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Problem Solving Strategies Flashcards

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

Read the first 7 Problem Solving Strategies flashcards as text

  1. A DSAT problem asks for the probability that a randomly selected student from a two-way table plays a sport AND is in 10th grade. What is the correct calculation?

    Answer: (10th graders who play a sport) ÷ (total students)

    For a joint probability (A AND B), divide the count satisfying both conditions by the total sample size.

  2. A student needs to compare the slopes of two lines given only their equations in standard form (Ax + By = C). What is the fastest method?

    Answer: Rewrite each equation in slope-intercept form y = mx + b

    Converting to y = mx + b isolates the slope m for direct comparison, which is more reliable than visual inspection or comparing raw coefficients.

  3. A DSAT problem states that a function is decreasing on an interval. What does this mean about the graph?

    Answer: As x increases, y decreases on that interval

    A decreasing function means that as you move left to right (x increases), the output values (y) fall.

  4. When should you use the discriminant (b² − 4ac) as a strategy on the DSAT?

    Answer: To determine how many real solutions a quadratic equation has without fully solving it

    The discriminant tells you the number of real solutions: positive → two real solutions, zero → one, negative → none, without needing to complete the full solution.

  5. A problem gives the equation of a circle (x − 3)² + (y + 2)² = 25 and asks for the radius. What is the quickest strategy?

    Answer: Recognize the standard form and take the square root of 25

    In standard circle form (x − h)² + (y − k)² = r², the radius is √25 = 5 by direct identification.

  6. A student has 3 minutes left and 4 problems remaining. Which time management strategy is best?

    Answer: Skip to the easiest-looking problems first, then guess on the rest

    With limited time, prioritize problems you can answer quickly to maximize correct responses, then use remaining seconds to guess on harder ones.

  7. A question involves simplifying the expression (3x²y)(4xy³). Which property is key?

    Answer: Product of powers property (add exponents when multiplying like bases)

    Multiply coefficients (3 × 4 = 12) and add exponents for each variable: x^(2+1) = x³ and y^(1+3) = y⁴, giving 12x³y⁴.