NCDAP Algebraic Concepts & Quantitative Reasoning

Question 1

What is the value of x in the equation 2x + 4 = 12?

Accepted Answer

6

Answer

To solve the equation 2x + 4 = 12, first isolate the term with x by subtracting 4 from both sides, which gives 2x = 8. Next, divide both sides by 2 to solve for x. This results in x = 4. (Note: The provided correct answer '6' is incorrect for the given equation; x=4 is the correct solution.)

Question 2

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

Accepted Answer

3

Answer

A linear equation in the form y = mx + b is known as the slope-intercept form. In this standard form, 'm' directly represents the slope of the line. For the equation y = 3x + 2, the coefficient of x is 3, which is the slope.

Question 3

Simplify: 5(x + 2) − 3x

Accepted Answer

2x + 10

Answer

To simplify the expression 5(x + 2) − 3x, first apply the distributive property to 5(x + 2), which yields 5x + 10. Then, combine the like terms (5x and -3x). This simplifies to 2x + 10.

Question 4

If f(x) = x² − 4x, what is f(3)?

Accepted Answer

-1

Answer

To evaluate f(3) for the function f(x) = x² − 4x, substitute 3 for every 'x' in the expression. This calculation becomes (3)² − 4(3), which simplifies to 9 − 12. Therefore, f(3) = -3. (Note: The provided correct answer '-1' is incorrect for the given function; -3 is the correct evaluation.)

Question 5

Which expression is equivalent to (x + 3)(x - 3)?

Accepted Answer

x² - 9

Answer

The expression (x + 3)(x - 3) is a special product known as the difference of squares. When multiplying two binomials of the form (a + b)(a - b), the result is a² - b². In this case, a = x and b = 3, so the product is x² - 3², which simplifies to x² - 9.

(NCDAP) North Carolina Diagnostic Placement Test Practice Test

(NCDAP) North Carolina Diagnostic Placement Test Practice Test

NCDAP Algebraic Concepts & Quantitative Reasoning