SATs Algebraic Expressions & Equations

Question 1

What is the correct simplified form of 2x + 3x?

Accepted Answer

5x

Answer

This question tests the basic algebraic principle of combining like terms. When terms have the same variable raised to the same power, their coefficients can be added together. Here, 2x and 3x are like terms, so adding their coefficients (2 + 3) results in 5, keeping the variable x to give 5x.

Question 2

Solve for x in the equation 5x - 3 = 12.

Accepted Answer

x = 3

Answer

To solve for x, we need to isolate it on one side of the equation. First, add 3 to both sides: 5x - 3 + 3 = 12 + 3, which simplifies to 5x = 15. Next, divide both sides by 5: 5x / 5 = 15 / 5, which yields x = 3.

Question 3

Which of the following is the correct expanded form of (x + 2)(x + 3)?

Accepted Answer

x² + 5x + 6

Answer

To expand the expression (x + 2)(x + 3), we use the FOIL method (First, Outer, Inner, Last). This involves multiplying the First terms (x * x = x²), Outer terms (x * 3 = 3x), Inner terms (2 * x = 2x), and Last terms (2 * 3 = 6). Combining these results in x² + 3x + 2x + 6, which simplifies to x² + 5x + 6.

Question 4

What is the solution to the equation 2x + 3 = 7?

Accepted Answer

x = 2

Answer

To solve for x, we first need to isolate the term with x. Subtract 3 from both sides of the equation: 2x + 3 - 3 = 7 - 3, which simplifies to 2x = 4. Then, divide both sides by 2: 2x / 2 = 4 / 2, resulting in x = 2.

Question 5

Which of the following represents the equation for the area of a rectangle?

Accepted Answer

Area = length × width

Answer

The area of a rectangle is a fundamental geometric concept representing the amount of surface it covers. This is universally calculated by multiplying its length by its width. The formula Area = length × width is the correct and standard equation for this calculation.

SATs (Standard Assessment Test) Practice Test

SATs (Standard Assessment Test) Practice Test

SATs Algebraic Expressions & Equations