Criterion-Referenced Practice Test Sample

Subtracting 5 from both sides gives 2x = 8, and dividing by 2 leads to x = 4. This straightforward operation demonstrates the process of isolating the variable in a linear equation.

First, add 2 and 4 to get 6, then multiply by 3 to obtain 18. This problem applies the order of operations and the distributive property in a basic scenario.

The expression x^2 - 9 is a difference of two squares and factors neatly into (x - 3)(x + 3). Recognizing this pattern is essential for simplifying quadratic expressions.

The slope is determined by the change in y divided by the change in x, so (10 - 2) / (3 - 1) equals 4. This calculation illustrates the basic concept of rate of change on a coordinate plane.

Calculating 5^2 gives 25 and 3^2 gives 9, and their difference is 16. This problem reinforces the operations of exponentiation followed by subtraction.

By adding the two equations, the variable y is eliminated and we obtain 2x = 10, hence x = 5. Substituting back into one of the equations yields y = 2, demonstrating the elimination method.

Factoring the quadratic expression leads to (x - 2)(x - 3) = 0, which implies that x can be 2 or 3. This reinforces the strategy of solving quadratic equations through factoring.

The square root of 50 can be expressed as √(25� - 2), which simplifies to 5√2. Recognizing and extracting perfect square factors is key in simplifying radicals.

Multiplying both sides of the equation by 4/3 isolates x, resulting in x = 12. This problem demonstrates how to solve equations that contain fractional coefficients.

Substituting x = 4 into the function f(x) yields f(4) = 2(4) + 1, which simplifies to 9. This reinforces the concept of function evaluation at a given point.

The distributive property states that a(b + c) can be expanded as ab + ac. This principle is fundamental when simplifying algebraic expressions.

When the data set is arranged in order, the median is the middle value, which is 9. This basic statistical measure is essential for understanding data analysis.

The area of a rectangle is calculated by multiplying its length by its width, so 7 � - 5 equals 35. This question tests the ability to apply the correct formula for the area of a rectangle.

Multiplying expressions with the same base requires adding the exponents, so x^3 * x^2 becomes x^(3+2), which is x^5. This exponent rule is fundamental in algebra.

Dividing both sides of the equation by 2 gives x - 3 = 5, and adding 3 to both sides yields x = 8. This question reinforces basic algebraic operations and equation solving.

A quadratic equation has a unique real solution when its discriminant is zero. Setting the discriminant (-4)^2 - 4(2)k equal to zero leads to 16 - 8k = 0, so k = 2.

The vertex of a parabola in the form ax^2 + bx + c is found using the formula x = -b/(2a), which in this case gives x = 2. Substituting x into the function yields f(2) = -1, resulting in the vertex (2, -1).

Let the sides be 3x, 4x, and 5x; their sum is 12x, which equals 36, giving x = 3. The longest side is then 5x = 15, which is the correct answer.

Since 10 raised to the power of 3 equals 1000, log₝₀(1000) is equal to 3. This problem reinforces the basic principles of logarithms and exponents.

Recognizing that 16 is a power of 2 (specifically 2^4) allows us to set the exponents equal, which gives x = 4. This problem tests understanding of exponential equations and the relationship between exponents.