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Help: Some Really Hard Questions for the SAT Math II!

StraferKevStraferKev Registered User Posts: 260 Junior Member
These are some questions I didn't understand from my practice test. I know it is a lot but I was hoping some could help me explain some of them to me. I think this is also good practice for anyone else who might be taking the Math II subject test soon.

12. The set of points (x,y,z) such that x² + y² + z² = 1 is
A) empty
B) a point
C) a sphere
D) a circle
E) a plane

18. What is the sum of the infinite geometric series
(1/4 + 1/8 + 1/16 + 1/32 + ...)?
A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2

36. The only prime factors of a number n are 2,5,7, and 17. Which of the following could NOT be a factor of n?
A) 10
B) 20
C) 25
D) 30
E) 34

38) If f(x) = 5√(2x), what is the value of f-1 (10)? (the -1 is above the f)
A) 0.04
B) 0.89
C) 2
D) 2.23
E) 22.36

39) The Fibonacci sequence can be defined recursively as
a1 = 1
a2 = 1
an = an-1 + an-2 for n>3.

What is the 10th term of this sequence?
A) 21
B) 34
C) 55
D) 89
E) 144

42) The set of all real numbers x such that √(x²) = -x consists of
A) zero only
B) nonpositive real numbers only
C) positive real numbers only
D) all real numbers
E) no real numbers

45) If log a 3 = x and log a 5 = y, then log a 45 =
A) 2x+y
B) x² + y
C) x²y
D) x + y
E) 9x + y
Post edited by StraferKev on

Replies to: Help: Some Really Hard Questions for the SAT Math II!

  • rspencerspence Registered User Posts: 2,118 Senior Member
    12. C) Sphere.

    18. This is equal to (1/2)(1/2 + 1/4 + 1/8 + ...). The sum 1/2 + 1/4 + 1/8 + ... is equal to 1, so the answer is A) 1/2.

    36. If 30 is a factor of n, then 3 is a factor of n. This cannot be true, D).

    38. Solve f(k) = 10:

    5sqrt(2x) = 10 --> x = 2, C).

    39. Might help to write the terms out (if you haven't memorized the sequence):

    The tenth term is 55, C).

    42. It helps to know that the absolute value of x is sometimes defined as

    |x| = sqrt(x^2).

    Here, you're essentially solving |x| = -x, in which the solution is the set of non-positive real numbers, B).

    45. Apply logarithm identities:
    log 45 = log 9 + log 5
    = 2 log 3 + log 5
    = 2x + y, A).
  • StraferKevStraferKev Registered User Posts: 260 Junior Member
    ^Thanks, I understand them all now. A lot of it was because I didn't know some of the rules needed for the question^
  • rspencerspence Registered User Posts: 2,118 Senior Member
    Great! Yeah, especially 12, 18, 45. For 12 it just helps to know that (alternatively, x^2 + y^2 + z^2 = radius^2 = 1, sphere). For 18 it helps to know how to sum a geometric series, and for 45 you pretty much need properties of logarithms (you could crank everything out on a calculator but that'd take too much time).
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