Bluebook SAT Test Digital SAT Hard Math

Question 1

If f(x) = x² - 6x + 9 and g(x) = x - 3, for what value of x does f(x)/g(x) = 7?

Accepted Answer

x = 10

Answer

f(x)/g(x) = (x-3)²/(x-3) = x-3 for x ≠ 3. Setting x - 3 = 7 gives x = 10.

Question 2

A population of bacteria triples every 4 hours. If there are 200 bacteria initially, which expression gives the number after t hours?

Accepted Answer

200 · 3^(t/4)

Answer

Every 4 hours the count multiplies by 3, so after t hours there are t/4 intervals of tripling, giving 200 · 3^(t/4).

Question 3

The system of equations 3x + ky = 12 and 6x + 4y = 24 has infinitely many solutions. What is the value of k?

Accepted Answer

2

Answer

For infinitely many solutions, the equations must be proportional. Multiplying the first by 2 gives 6x + 2ky = 24. For this to match 6x + 4y = 24, we need 2k = 4, so k = 2.

Question 4

A quadratic equation has roots at x = 2 + √5 and x = 2 - √5. Which of the following could be the equation?

Accepted Answer

x² - 4x - 1 = 0

Answer

Sum of roots = 4 (coefficient of x is -4), product of roots = (2)² - (√5)² = 4 - 5 = -1 (constant term is -1).

Question 5

If 2^(x+1) = 5^(x-1), what is the value of x? (Round to the nearest hundredth.)

Accepted Answer

x ≈ 4.31

Answer

Taking log of both sides: (x+1)ln2 = (x-1)ln5. Solving: x(ln2-ln5) = -ln5-ln2, so x = (ln5+ln2)/(ln5-ln2) ≈ 4.31.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test Digital SAT Hard Math