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Quizzes > High School Quizzes > Mathematics

Chapter 4 Practice Quiz

Sharpen your skills with Section 4.3 review

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art promoting the Beyond 4.3 Challenge, a math practice quiz for high school students.

Solve for x: 3x - 7 = 8.
5
7
8
11/3
Adding 7 to both sides gives 3x = 15, and dividing by 3 results in x = 5. This linear equation is solved step”by”step using basic algebra.
Evaluate the function f(x) = 2x + 3 when x = 4.
11
8
10
9
Substituting x = 4 into f(x) = 2x + 3 gives 2(4) + 3, which equals 11. This confirms the correct evaluation of the function.
What is the slope of the line passing through the points (1, 2) and (3, 8)?
4
2
3/2
3
The slope is computed as (8 - 2) divided by (3 - 1), which simplifies to 6/2 = 3. This basic calculation applies the slope formula.
Write the equation of a line with slope 2 and y-intercept -3 in slope-intercept form.
y = 2x + 3
y = -2x + 3
y = -2x - 3
y = 2x - 3
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Substituting m = 2 and b = -3 gives y = 2x - 3.
Solve for y in the equation 4y + 8 = 20.
2
3
5
4
Subtracting 8 from both sides results in 4y = 12, and dividing by 4 yields y = 3. This is a straightforward solution of a linear equation.
What are the solutions to the quadratic equation x² - 5x + 6 = 0?
x = 2 and x = 3
x = -2 and x = -3
x = 2 only
x = 1 and x = 6
Factoring the quadratic x² - 5x + 6 gives (x - 2)(x - 3) = 0, leading to solutions x = 2 and x = 3. Factoring is an efficient method to solve this equation.
Determine the vertex of the quadratic function f(x) = x² - 4x + 1.
(-2, 1)
(2, -3)
(2, 3)
(4, 1)
The vertex is found by calculating h = -(-4)/(2*1) = 2 and k = f(2) = 2² - 4(2) + 1 = -3, so the vertex is (2, -3). This method uses the vertex formula for quadratics.
Which of the following points lies on the line given by the equation y = -3x + 7?
(1, 3)
(2, 3)
(2, 1)
(0, -3)
Substituting x = 2 into the equation y = -3x + 7 gives y = -6 + 7 = 1, confirming that (2, 1) lies on the line. The other options do not satisfy the equation.
Factor the expression 2x² + 8x.
2(x + 4)
2x² + 4
x(2x + 8)
2x(x + 4)
The greatest common factor of 2x² and 8x is 2x, so factoring yields 2x(x + 4). This technique is a basic application of factoring.
Solve the system of equations: x + y = 7 and x - y = 3.
x = 4, y = 3
x = 2, y = 5
x = 3, y = 4
x = 5, y = 2
Adding the equations eliminates y, resulting in 2x = 10 and hence x = 5, then substituting back gives y = 2. This elimination method efficiently solves the system.
Simplify the expression: (3x²y) * (2xy³).
6x³y❴
5x³y❴
6xy❴
6x²y³
Multiply the coefficients (3*2 = 6), add the exponents for x (2+1=3) and for y (1+3=4) to obtain 6x³y❴. This demonstrates the laws of exponents.
Determine the greatest common factor (GCF) of 18x² and 24x.
6x²
18x
12x
6x
The GCF of the numerical coefficients 18 and 24 is 6, and the variable part common to both is x. Therefore, the GCF is 6x.
What is the solution set of the inequality 2x - 5 > 1?
x ≤ 3
x < 3
x > 3
x ≥ 3
Adding 5 to both sides gives 2x > 6, and dividing by 2 results in x > 3. This procedure correctly solves the inequality.
If f(x) = x² - 1, what is f(3)?
6
9
8
7
Substituting x = 3 into f(x) = x² - 1 gives 3² - 1 = 9 - 1, which equals 8. This is a straightforward evaluation of the function.
Solve for x: 1/(x - 3) = 2/(x + 3).
6
0
9
3
By cross-multiplying, we obtain (x + 3) = 2(x - 3). Simplifying the equation leads to x = 9, which is the correct and unique solution.
Determine the equation of the circle with center (2, -3) and radius 5.
(x + 2)² + (y + 3)² = 25
(x - 2)² + (y + 3)² = 25
(x - 2)² + (y - 3)² = 25
(x + 2)² + (y - 3)² = 25
The standard form of a circle is (x - h)² + (y - k)² = r². With center (2, -3) and radius 5, substituting gives (x - 2)² + (y + 3)² = 25.
Solve the quadratic equation 2x² - 4x - 6 = 0 by first simplifying it.
x = 3 only
x = -1 only
x = 3 or x = -1
x = 1 or x = -3
Dividing the entire equation by 2 results in x² - 2x - 3 = 0, which factors into (x - 3)(x + 1) = 0. Thus, the solutions are x = 3 and x = -1.
Find the value of k such that the system of equations y = x² + k and y = 2x + 3 has exactly one real solution.
5
3
2
4
Setting x² + k equal to 2x + 3 leads to the quadratic x² - 2x + (k - 3) = 0, which has one real solution when its discriminant is zero. Solving 4 - 4(k - 3) = 0 gives k = 4.
Solve the radical equation √(2x + 9) = x - 1 and identify the valid solution.
x = 1 + 2√3
x = 2 + 2√3
x = 2 + √3
x = 2 - 2√3
Squaring both sides transforms the equation into 2x + 9 = (x - 1)², which simplifies to x² - 4x - 8 = 0. Checking for extraneous solutions shows that only x = 2 + 2√3 is valid.
Determine the sum of the arithmetic sequence: 4, 7, 10, ..., 31.
165
170
175
180
The sequence has a common difference of 3, with 4 as the first term and 31 as the last term. There are 10 terms, and using the formula S = n/2 (first term + last term) gives a sum of 175.
Find the domain of the function f(x) = √(x - 2) / (x - 5).
All real numbers
x > 2
x ≥ 5
x ≥ 2 and x ≠ 5
The radicand √(x - 2) requires x to be at least 2, and the denominator (x - 5) cannot equal zero. Thus, the domain is all x such that x ≥ 2 and x ≠ 5.
0
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Study Outcomes

  1. Analyze advanced mathematical problems to enhance problem-solving strategies.
  2. Apply section 4.3 concepts to solve challenging quantitative tasks.
  3. Evaluate the effectiveness of different approaches to complex equations.
  4. Synthesize multiple mathematical ideas to develop comprehensive solutions.
  5. Interpret problem conditions critically to make precise mathematical decisions.

Chapter 4 Quiz: Review After Section 4.3 Cheat Sheet

  1. Scatter Plot Basics - Scatter plots let you visualize how two variables hang out together on a graph, revealing cool patterns or trends in your data. It's like connecting the dots to see if they form a straight line, curve, or a funky blob! Boost your understanding with more details OpenStax Key Concepts.
  2. Linear vs. Non‑Linear Relationships - Some scatter plots form nice straight lines (linear), while others curve or twist in all sorts of ways (non‑linear). Recognizing which type you've got helps you pick the right analysis tool and avoid wild guesses. Dive deeper into these relationship types OpenStax Key Concepts.
  3. Line of Best Fit - The line of best fit is your trusty trend‑spotter, slicing through the cloud of points to show the central direction of your data. Whether you eyeball it or use a calculator, it's your go‑to for summarizing the overall pattern. Learn how it's drawn and why it works OpenStax Key Concepts.
  4. Interpolation vs. Extrapolation - Interpolation lets you make safe predictions within your existing data range, like estimating your test score if you study two more hours. Extrapolation ventures into unknown territory beyond your data, which can be exciting but risky - think forecasting next month's weather! Get clear definitions and tips OpenStax Key Concepts.
  5. Correlation Coefficient (r) - The correlation coefficient, r, measures how tight or loose your scatter points cluster around a line, with values from - 1 (perfect negative) to +1 (perfect positive). It's like a relationship rating: closer to ±1 means stronger connection; near 0 means "meh" - no clear relationship. Check out the full breakdown OpenStax Key Concepts.
  6. Regression Line Fundamentals - A regression line is the superstar version of the best-fit line, minimizing the sum of squared differences between actual points and the line itself. It gives you the most balanced summary of the trend, kind of like finding the perfect compromise in a group project. Explore why it's so powerful OpenStax Key Concepts.
  7. Least Squares Method - The least squares regression line uses math magic to minimize the sum of squared vertical distances of data points from the line. This approach ensures your trend line is as close as possible to all points, making your predictions more reliable. Learn the step‑by‑step process OpenStax Key Concepts.
  8. Making Predictions - Once you've got your least squares line, you can plug in a value for one variable and predict the other - super handy for forecasting sales, grades, or even sports stats! Just remember: predictions are as good as your data quality. Find practical examples and exercises OpenStax Key Concepts.
  9. Slope Interpretation - The slope of your regression line tells you how much the dependent variable changes for each one‑unit increase in the independent variable - think "rise over run" meets everyday life. A steep slope means big changes; a flat slope means everything's pretty chill. See more slope insights OpenStax Key Concepts.
  10. Y‑Intercept Meaning - The y‑intercept is where your regression line crosses the vertical axis, showing the expected value of your response variable when the predictor is zero. It's your starting point before any change kicks in - like the base camp of your data expedition. Understand its role in predictions OpenStax Key Concepts.
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