Bluebook SAT Test Digital SAT Hard Math Practice 1

Question 1

The function f(x) = x³ − 6x² + 9x − 4 has a local minimum at x = a and a local maximum at x = b. What is the value of a + b?

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 2

If sin θ + cos θ = √2, what is the value of sin θ · cos θ?

Accepted Answer

1/2

Answer

0

Answer

√2/2

Answer

1

Question 3

A nonlinear system consists of y = x² − 3x + 2 and y = 2x − 4. How many real solutions does the system have, and what is the sum of the x-coordinates?

Accepted Answer

2 solutions; sum = 5

Answer

1 solution; sum = 2

Answer

2 solutions; sum = 6

Answer

0 solutions

Question 4

If f(x) = (x² + 4x − 5) / (x − 1), for x ≠ 1, which expression is equivalent to f(x) for all x ≠ 1?

Accepted Answer

x + 5

Answer

x − 5

Answer

x + 5 + 0/(x−1)

Answer

x² + 5x

Question 5

A projectile follows h(t) = −16t² + 80t + 6, where h is height in feet and t is time in seconds. What is the maximum height reached, in feet?

Accepted Answer

106

Answer

86

Answer

96

Answer

112

Question 6

The system of equations kx + 3y = 12 and 2x + ky = 8 has infinitely many solutions when k equals which value?

Accepted Answer

6

Answer

√6

Answer

−√6

Answer

3

Question 7

If g(x) = 2x² − 8x + c and g has a minimum value of 5, what is the value of c?

Accepted Answer

13

Answer

5

Answer

8

Answer

3