12th Grade Practice Quiz Worksheets

Distributing 2 gives 6x - 8, and adding 5 results in 6x - 3. This is the correct simplified expression.

Subtracting 4 from both sides gives 3x = 15, so x = 15/3 = 5. This is the correct solution.

When x = 3, f(x) becomes 2*(3²) = 2*9 = 18. This is the correct evaluation.

A linear function has the form f(x) = mx + b. The function f(x) = 3x + 2 fits this format, making it linear.

The y-intercept is found by setting x = 0. Substituting x = 0 in y = -4x + 7 gives y = 7.

The quadratic factors as (x - 2)(x - 3) = 0, which gives the solutions x = 2 and x = 3. These are the correct roots.

Using the vertex formula x = -b/(2a) gives x = 3. Substituting into the function yields f(3) = -1, so the vertex is (3, -1).

The square root function is defined when the radicand is non-negative. Since x - 2 ≥ 0, the domain is x ≥ 2.

Converting the logarithmic equation to exponential form gives x = 2³, which equals 8. This is the correct solution.

The fundamental Pythagorean identity in trigonometry is sin²θ + cos²θ = 1, which holds for all angles.

Using the power rule, the derivative of 3x² is computed as 3 * 2x = 6x. This is the correct derivative.

The limit lim�"�'0 (sin(x)/x) is a well-known result in calculus and equals 1. This result is foundational in understanding derivatives of trigonometric functions.

Since f(x) = eˣ, substituting x = ln 5 gives e^(ln 5) = 5. This is due to the inverse properties of logarithms and exponentials.

The product rule for logarithms states that log(ab) equals log(a) + log(b). This is a basic identity in logarithmic operations.

Adding the two equations gives 2x = 6, so x = 3. Substituting back into one of the equations results in y = 2, which is the correct solution.

To find the inverse, replace f(x) with y, swap x and y to get x = 2y - 3, and solve for y. This leads to y = (x + 3)/2, which is the correct inverse function.

Factor the numerator to get (x - 3)(x + 3) and note the critical points at x = -3, -1, and 3. Testing intervals shows the expression is positive for x in (-3, -1) and (3, ∞).

The sum of a geometric series is given by Sₙ = a(r❿ - 1)/(r - 1). With a = 3, r = 2, and n = 10, the sum is 3*(2¹❰ - 1)/(2 - 1) = 3*(1024 - 1) = 3069.

Using the chain rule, the derivative of ln(sin x) is (1/sin x)*(cos x), which simplifies to cot x. This derivative is valid for values of x between 0 and π.