Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Mixed Deck — All AMC12 Topics Flashcards

100 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. In the Fibonacci sequence 1, 1, 2, 3, 5, 8, ..., what is the 8th term?

    Answer: 21

    Continuing the Fibonacci sequence: the 8th term is 21.

  2. If z = cos(π/6) + i·sin(π/6), what is z + z̄ (z plus its complex conjugate)?

    Answer: √3

    z = √3/2 + i/2 and z̄ = √3/2 − i/2, so z + z̄ = √3 (the imaginary parts cancel).

  3. How many solutions does sin(x) = sqrt(3)/2 have in [0, 2pi)?

    Answer: 2

    sin(x)=sqrt(3)/2 at x=pi/3 and x=2pi/3, giving 2 solutions.

  4. A committee of 3 is chosen from 7 people. How many ways can this be done?

    Answer: 35

    C(7, 3) = 7!/(3! × 4!) = 35.

  5. If log(xy)=5 and log(x/y)=1, what is log x?

    Answer: 3

    Adding the two equations gives 2log(x)=6, so log(x)=3.

  6. What is the product of the three terms of the geometric sequence 2, 6, 18?

    Answer: 216

    2 × 6 × 18 = 216; note 6 = ∛216, which confirms the middle term property.

  7. What is C(8, 3)?

    Answer: 56

    C(8, 3) = 8 × 7 × 6 / (3 × 2 × 1) = 336/6 = 56.

  8. What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?

    Answer: 39

    The common difference is 4, so a₁₀ = 3 + 9 × 4 = 3 + 36 = 39.

  9. What is cos(π)?

    Answer: −1

    cos(π) = −1 since π radians corresponds to 180°.

  10. A triangle has vertices (0,0), (4,0), and (0,3). What is its area?

    Answer: 6

    Area=(1/2)*base*height=(1/2)(4)(3)=6.

  11. What is the arithmetic mean of 2, 5, 8, 11, 14?

    Answer: 8

    The sum is 40, divided by 5 gives mean = 8; it also equals the middle term of this AP.

  12. In a group of 30 people, the probability that at least two share a birthday is approximately:

    Answer: Greater than 70%

    The birthday problem gives approximately 70.6% for 30 people.

  13. What is 0! (zero factorial)?

    Answer: 1

    By convention (and the gamma function), 0! = 1.

  14. If P(A)=0.4 and P(B)=0.5 and A and B are independent, what is P(A and B)?

    Answer: 0.2

    For independent events, P(A and B)=P(A)*P(B)=0.4*0.5=0.2.

  15. What is the sum from k=1 to 100 of (1/k - 1/(k+1))?

    Answer: 100/101

    This telescoping series sums to 1-1/101=100/101.

  16. What is the 7th term of a geometric sequence with first term 2 and ratio 3?

    Answer: 1458

    a_7=2*3^6=2*729=1458.

  17. What is the real part of (3 + 4i) / (1 + 2i)?

    Answer: 11/5

    Multiply numerator and denominator by the conjugate (1−2i): (3+4i)(1−2i)/5 = (11−2i)/5, giving real part 11/5.

  18. A fair die is rolled. What is the probability of getting a number greater than 4?

    Answer: 1/3

    The favorable outcomes are {5, 6}, so probability = 2/6 = 1/3.

  19. What is the sum to infinity of 1 + 1/2 + 1/4 + ...?

    Answer: 2

    S=a/(1-r)=1/(1-1/2)=2.

  20. What is the probability of rolling a sum of 7 with two standard dice?

    Answer: 1/6

    The 6 outcomes summing to 7 give P=6/36=1/6.