Bluebook SAT Test Nonlinear Equations and Systems 10 — Questions and Answers
Question 1: A rocket's height in feet is h(t) = −16t² + 80t. What is the maximum height the rocket reaches?
- 80 feet
- 100 feet (Correct answer)
- 120 feet
- 160 feet
Correct answer: 100 feet
Vertex time: t = −80/(2 × −16) = 2.5 s; h(2.5) = −16(6.25) + 80(2.5) = −100 + 200 = 100 feet.
Question 2: How many solutions does the system y = x² − 2x + 1 and y = 4 have?
- 0 solutions
- 1 solution
- 2 solutions (Correct answer)
- 3 solutions
Correct answer: 2 solutions
x² − 2x + 1 = 4 → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0; two solutions: x = 3 and x = −1.
Question 3: The equation x² − kx + 9 = 0 has two equal real roots. What is the positive value of k?
- 3
- 6 (Correct answer)
- 9
- 18
Correct answer: 6
For equal roots, discriminant = 0: k² − 36 = 0; k² = 36; k = 6.
Question 4: Which value of x satisfies both x² = 2x + 8 and x > 0?
- x = 2
- x = 4 (Correct answer)
- x = 6
- x = 8
Correct answer: x = 4
x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0; the positive solution is x = 4.
Question 5: The graph of y = −(x − 3)² + 5 has its vertex at which point?
- (−3, 5)
- (3, −5)
- (3, 5) (Correct answer)
- (−3, −5)
Correct answer: (3, 5)
In vertex form y = a(x − h)² + k, the vertex is (h, k) = (3, 5).
Question 6: If x² + bx + 36 = 0 has two equal real roots, which of the following could be a value of b?
- −6
- 9
- −12 (Correct answer)
- 18
Correct answer: −12
Equal roots: b² − 4(36) = 0 → b² = 144 → b = ±12; b = −12 is listed.
Question 7: The system y = x + 3 and y = x² − x is solved. What is the sum of the x-values at the intersection points?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
x + 3 = x² − x → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0; x = 3 or x = −1; sum = 2.
Bluebook SAT Test Nonlinear Equations and Systems 10
A rocket's height in feet is h(t) = −16t² + 80t.
What is the maximum height the rocket reaches?