Digital SAT Hard Math Practice Flashcards

For a set of 8 data values, the mean is 12 and the standard deviation is 4. If 3 is added to every value, what are the new mean and standard deviation?

Answer: Mean 15, SD 4

Adding a constant shifts the mean by that constant (12 + 3 = 15) but does not change the standard deviation (still 4).

The complex number (2 + 3i)² is equal to which of the following?

Answer: −5 + 12i

(2 + 3i)² = 4 + 12i + 9i² = 4 + 12i − 9 = −5 + 12i.

If 2sin²x − sinx − 1 = 0 for 0 ≤ x < 2π, how many solutions does the equation have?

Answer: 3

Factor: (2sinx + 1)(sinx − 1) = 0 → sinx = −1/2 (two solutions in [0, 2π): 7π/6 and 11π/6) or sinx = 1 (one solution: π/2); total 3 solutions.

The median of five consecutive even integers is 14. What is the sum of the largest and smallest integers?

Answer: 28

Consecutive even integers: 10, 12, 14, 16, 18; median is the middle one = 14. Largest + smallest = 18 + 10 = 28.

If f(x) = e^x and g(x) = ln(x + 3), what is f(g(1))?

Answer: 4

g(1) = ln(4); f(g(1)) = e^(ln 4) = 4.

A line segment has endpoints A(−2, 5) and B(4, −3). What are the coordinates of the point that divides AB in the ratio 2:1 from A to B?

Answer: (2, −1/3)

Section formula with ratio 2:1: x = (−2+8)/3 = 2; y = (5−6)/3 = −1/3; point = (2, −1/3).

A tank drains at a rate modeled by dV/dt = −kV, where V is volume and k = 0.2 per minute. If V(0) = 500 liters, what is V(10) to the nearest liter?

Answer: 68

Solution: V(t) = 500e^(−0.2t); V(10) = 500e^(−2) ≈ 500 × 0.1353 ≈ 67.7 ≈ 68 liters.