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Mathematical Problem-Solving Flashcards

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

Read the first 7 Mathematical Problem-Solving flashcards as text

  1. A function is defined as g(x) = (x² − 9)/(x − 3). What is the value of lim(x→3) g(x)?

    Answer: 6

    Factor the numerator: (x−3)(x+3)/(x−3) = x+3; as x→3, the limit is 3+3 = 6.

  2. How many different 4-letter arrangements can be made from the letters of MATH if no letter is repeated?

    Answer: 24

    This is a permutation: P(4,4) = 4! = 24.

  3. The profit P (in dollars) from selling x items is P(x) = −2x² + 40x − 100. How many items should be sold to maximize profit?

    Answer: 10

    The vertex is at x = −40/(2×−2) = 40/4 = 10.

  4. If sin θ = 3/5 and θ is in the first quadrant, what is tan θ?

    Answer: 3/4

    With sin θ = 3/5, cos θ = 4/5 (Pythagorean theorem), so tan θ = sin/cos = 3/4.

  5. A sequence is defined by aₙ = 3n − 1. What is the sum of the first 10 terms?

    Answer: 140

    Sum = Σ(3n−1) from n=1 to 10 = 3(55) − 10 = 165 − 25 = 140.

  6. A bag has 4 green, 3 yellow, and 2 purple chips. What is the probability of NOT drawing a yellow chip on one draw?

    Answer: 2/3

    P(not yellow) = 1 − 3/9 = 6/9 = 2/3.

  7. What is the solution set of 2x² − 8 ≥ 0?

    Answer: x ≤ −2 or x ≥ 2

    2(x²−4) ≥ 0 → x² ≥ 4 → x ≤ −2 or x ≥ 2.