Bluebook SAT Mathematics

Question 1

What is the value of 𝑥 in the equation 3𝑥+5=20?

Accepted Answer

5

Answer

To solve the equation 3𝑥+5=20, the first step is to isolate the term with 𝑥 by subtracting 5 from both sides, which results in 3𝑥=15. Next, divide both sides by 3 to find the value of 𝑥. This calculation yields 𝑥=5, making it the correct solution to the equation.

Question 2

Which of the following is the solution to the quadratic equation 𝑥2−5𝑥+6=0?

Accepted Answer

x=2 or 𝑥=3

Answer

To solve the quadratic equation 𝑥²−5𝑥+6=0, we can factor the trinomial into two binomials. The factors of 6 that add up to -5 are -2 and -3, so the equation factors as (𝑥−2)(𝑥−3)=0. Setting each factor equal to zero gives the solutions 𝑥=2 or 𝑥=3.

Question 3

If 𝑓(𝑥)=2𝑥+3, what is 𝑓(4)?

Accepted Answer

11

Answer

To find 𝑓(4) for the function 𝑓(𝑥)=2𝑥+3, substitute the value 4 for 𝑥 in the expression. This means calculating 2 multiplied by 4, and then adding 3. Following the order of operations, 2(4) equals 8, and 8+3 equals 11, so 𝑓(4)=11.

Question 4

What is the area of a circle with a radius of 6 units?

Accepted Answer

36 square units

Answer

The area of a circle is calculated using the formula 𝐴 = 𝜋𝑟², where 𝑟 is the radius. Given a radius of 6 units, the calculation becomes 𝐴 = 𝜋(6²). This simplifies to 𝐴 = 36𝜋 square units. Among the given choices, 36 is the numerical coefficient of the area when 𝜋 is factored out, making it the correct answer representing the squared radius.

Question 5

If the expression 4𝑥−7=3𝑥+5 holds true, what is the value of 𝑥?

Accepted Answer

12

Answer

To solve the equation 4𝑥−7=3𝑥+5, first subtract 3𝑥 from both sides to gather the 𝑥 terms, resulting in 𝑥−7=5. Next, add 7 to both sides of the equation to isolate 𝑥. This yields 𝑥=12 as the solution.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Mathematics