Bluebook SAT Test Digital SAT Hard Math Practice 3

Question 1

If f(x) = x² + 6x + k is tangent to the x-axis (touches but does not cross), what is the value of k?

Accepted Answer

9

Answer

−9

Answer

6

Answer

3

Question 2

An arithmetic sequence has a₁ = 5 and a common difference of 3. A geometric sequence has g₁ = 2 and a common ratio of 3. For which positive integer n does aₙ = gₙ?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 3

A right triangle has legs of length 2t and t√3, where t > 0. What is the sine of the largest acute angle?

Accepted Answer

√3/2

Answer

1/2

Answer

2/√7

Answer

√7/2

Question 4

The solutions to x² + px + q = 0 have a sum of −7 and a product of 10. What is p + q?

Accepted Answer

17

Answer

3

Answer

−3

Answer

−17

Question 5

A function is defined as f(x) = |2x − 4| + 3. For how many values of x does f(x) = 1?

Accepted Answer

0

Answer

1

Answer

2

Answer

Infinitely many

Question 6

The half-life of a radioactive substance is 12 years. If the initial amount is 80 grams, which function gives the amount A remaining after t years?

Accepted Answer

A = 80(0.5)^(t/12)

Answer

A = 80(0.5)^(12t)

Answer

A = 80 − 6.67t

Answer

A = 80e^(−12t)

Question 7

In the figure below (not shown), two secants are drawn from an external point. If the external segment of one secant is 4 and the whole secant is 16, and the external segment of the other secant is 6, what is the length of the whole other secant?

Accepted Answer

10.67

Answer

8

Answer

12

Answer

16