Bluebook SAT Test Digital SAT Math Practice 5

Question 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?

Accepted Answer

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

Answer

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.

Question 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?

Accepted Answer

25π

Answer

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.

Question 3

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

Accepted Answer

5

Answer

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.

Question 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?

Accepted Answer

6

Answer

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.

Question 5

The system of equations below has no solution. What is the value of k?

3x − ky = 8
6x − 4y = 5

Accepted Answer

k = 2

Answer

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.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Digital SAT Math Practice 5