SAT Algebra & Functions

Question 1

What is the value of x in the equation 2x + 5 = 13?

Accepted Answer

x = 3

Answer

To solve the equation 2x + 5 = 13, first subtract 5 from both sides, which results in 2x = 8. Next, divide both sides by 2 to isolate x, yielding x = 4. Therefore, x=4 is the correct solution to this equation, making the provided answer of x=3 inconsistent with the given equation.

Question 2

What is the solution to the system of equations: x + y = 10 and 2x - y = 5?

Accepted Answer

x = 5, y = 5

Answer

To solve the system, add the two equations (x + y = 10) and (2x - y = 5) together. The 'y' terms cancel out, leaving 3x = 15. Dividing by 3 gives x = 5. Substitute x = 5 into the first equation (5 + y = 10) to find y = 5.

Question 3

Which of the following is the correct factorization of x^2 - 5x + 6?

Accepted Answer

(x - 1)(x - 6)

Answer

To factor the quadratic expression x^2 - 5x + 6, we need to find two numbers that multiply to +6 and add up to -5. These numbers are -2 and -3, leading to the factorization (x - 2)(x - 3). The provided answer (x - 1)(x - 6) is incorrect because (-1) + (-6) equals -7, not -5.

Question 4

If f(x) = 3x^2 - 2x + 1, what is f(2)?

Accepted Answer

f(2) = 11

Answer

To evaluate f(2) for the function f(x) = 3x^2 - 2x + 1, substitute x=2 into the expression. This gives f(2) = 3(2)^2 - 2(2) + 1, which simplifies to 3(4) - 4 + 1. Performing the arithmetic yields 12 - 4 + 1 = 9. Therefore, f(2) = 9, making the provided answer of f(2)=11 inconsistent with the calculation.

Question 5

What is the slope of the line represented by the equation y = 4x + 3?

Accepted Answer

4

Answer

The equation y = 4x + 3 is in the slope-intercept form, y = mx + b. In this form, 'm' represents the slope of the line and 'b' represents the y-intercept. By comparing the given equation to the slope-intercept form, we can directly identify the slope 'm' as 4.

SAT Practice Test

SAT Practice Test

SAT Algebra & Functions