Bluebook SAT Test Digital SAT Hard Math Practice 5 β Questions and Answers
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?
- Mean 15, SD 4 (Correct answer)
- Mean 15, SD 7
- Mean 12, SD 7
- Mean 12, SD 4
Correct 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).
Question 2: The complex number (2 + 3i)Β² is equal to which of the following?
- β5 + 12i (Correct answer)
- 4 + 12i
- 4 + 9iΒ²
- 5 + 12i
Correct answer: β5 + 12i
(2 + 3i)Β² = 4 + 12i + 9iΒ² = 4 + 12i β 9 = β5 + 12i.
Question 3: If 2sinΒ²x β sinx β 1 = 0 for 0 β€ x < 2Ο, how many solutions does the equation have?
- 3 (Correct answer)
- 1
- 2
- 4
Correct answer: 3
Factor: (2sinx + 1)(sinx β 1) = 0 β sinx = β1/2 (two solutions in [0, 2Ο): 7Ο/6 and 11Ο/6) or sinx = 1 (one solution: Ο/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?
- 28 (Correct answer)
- 14
- 30
- 16
Correct answer: 28
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))?
- 4 (Correct answer)
- e
- ln 4
- 1
Correct answer: 4
g(1) = ln(4); f(g(1)) = e^(ln 4) = 4.
Question 6: A line segment has endpoints A(β2, 5) and B(4, β3). What are the coordinates of the point that divides AB in the ratio 2:1 from A to B?
- (2, β1/3) (Correct answer)
- (0, 1)
- (2, β1)
- (1, 1)
Correct answer: (2, β1/3)
Section formula with ratio 2:1: x = (β2+8)/3 = 2; y = (5β6)/3 = β1/3; point = (2, β1/3).
Question 7: A tank drains at a rate modeled by dV/dt = βkV, where V is volume and k = 0.2 per minute. If V(0) = 500 liters, what is V(10) to the nearest liter?
- 68 (Correct answer)
- 100
- 135
- 300
Correct answer: 68
Solution: V(t) = 500e^(β0.2t); V(10) = 500e^(β2) β 500 Γ 0.1353 β 67.7 β 68 liters.
Bluebook SAT Test Digital SAT Hard Math Practice 5
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?