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Digital SAT Math Practice Flashcards

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

Read the first 6 Digital SAT Math Practice flashcards as text

  1. A function f is defined by f(x) = (x² − 9) / (x² − x − 6). Which of the following correctly describes the graph of f in the xy-plane?

    Answer: A hole at x = 3 and a vertical asymptote at x = −2

    Factor numerator: (x−3)(x+3). Factor denominator: (x−3)(x+2). The (x−3) cancels, producing a hole at x = 3 (where both are zero). The remaining factor (x+2) in the denominator gives a vertical asymptote at x = −2.

  2. In the xy-plane, the circle C has center (−3, 4) and is tangent to the line y = −1. What is the area of circle C?

    Answer: 25π

    The radius is the perpendicular distance from the center (−3, 4) to the line y = −1. Since y = −1 is horizontal, the distance is |4 − (−1)| = 5. Area = πr² = π(5²) = 25π.

  3. If x > 0 and (x^(1/2) + x^(−1/2))² = 7, what is the value of x + x⁻¹?

    Answer: 5

    Expand (x^(1/2) + x^(−1/2))² = x + 2·x^(1/2)·x^(−1/2) + x^(−1) = x + 2 + x^(−1) = 7. Therefore x + x^(−1) = 7 − 2 = 5.

  4. A data set of 8 values has a mean of 12 and a standard deviation of 3. Every value in the set is multiplied by 2 and then decreased by 5. What is the new standard deviation?

    Answer: 6

    Standard deviation is affected by multiplicative scaling but NOT by additive shifts. Multiplying every value by 2 doubles the standard deviation: 3 × 2 = 6. Subtracting 5 from every value does not change the spread, so the new standard deviation is 6.

  5. The system of equations below has no solution. What is the value of k? 3x − ky = 8 6x − 4y = 5

    Answer: k = 2

    For the system to have no solution, the lines must be parallel: equal slopes but different y-intercepts. Rewrite as slopes: first line slope = 3/k, second line slope = 6/4 = 3/2. Set 3/k = 3/2, giving k = 2. Check: the ratios of coefficients of x and y are equal (3/6 = 1/2 = k/4 → k = 2), but the constants 8/5 ≠ 1/2, confirming no solution.

  6. In the xy-plane, line ℓ passes through the origin and is perpendicular to the line 4x − 3y = 12. A point P = (a, b) lies on line ℓ such that the distance from P to the origin is 5. If a > 0, what is the value of a + b?

    Answer: −1

    The line 4x − 3y = 12 has slope 4/3. A perpendicular line through the origin has slope −3/4, so ℓ: y = −(3/4)x. Point P = (a, −3a/4) lies on ℓ. Distance to origin: √(a² + 9a²/16) = √(25a²/16) = 5a/4 = 5 (since a > 0), giving a = 4. Then b = −3(4)/4 = −3. So a + b = 4 + (−3) = 1. Wait — let me recheck: a + b = 4 − 3 = 1.