PSAT Algebra & Functions 1 — Questions and Answers

Question 1: What is the solution to the equation 2x + 5 = 11?

x = 3 (Correct answer)
x = 2
x = 6
x = -3

Correct answer: x = 3

To solve the equation 2x + 5 = 11, first subtract 5 from both sides of the equation, which gives 2x = 6. Then, divide both sides by 2 to isolate x. This results in x = 3, which is the correct solution.

Question 2: What is the value of x in the equation x^2 = 16?

x = 4 or x = -4 (Correct answer)
x = 4
x = -4
x = 16

Correct answer: x = 4 or x = -4

To find the value of x in the equation x^2 = 16, you need to take the square root of both sides. Remember that a positive number has two square roots: a positive one and a negative one. Therefore, both 4 (since 4*4=16) and -4 (since -4*-4=16) are valid solutions for x.

Question 3: What is the slope of the line represented by the equation y = 3x + 2?

Slope = 3 (Correct answer)
Slope = 2
Slope = 1
Slope = -3

Correct answer: Slope = 3

The equation y = 3x + 2 is in the slope-intercept form, which is y = mx + b. In this standard form, 'm' represents the slope of the line and 'b' represents the y-intercept. Therefore, by direct comparison, the coefficient of x, which is 3, is the slope of the line.

Question 4: What is the solution to the equation 3(x + 2) = 18?

x = 4 (Correct answer)
x = 6
x = 2
x = 10

Correct answer: x = 4

To solve the equation 3(x + 2) = 18, first divide both sides by 3, which simplifies the equation to x + 2 = 6. Next, subtract 2 from both sides of the equation to isolate x. This operation yields x = 4 as the solution.

Question 5: What is the value of y when x = 2 in the equation y = 2x + 3?

y = 7 (Correct answer)
y = 6
y = 5
y = 4

Correct answer: y = 7

To find the value of y when x = 2 in the equation y = 2x + 3, simply substitute the value of x into the equation. This gives y = 2(2) + 3. Performing the multiplication first, y = 4 + 3, which simplifies to y = 7.

Question 6: What is the solution to the equation 4x - 7 = 13?

x = 5 (Correct answer)
x = 2
x = 3
x = 6

Correct answer: x = 5

To solve the equation 4x - 7 = 13, first add 7 to both sides of the equation to isolate the term with x, resulting in 4x = 20. Then, divide both sides by 4 to solve for x. This yields x = 5 as the solution.

Question 7: What is the value of x in the equation x + 5 = 10?

x = 5 (Correct answer)
x = 10
x = 0
x = -5

Correct answer: x = 5

To solve the equation x + 5 = 10, you need to isolate the variable x. This is achieved by performing the inverse operation of adding 5, which is subtracting 5 from both sides of the equation. Therefore, x = 10 - 5, which simplifies to x = 5.

Question 8: Which equation represents the line with a slope of 2 and a y-intercept of -3?

y = 2x - 3 (Correct answer)
y = -2x - 3
y = 2x + 3
y = -2x + 3

Correct answer: y = 2x - 3

The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept. Given a slope of 2 (m=2) and a y-intercept of -3 (b=-3), substituting these values directly into the formula yields the equation y = 2x - 3.

Question 9: What is the solution to the equation x^2 = 25?

x = 5 or x = -5 (Correct answer)
x = 5
x = -5
x = 25

Correct answer: x = 5 or x = -5

To solve the equation x^2 = 25, you must take the square root of both sides. It's important to remember that a positive number has two square roots: a positive one and a negative one. Therefore, both 5 (since 5*5=25) and -5 (since -5*-5=25) are valid solutions for x.

PSAT Algebra & Functions 1

What is the solution to the equation 2x + 5 = 11?