Bluebook SAT Test Digital SAT Hard Math Practice 5

Question 1

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?

Accepted Answer

Mean 15, SD 4

Answer

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

Question 2

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

Accepted Answer

−5 + 12i

Answer

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

Question 3

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

Accepted Answer

3

Answer

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.

Question 4

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

Accepted Answer

28

Answer

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

Question 5

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

Accepted Answer

4

Answer

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

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Digital SAT Hard Math Practice 5