 36
  2. 40
  3. 37
  4. 38
Show Answer and Explanation

Correct answer: C. 37

Substitute x=5: 6×5+7=37.

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Practice Set 4 · Question 36 of 150

Question 36. Evaluate f(6) for f(x)=7x+8.

  1. 53
  2. 50
  3. 51
  4. 49
Show Answer and Explanation

Correct answer: B. 50

Substitute x=6: 7×6+8=50.

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Practice Set 4 · Question 37 of 150

Question 37. Evaluate f(7) for f(x)=8x+9.

  1. 65
  2. 66
  3. 64
  4. 68
Show Answer and Explanation

Correct answer: A. 65

Substitute x=7: 8×7+9=65.

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Practice Set 4 · Question 38 of 150

Question 38. Evaluate f(8) for f(x)=9x+10.

  1. 83
  2. 81
  3. 85
  4. 82
Show Answer and Explanation

Correct answer: D. 82

Substitute x=8: 9×8+10=82.

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Practice Set 4 · Question 39 of 150

Question 39. Evaluate f(9) for f(x)=10x+11.

  1. 100
  2. 104
  3. 101
  4. 102
Show Answer and Explanation

Correct answer: C. 101

Substitute x=9: 10×9+11=101.

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Practice Set 4 · Question 40 of 150

Question 40. Evaluate f(10) for f(x)=11x+12.

  1. 125
  2. 122
  3. 123
  4. 121
Show Answer and Explanation

Correct answer: B. 122

Substitute x=10: 11×10+12=122.

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Practice Set 5 · Question 41 of 150

Question 41. Find the sum of the roots of (x−1)(x−4)=0.

  1. 5
  2. 6
  3. 4
  4. 8
Show Answer and Explanation

Correct answer: A. 5

The roots are 1 and 4; their sum is 5.

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Practice Set 5 · Question 42 of 150

Question 42. Find the sum of the roots of (x−2)(x−5)=0.

  1. 8
  2. 6
  3. 10
  4. 7
Show Answer and Explanation

Correct answer: D. 7

The roots are 2 and 5; their sum is 7.

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Practice Set 5 · Question 43 of 150

Question 43. Find the sum of the roots of (x−3)(x−6)=0.

  1. 8
  2. 12
  3. 9
  4. 10
Show Answer and Explanation

Correct answer: C. 9

The roots are 3 and 6; their sum is 9.

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Practice Set 5 · Question 44 of 150

Question 44. Find the sum of the roots of (x−4)(x−7)=0.

  1. 14
  2. 11
  3. 12
  4. 10
Show Answer and Explanation

Correct answer: B. 11

The roots are 4 and 7; their sum is 11.

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Practice Set 5 · Question 45 of 150

Question 45. Find the sum of the roots of (x−5)(x−8)=0.

  1. 13
  2. 14
  3. 12
  4. 16
Show Answer and Explanation

Correct answer: A. 13

The roots are 5 and 8; their sum is 13.

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Practice Set 5 · Question 46 of 150

Question 46. Find the sum of the roots of (x−6)(x−9)=0.

  1. 16
  2. 14
  3. 18
  4. 15
Show Answer and Explanation

Correct answer: D. 15

The roots are 6 and 9; their sum is 15.

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Practice Set 5 · Question 47 of 150

Question 47. Find the sum of the roots of (x−7)(x−10)=0.

  1. 16
  2. 20
  3. 17
  4. 18
Show Answer and Explanation

Correct answer: C. 17

The roots are 7 and 10; their sum is 17.

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Practice Set 5 · Question 48 of 150

Question 48. Find the sum of the roots of (x−8)(x−11)=0.

  1. 22
  2. 19
  3. 20
  4. 18
Show Answer and Explanation

Correct answer: B. 19

The roots are 8 and 11; their sum is 19.

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Practice Set 5 · Question 49 of 150

Question 49. Find the sum of the roots of (x−9)(x−12)=0.

  1. 21
  2. 22
  3. 20
  4. 24
Show Answer and Explanation

Correct answer: A. 21

The roots are 9 and 12; their sum is 21.

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Practice Set 5 · Question 50 of 150

Question 50. Find the sum of the roots of (x−10)(x−13)=0.

  1. 24
  2. 22
  3. 26
  4. 23
Show Answer and Explanation

Correct answer: D. 23

The roots are 10 and 13; their sum is 23.

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Practice Set 6 · Question 51 of 150

Question 51. Compute det([[2,1],[2,5]]).

  1. 7
  2. 11
  3. 8
  4. 9
Show Answer and Explanation

Correct answer: C. 8

Use ad−bc: 2×5−1×2=8.

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Practice Set 6 · Question 52 of 150

Question 52. Compute det([[3,2],[2,6]]).

  1. 17
  2. 14
  3. 15
  4. 13
Show Answer and Explanation

Correct answer: B. 14

Use ad−bc: 3×6−2×2=14.

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Practice Set 6 · Question 53 of 150

Question 53. Compute det([[4,3],[2,7]]).

  1. 22
  2. 23
  3. 21
  4. 25
Show Answer and Explanation

Correct answer: A. 22

Use ad−bc: 4×7−3×2=22.

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Practice Set 6 · Question 54 of 150

Question 54. Compute det([[5,4],[2,8]]).

  1. 33
  2. 31
  3. 35
  4. 32
Show Answer and Explanation

Correct answer: D. 32

Use ad−bc: 5×8−4×2=32.

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Practice Set 6 · Question 55 of 150

Question 55. Compute det([[6,5],[2,9]]).

  1. 43
  2. 47
  3. 44
  4. 45
Show Answer and Explanation

Correct answer: C. 44

Use ad−bc: 6×9−5×2=44.

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Practice Set 6 · Question 56 of 150

Question 56. Compute det([[7,6],[2,10]]).

  1. 61
  2. 58
  3. 59
  4. 57
Show Answer and Explanation

Correct answer: B. 58

Use ad−bc: 7×10−6×2=58.

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Practice Set 6 · Question 57 of 150

Question 57. Compute det([[8,7],[2,11]]).

  1. 74
  2. 75
  3. 73
  4. 77
Show Answer and Explanation

Correct answer: A. 74

Use ad−bc: 8×11−7×2=74.

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Practice Set 6 · Question 58 of 150

Question 58. Compute det([[9,8],[2,12]]).

  1. 93
  2. 91
  3. 95
  4. 92
Show Answer and Explanation

Correct answer: D. 92

Use ad−bc: 9×12−8×2=92.

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Practice Set 6 · Question 59 of 150

Question 59. Compute det([[10,9],[2,13]]).

  1. 111
  2. 115
  3. 112
  4. 113
Show Answer and Explanation

Correct answer: C. 112

Use ad−bc: 10×13−9×2=112.

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Practice Set 6 · Question 60 of 150

Question 60. Compute det([[11,10],[2,14]]).

  1. 137
  2. 134
  3. 135
  4. 133
Show Answer and Explanation

Correct answer: B. 134

Use ad−bc: 11×14−10×2=134.

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Practice Set 7 · Question 61 of 150

Question 61. How many subsets are there in a set containing 3 distinct elements?

  1. 8
  2. 9
  3. 7
  4. 11
Show Answer and Explanation

Correct answer: A. 8

A set of n elements has 2^n subsets, giving 2^3=8.

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Practice Set 7 · Question 62 of 150

Question 62. How many subsets are there in a set containing 4 distinct elements?

  1. 17
  2. 15
  3. 19
  4. 16
Show Answer and Explanation

Correct answer: D. 16

A set of n elements has 2^n subsets, giving 2^4=16.

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Practice Set 7 · Question 63 of 150

Question 63. How many subsets are there in a set containing 5 distinct elements?

  1. 31
  2. 35
  3. 32
  4. 33
Show Answer and Explanation

Correct answer: C. 32

A set of n elements has 2^n subsets, giving 2^5=32.

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Practice Set 7 · Question 64 of 150

Question 64. How many subsets are there in a set containing 6 distinct elements?

  1. 67
  2. 64
  3. 65
  4. 63
Show Answer and Explanation

Correct answer: B. 64

A set of n elements has 2^n subsets, giving 2^6=64.

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Practice Set 7 · Question 65 of 150

Question 65. How many subsets are there in a set containing 7 distinct elements?

  1. 128
  2. 129
  3. 127
  4. 131
Show Answer and Explanation

Correct answer: A. 128

A set of n elements has 2^n subsets, giving 2^7=128.

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Practice Set 7 · Question 66 of 150

Question 66. How many subsets are there in a set containing 8 distinct elements?

  1. 257
  2. 255
  3. 259
  4. 256
Show Answer and Explanation

Correct answer: D. 256

A set of n elements has 2^n subsets, giving 2^8=256.

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Practice Set 7 · Question 67 of 150

Question 67. How many subsets are there in a set containing 9 distinct elements?

  1. 511
  2. 515
  3. 512
  4. 513
Show Answer and Explanation

Correct answer: C. 512

A set of n elements has 2^n subsets, giving 2^9=512.

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Practice Set 7 · Question 68 of 150

Question 68. How many subsets are there in a set containing 10 distinct elements?

  1. 1027
  2. 1024
  3. 1025
  4. 1023
Show Answer and Explanation

Correct answer: B. 1024

A set of n elements has 2^n subsets, giving 2^10=1024.

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Practice Set 7 · Question 69 of 150

Question 69. How many subsets are there in a set containing 11 distinct elements?

  1. 2048
  2. 2049
  3. 2047
  4. 2051
Show Answer and Explanation

Correct answer: A. 2048

A set of n elements has 2^n subsets, giving 2^11=2048.

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Practice Set 7 · Question 70 of 150

Question 70. How many subsets are there in a set containing 12 distinct elements?

  1. 4097
  2. 4095
  3. 4099
  4. 4096
Show Answer and Explanation

Correct answer: D. 4096

A set of n elements has 2^n subsets, giving 2^12=4096.

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Practice Set 8 · Question 71 of 150

Question 71. What is the coefficient of x² in (1+x)^4?

  1. 5
  2. 9
  3. 6
  4. 7
Show Answer and Explanation

Correct answer: C. 6

The binomial coefficient C(4,2)=6.

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Practice Set 8 · Question 72 of 150

Question 72. What is the coefficient of x² in (1+x)^5?

  1. 13
  2. 10
  3. 11
  4. 9
Show Answer and Explanation

Correct answer: B. 10

The binomial coefficient C(5,2)=10.

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Practice Set 8 · Question 73 of 150

Question 73. What is the coefficient of x² in (1+x)^6?

  1. 15
  2. 16
  3. 14
  4. 18
Show Answer and Explanation

Correct answer: A. 15

The binomial coefficient C(6,2)=15.

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Practice Set 8 · Question 74 of 150

Question 74. What is the coefficient of x² in (1+x)^7?

  1. 22
  2. 20
  3. 24
  4. 21
Show Answer and Explanation

Correct answer: D. 21

The binomial coefficient C(7,2)=21.

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Practice Set 8 · Question 75 of 150

Question 75. What is the coefficient of x² in (1+x)^8?

  1. 27
  2. 31
  3. 28
  4. 29
Show Answer and Explanation

Correct answer: C. 28

The binomial coefficient C(8,2)=28.

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Practice Set 8 · Question 76 of 150

Question 76. What is the coefficient of x² in (1+x)^9?

  1. 39
  2. 36
  3. 37
  4. 35
Show Answer and Explanation

Correct answer: B. 36

The binomial coefficient C(9,2)=36.

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Practice Set 8 · Question 77 of 150

Question 77. What is the coefficient of x² in (1+x)^10?

  1. 45
  2. 46
  3. 44
  4. 48
Show Answer and Explanation

Correct answer: A. 45

The binomial coefficient C(10,2)=45.

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Practice Set 8 · Question 78 of 150

Question 78. What is the coefficient of x² in (1+x)^11?

  1. 56
  2. 54
  3. 58
  4. 55
Show Answer and Explanation

Correct answer: D. 55

The binomial coefficient C(11,2)=55.

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Practice Set 8 · Question 79 of 150

Question 79. What is the coefficient of x² in (1+x)^12?

  1. 65
  2. 69
  3. 66
  4. 67
Show Answer and Explanation

Correct answer: C. 66

The binomial coefficient C(12,2)=66.

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Practice Set 8 · Question 80 of 150

Question 80. What is the coefficient of x² in (1+x)^13?

  1. 81
  2. 78
  3. 79
  4. 77
Show Answer and Explanation

Correct answer: B. 78

The binomial coefficient C(13,2)=78.

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Practice Set 9 · Question 81 of 150

Question 81. An arithmetic sequence has first term 2 and common difference 3. Find term 5.

  1. 14
  2. 15
  3. 13
  4. 17
Show Answer and Explanation

Correct answer: A. 14

Use a_n=a_1+(n−1)d=2+4×3=14.

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Practice Set 9 · Question 82 of 150

Question 82. An arithmetic sequence has first term 3 and common difference 4. Find term 6.

  1. 24
  2. 22
  3. 26
  4. 23
Show Answer and Explanation

Correct answer: D. 23

Use a_n=a_1+(n−1)d=3+5×4=23.

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Practice Set 9 · Question 83 of 150

Question 83. An arithmetic sequence has first term 4 and common difference 5. Find term 7.

  1. 33
  2. 37
  3. 34
  4. 35
Show Answer and Explanation

Correct answer: C. 34

Use a_n=a_1+(n−1)d=4+6×5=34.

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Practice Set 9 · Question 84 of 150

Question 84. An arithmetic sequence has first term 5 and common difference 6. Find term 8.

  1. 50
  2. 47
  3. 48
  4. 46
Show Answer and Explanation

Correct answer: B. 47

Use a_n=a_1+(n−1)d=5+7×6=47.

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Practice Set 9 · Question 85 of 150

Question 85. An arithmetic sequence has first term 6 and common difference 7. Find term 9.

  1. 62
  2. 63
  3. 61
  4. 65
Show Answer and Explanation

Correct answer: A. 62

Use a_n=a_1+(n−1)d=6+8×7=62.

Next Question →

Practice Set 9 · Question 86 of 150

Question 86. An arithmetic sequence has first term 7 and common difference 8. Find term 10.

  1. 80
  2. 78
  3. 82
  4. 79
Show Answer and Explanation

Correct answer: D. 79

Use a_n=a_1+(n−1)d=7+9×8=79.

Next Question →

Practice Set 9 · Question 87 of 150

Question 87. An arithmetic sequence has first term 8 and common difference 9. Find term 11.

  1. 97
  2. 101
  3. 98
  4. 99
Show Answer and Explanation

Correct answer: C. 98

Use a_n=a_1+(n−1)d=8+10×9=98.

Next Question →

Practice Set 9 · Question 88 of 150

Question 88. An arithmetic sequence has first term 9 and common difference 10. Find term 12.

  1. 122
  2. 119
  3. 120
  4. 118
Show Answer and Explanation

Correct answer: B. 119

Use a_n=a_1+(n−1)d=9+11×10=119.

Next Question →

Practice Set 9 · Question 89 of 150

Question 89. An arithmetic sequence has first term 10 and common difference 11. Find term 13.

  1. 142
  2. 143
  3. 141
  4. 145
Show Answer and Explanation

Correct answer: A. 142

Use a_n=a_1+(n−1)d=10+12×11=142.

Next Question →

Practice Set 9 · Question 90 of 150

Question 90. An arithmetic sequence has first term 11 and common difference 12. Find term 14.

  1. 168
  2. 166
  3. 170
  4. 167
Show Answer and Explanation

Correct answer: D. 167

Use a_n=a_1+(n−1)d=11+13×12=167.

Next Question →

Practice Set 10 · Question 91 of 150

Question 91. A geometric sequence starts at 2 with common ratio 2. Find term 3.

  1. 7
  2. 11
  3. 8
  4. 9
Show Answer and Explanation

Correct answer: C. 8

Use a_n=a_1 r^(n−1)=2×2^2=8.

Next Question →

Practice Set 10 · Question 92 of 150

Question 92. A geometric sequence starts at 3 with common ratio 2. Find term 4.

  1. 27
  2. 24
  3. 25
  4. 23
Show Answer and Explanation

Correct answer: B. 24

Use a_n=a_1 r^(n−1)=3×2^3=24.

Next Question →

Practice Set 10 · Question 93 of 150

Question 93. A geometric sequence starts at 4 with common ratio 2. Find term 5.

  1. 64
  2. 65
  3. 63
  4. 67
Show Answer and Explanation

Correct answer: A. 64

Use a_n=a_1 r^(n−1)=4×2^4=64.

Next Question →

Practice Set 10 · Question 94 of 150

Question 94. A geometric sequence starts at 5 with common ratio 2. Find term 6.

  1. 161
  2. 159
  3. 163
  4. 160
Show Answer and Explanation

Correct answer: D. 160

Use a_n=a_1 r^(n−1)=5×2^5=160.

Next Question →

Practice Set 10 · Question 95 of 150

Question 95. A geometric sequence starts at 6 with common ratio 2. Find term 7.

  1. 383
  2. 387
  3. 384
  4. 385
Show Answer and Explanation

Correct answer: C. 384

Use a_n=a_1 r^(n−1)=6×2^6=384.

Next Question →

Practice Set 10 · Question 96 of 150

Question 96. A geometric sequence starts at 7 with common ratio 2. Find term 8.

  1. 899
  2. 896
  3. 897
  4. 895
Show Answer and Explanation

Correct answer: B. 896

Use a_n=a_1 r^(n−1)=7×2^7=896.

Next Question →

Practice Set 10 · Question 97 of 150

Question 97. A geometric sequence starts at 8 with common ratio 2. Find term 9.

  1. 2048
  2. 2049
  3. 2047
  4. 2051
Show Answer and Explanation

Correct answer: A. 2048

Use a_n=a_1 r^(n−1)=8×2^8=2048.

Next Question →

Practice Set 10 · Question 98 of 150

Question 98. A geometric sequence starts at 9 with common ratio 2. Find term 10.

  1. 4609
  2. 4607
  3. 4611
  4. 4608
Show Answer and Explanation

Correct answer: D. 4608

Use a_n=a_1 r^(n−1)=9×2^9=4608.

Next Question →

Practice Set 10 · Question 99 of 150

Question 99. A geometric sequence starts at 10 with common ratio 2. Find term 11.

  1. 10239
  2. 10243
  3. 10240
  4. 10241
Show Answer and Explanation

Correct answer: C. 10240

Use a_n=a_1 r^(n−1)=10×2^10=10240.

Next Question →

Practice Set 10 · Question 100 of 150

Question 100. A geometric sequence starts at 11 with common ratio 2. Find term 12.

  1. 22531
  2. 22528
  3. 22529
  4. 22527
Show Answer and Explanation

Correct answer: B. 22528

Use a_n=a_1 r^(n−1)=11×2^11=22528.

Next Question →

Practice Set 11 · Question 101 of 150

Question 101. For finite sets with |A|=8, |B|=6 and |A∩B|=2, find |A∪B|.

  1. 12
  2. 13
  3. 11
  4. 15
Show Answer and Explanation

Correct answer: A. 12

Inclusion-exclusion gives 8+6−2=12.

Next Question →

Practice Set 11 · Question 102 of 150

Question 102. For finite sets with |A|=9, |B|=7 and |A∩B|=3, find |A∪B|.

  1. 14
  2. 12
  3. 16
  4. 13
Show Answer and Explanation

Correct answer: D. 13

Inclusion-exclusion gives 9+7−3=13.

Next Question →

Practice Set 11 · Question 103 of 150

Question 103. For finite sets with |A|=10, |B|=8 and |A∩B|=4, find |A∪B|.

  1. 13
  2. 17
  3. 14
  4. 15
Show Answer and Explanation

Correct answer: C. 14

Inclusion-exclusion gives 10+8−4=14.

Next Question →

Practice Set 11 · Question 104 of 150

Question 104. For finite sets with |A|=11, |B|=9 and |A∩B|=5, find |A∪B|.

  1. 18
  2. 15
  3. 16
  4. 14
Show Answer and Explanation

Correct answer: B. 15

Inclusion-exclusion gives 11+9−5=15.

Next Question →

Practice Set 11 · Question 105 of 150

Question 105. For finite sets with |A|=12, |B|=10 and |A∩B|=6, find |A∪B|.

  1. 16
  2. 17
  3. 15
  4. 19
Show Answer and Explanation

Correct answer: A. 16

Inclusion-exclusion gives 12+10−6=16.

Next Question →

Practice Set 11 · Question 106 of 150

Question 106. For finite sets with |A|=13, |B|=11 and |A∩B|=7, find |A∪B|.

  1. 18
  2. 16
  3. 20
  4. 17
Show Answer and Explanation

Correct answer: D. 17

Inclusion-exclusion gives 13+11−7=17.

Next Question →

Practice Set 11 · Question 107 of 150

Question 107. For finite sets with |A|=14, |B|=12 and |A∩B|=8, find |A∪B|.

  1. 17
  2. 21
  3. 18
  4. 19
Show Answer and Explanation

Correct answer: C. 18

Inclusion-exclusion gives 14+12−8=18.

Next Question →

Practice Set 11 · Question 108 of 150

Question 108. For finite sets with |A|=15, |B|=13 and |A∩B|=9, find |A∪B|.

  1. 22
  2. 19
  3. 20
  4. 18
Show Answer and Explanation

Correct answer: B. 19

Inclusion-exclusion gives 15+13−9=19.

Next Question →

Practice Set 11 · Question 109 of 150

Question 109. For finite sets with |A|=16, |B|=14 and |A∩B|=10, find |A∪B|.

  1. 20
  2. 21
  3. 19
  4. 23
Show Answer and Explanation

Correct answer: A. 20

Inclusion-exclusion gives 16+14−10=20.

Next Question →

Practice Set 11 · Question 110 of 150

Question 110. For finite sets with |A|=17, |B|=15 and |A∩B|=11, find |A∪B|.

  1. 22
  2. 20
  3. 24
  4. 21
Show Answer and Explanation

Correct answer: D. 21

Inclusion-exclusion gives 17+15−11=21.

Next Question →

Practice Set 12 · Question 111 of 150

Question 111. Which formula gives the inverse of f(x)=2x+1?

  1. 2x−1
  2. (x−2)/1
  3. (x−1)/2
  4. (x+1)/2
Show Answer and Explanation

Correct answer: C. (x−1)/2

Solve y=2x+1 for x: x=(y−1)/2.

Next Question →

Practice Set 12 · Question 112 of 150

Question 112. Which formula gives the inverse of f(x)=3x+2?

  1. (x−3)/2
  2. (x−2)/3
  3. (x+2)/3
  4. 3x−2
Show Answer and Explanation

Correct answer: B. (x−2)/3

Solve y=3x+2 for x: x=(y−2)/3.

Next Question →

Practice Set 12 · Question 113 of 150

Question 113. Which formula gives the inverse of f(x)=4x+3?

  1. (x−3)/4
  2. (x+3)/4
  3. 4x−3
  4. (x−4)/3
Show Answer and Explanation

Correct answer: A. (x−3)/4

Solve y=4x+3 for x: x=(y−3)/4.

Next Question →

Practice Set 12 · Question 114 of 150

Question 114. Which formula gives the inverse of f(x)=5x+4?

  1. (x+4)/5
  2. 5x−4
  3. (x−5)/4
  4. (x−4)/5
Show Answer and Explanation

Correct answer: D. (x−4)/5

Solve y=5x+4 for x: x=(y−4)/5.

Next Question →

Practice Set 12 · Question 115 of 150

Question 115. Which formula gives the inverse of f(x)=6x+5?

  1. 6x−5
  2. (x−6)/5
  3. (x−5)/6
  4. (x+5)/6
Show Answer and Explanation

Correct answer: C. (x−5)/6

Solve y=6x+5 for x: x=(y−5)/6.

Next Question →

Practice Set 12 · Question 116 of 150

Question 116. Which formula gives the inverse of f(x)=7x+6?

  1. (x−7)/6
  2. (x−6)/7
  3. (x+6)/7
  4. 7x−6
Show Answer and Explanation

Correct answer: B. (x−6)/7

Solve y=7x+6 for x: x=(y−6)/7.

Next Question →

Practice Set 12 · Question 117 of 150

Question 117. Which formula gives the inverse of f(x)=8x+7?

  1. (x−7)/8
  2. (x+7)/8
  3. 8x−7
  4. (x−8)/7
Show Answer and Explanation

Correct answer: A. (x−7)/8

Solve y=8x+7 for x: x=(y−7)/8.

Next Question →

Practice Set 12 · Question 118 of 150

Question 118. Which formula gives the inverse of f(x)=9x+8?

  1. (x+8)/9
  2. 9x−8
  3. (x−9)/8
  4. (x−8)/9
Show Answer and Explanation

Correct answer: D. (x−8)/9

Solve y=9x+8 for x: x=(y−8)/9.

Next Question →

Practice Set 12 · Question 119 of 150

Question 119. Which formula gives the inverse of f(x)=10x+9?

  1. 10x−9
  2. (x−10)/9
  3. (x−9)/10
  4. (x+9)/10
Show Answer and Explanation

Correct answer: C. (x−9)/10

Solve y=10x+9 for x: x=(y−9)/10.

Next Question →

Practice Set 12 · Question 120 of 150

Question 120. Which formula gives the inverse of f(x)=11x+10?

  1. (x−11)/10
  2. (x−10)/11
  3. (x+10)/11
  4. 11x−10
Show Answer and Explanation

Correct answer: B. (x−10)/11

Solve y=11x+10 for x: x=(y−10)/11.

Next Question →

Practice Set 13 · Question 121 of 150

Question 121. Evaluate (3+3)²−4×9.

  1. 0
  2. 1
  3. -1
  4. 3
Show Answer and Explanation

Correct answer: A. 0

The expression is (2×3)²−4×3²=0.

Next Question →

Practice Set 13 · Question 122 of 150

Question 122. Evaluate (4+4)²−4×16.

  1. 1
  2. -1
  3. 3
  4. 0
Show Answer and Explanation

Correct answer: D. 0

The expression is (2×4)²−4×4²=0.

Next Question →

Practice Set 13 · Question 123 of 150

Question 123. Evaluate (5+5)²−4×25.

  1. -1
  2. 3
  3. 0
  4. 1
Show Answer and Explanation

Correct answer: C. 0

The expression is (2×5)²−4×5²=0.

Next Question →

Practice Set 13 · Question 124 of 150

Question 124. Evaluate (6+6)²−4×36.

  1. 3
  2. 0
  3. 1
  4. -1
Show Answer and Explanation

Correct answer: B. 0

The expression is (2×6)²−4×6²=0.

Next Question →

Practice Set 13 · Question 125 of 150

Question 125. Evaluate (7+7)²−4×49.

  1. 0
  2. 1
  3. -1
  4. 3
Show Answer and Explanation

Correct answer: A. 0

The expression is (2×7)²−4×7²=0.

Next Question →

Practice Set 13 · Question 126 of 150

Question 126. Evaluate (8+8)²−4×64.

  1. 1
  2. -1
  3. 3
  4. 0
Show Answer and Explanation

Correct answer: D. 0

The expression is (2×8)²−4×8²=0.

Next Question →

Practice Set 13 · Question 127 of 150

Question 127. Evaluate (9+9)²−4×81.

  1. -1
  2. 3
  3. 0
  4. 1
Show Answer and Explanation

Correct answer: C. 0

The expression is (2×9)²−4×9²=0.

Next Question →

Practice Set 13 · Question 128 of 150

Question 128. Evaluate (10+10)²−4×100.

  1. 3
  2. 0
  3. 1
  4. -1
Show Answer and Explanation

Correct answer: B. 0

The expression is (2×10)²−4×10²=0.

Next Question →

Practice Set 13 · Question 129 of 150

Question 129. Evaluate (11+11)²−4×121.

  1. 0
  2. 1
  3. -1
  4. 3
Show Answer and Explanation

Correct answer: A. 0

The expression is (2×11)²−4×11²=0.

Next Question →

Practice Set 13 · Question 130 of 150

Question 130. Evaluate (12+12)²−4×144.

  1. 1
  2. -1
  3. 3
  4. 0
Show Answer and Explanation

Correct answer: D. 0

The expression is (2×12)²−4×12²=0.

Next Question →

Practice Set 14 · Question 131 of 150

Question 131. Find the modulus of the complex number 6+8i.

  1. 9
  2. 13
  3. 10
  4. 11
Show Answer and Explanation

Correct answer: C. 10

The modulus is sqrt((6)²+(8)²)=10.

Next Question →

Practice Set 14 · Question 132 of 150

Question 132. Find the modulus of the complex number 9+12i.

  1. 18
  2. 15
  3. 16
  4. 14
Show Answer and Explanation

Correct answer: B. 15

The modulus is sqrt((9)²+(12)²)=15.

Next Question →

Practice Set 14 · Question 133 of 150

Question 133. Find the modulus of the complex number 12+16i.

  1. 20
  2. 21
  3. 19
  4. 23
Show Answer and Explanation

Correct answer: A. 20

The modulus is sqrt((12)²+(16)²)=20.

Next Question →

Practice Set 14 · Question 134 of 150

Question 134. Find the modulus of the complex number 15+20i.

  1. 26
  2. 24
  3. 28
  4. 25
Show Answer and Explanation

Correct answer: D. 25

The modulus is sqrt((15)²+(20)²)=25.

Next Question →

Practice Set 14 · Question 135 of 150

Question 135. Find the modulus of the complex number 18+24i.

  1. 29
  2. 33
  3. 30
  4. 31
Show Answer and Explanation

Correct answer: C. 30

The modulus is sqrt((18)²+(24)²)=30.

Next Question →

Practice Set 14 · Question 136 of 150

Question 136. Find the modulus of the complex number 21+28i.

  1. 38
  2. 35
  3. 36
  4. 34
Show Answer and Explanation

Correct answer: B. 35

The modulus is sqrt((21)²+(28)²)=35.

Next Question →

Practice Set 14 · Question 137 of 150

Question 137. Find the modulus of the complex number 24+32i.

  1. 40
  2. 41
  3. 39
  4. 43
Show Answer and Explanation

Correct answer: A. 40

The modulus is sqrt((24)²+(32)²)=40.

Next Question →

Practice Set 14 · Question 138 of 150

Question 138. Find the modulus of the complex number 27+36i.

  1. 46
  2. 44
  3. 48
  4. 45
Show Answer and Explanation

Correct answer: D. 45

The modulus is sqrt((27)²+(36)²)=45.

Next Question →

Practice Set 14 · Question 139 of 150

Question 139. Find the modulus of the complex number 30+40i.

  1. 49
  2. 53
  3. 50
  4. 51
Show Answer and Explanation

Correct answer: C. 50

The modulus is sqrt((30)²+(40)²)=50.

Next Question →

Practice Set 14 · Question 140 of 150

Question 140. Find the modulus of the complex number 33+44i.

  1. 58
  2. 55
  3. 56
  4. 54
Show Answer and Explanation

Correct answer: B. 55

The modulus is sqrt((33)²+(44)²)=55.

Next Question →

Practice Set 15 · Question 141 of 150

Question 141. How many ordered pairs are in A×B if |A|=3 and |B|=5?

  1. 15
  2. 16
  3. 14
  4. 18
Show Answer and Explanation

Correct answer: A. 15

The Cartesian product has 3×5=15 pairs.

Next Question →

Practice Set 15 · Question 142 of 150

Question 142. How many ordered pairs are in A×B if |A|=4 and |B|=6?

  1. 25
  2. 23
  3. 27
  4. 24
Show Answer and Explanation

Correct answer: D. 24

The Cartesian product has 4×6=24 pairs.

Next Question →

Practice Set 15 · Question 143 of 150

Question 143. How many ordered pairs are in A×B if |A|=5 and |B|=7?

  1. 34
  2. 38
  3. 35
  4. 36
Show Answer and Explanation

Correct answer: C. 35

The Cartesian product has 5×7=35 pairs.

Next Question →

Practice Set 15 · Question 144 of 150

Question 144. How many ordered pairs are in A×B if |A|=6 and |B|=8?

  1. 51
  2. 48
  3. 49
  4. 47
Show Answer and Explanation

Correct answer: B. 48

The Cartesian product has 6×8=48 pairs.

Next Question →

Practice Set 15 · Question 145 of 150

Question 145. How many ordered pairs are in A×B if |A|=7 and |B|=9?

  1. 63
  2. 64
  3. 62
  4. 66
Show Answer and Explanation

Correct answer: A. 63

The Cartesian product has 7×9=63 pairs.

Next Question →

Practice Set 15 · Question 146 of 150

Question 146. How many ordered pairs are in A×B if |A|=8 and |B|=10?

  1. 81
  2. 79
  3. 83
  4. 80
Show Answer and Explanation

Correct answer: D. 80

The Cartesian product has 8×10=80 pairs.

Next Question →

Practice Set 15 · Question 147 of 150

Question 147. How many ordered pairs are in A×B if |A|=9 and |B|=11?

  1. 98
  2. 102
  3. 99
  4. 100
Show Answer and Explanation

Correct answer: C. 99

The Cartesian product has 9×11=99 pairs.

Next Question →

Practice Set 15 · Question 148 of 150

Question 148. How many ordered pairs are in A×B if |A|=10 and |B|=12?

  1. 123
  2. 120
  3. 121
  4. 119
Show Answer and Explanation

Correct answer: B. 120

The Cartesian product has 10×12=120 pairs.

Next Question →

Practice Set 15 · Question 149 of 150

Question 149. How many ordered pairs are in A×B if |A|=11 and |B|=13?

  1. 143
  2. 144
  3. 142
  4. 146
Show Answer and Explanation

Correct answer: A. 143

The Cartesian product has 11×13=143 pairs.

Next Question →

Practice Set 15 · Question 150 of 150

Question 150. How many ordered pairs are in A×B if |A|=12 and |B|=14?

  1. 169
  2. 167
  3. 171
  4. 168
Show Answer and Explanation

Correct answer: D. 168

The Cartesian product has 12×14=168 pairs.

Restart from Question 1

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