9th Grade Math Practice Quiz

Subtracting 3 from both sides gives 2x = 4, and dividing both sides by 2 shows that x = 2. This straightforward linear equation tests basic algebraic manipulation.

Substituting x with 4 gives 3(4) - 5 = 12 - 5, which equals 7. This question checks basic substitution skills in algebra.

First, add the numbers inside the parentheses (2 + 3 = 5), then multiply by 4 to obtain 20. This reinforces the order of operations.

Using the slope formula (y2 - y1)/(x2 - x1), we calculate (6 - 2)/(3 - 1) = 4/2 = 2. This problem reinforces understanding of the concept of slope.

The midpoint formula ((x1 + x2)/2, (y1 + y2)/2) gives ((2 + 10)/2, (8 + 4)/2) = (6, 6). This checks basic coordinate geometry skills.

Subtract 2x from both sides and add 7 to get 3x = 15, which simplifies to x = 5. This question reinforces solving linear equations.

Distribute 2 to get 2x + 6, then subtract 4x to arrive at -2x + 6. This tests the ability to simplify algebraic expressions.

The expression factors into (x + 2)(x + 3) because 2 and 3 multiply to 6 and add to 5. Factoring quadratics is a key algebra skill.

Recognize this as a difference of squares that factors to (x - 3)(x + 3) = 0, yielding x = 3 or x = -3. This reinforces quadratic factoring techniques.

The y-intercept occurs when x = 0, and substituting x = 0 into the equation gives y = 5, resulting in the point (0, 5). This tests understanding of linear equations in slope-intercept form.

Apply the distance formula: √[(4 - 1)² + (6 - 2)²] = √(9 + 16) = √25 = 5. This reinforces the use of the Pythagorean theorem in coordinate geometry.

Substitute 5 into the function: f(5) = 2(5) + 3 = 10 + 3, which equals 13. This problem assesses the ability to evaluate functions.

Using substitution, express y from x - y = 1 as y = x - 1 and substitute into 2x + y = 7, leading to x = 8/3 and subsequently y = 5/3. This question tests solving simultaneous equations.

Rearrange the equation by subtracting y from both sides to obtain 3x - y = 4, which is the standard form (Ax + By = C). This helps in understanding different representations of linear equations.

Add 3 to both sides to get 2x < 8, then divide by 2 to yield x < 4. This question reinforces the process of solving inequalities.

Using the quadratic formula with a discriminant of 49, we obtain x = (3 ± 7)/4, which simplifies to x = 5/2 and x = -1. This problem tests proficiency in solving quadratic equations.

Compose the functions by substituting g(x) into f(x): f(g(x)) = (2x + 1)², which expands to 4x² + 4x + 1. This problem examines understanding of function composition.

The series has a first term a = 8 and a common ratio r = 1/2, so the sum is given by a/(1 - r) = 8/(1/2) = 16. This question tests understanding of convergent infinite series.

Using the definition of a logarithm, log₂(x) = 5 means that 2❵ = x, so x must equal 32. This tests the understanding of logarithmic and exponential relationships.

First, calculate the mean (which is 5), then determine the squared deviations and average them to find the variance (4), and finally take the square root to obtain the standard deviation, which is 2. This problem assesses statistical computation skills.