Bluebook SAT Mathematics 1 — Questions and Answers

Question 1: What is the value of 𝑥 in the equation 3𝑥+5=20?

3
5 (Correct answer)
10
15

Correct answer: 5

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?

𝑥=1 or 𝑥=6
x=−1 or 𝑥=−6
x=2 or 𝑥=3 (Correct answer)
𝑥=−2 or 𝑥=−3

Correct answer: x=2 or 𝑥=3

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)?

7
11 (Correct answer)
9
8

Correct answer: 11

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?

36 square units (Correct answer)
12 square units
18 square units
6 square units

Correct answer: 36 square units

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?

5
12 (Correct answer)
-12
12/7

Correct answer: 12

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 Mathematics 1

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

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