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Quizzes > High School Quizzes > Mathematics

Chapter 8 Practice Quiz

Practice with Chapter 8 Review and Chapter 11 Test

Difficulty: Moderate
Grade: Other
Study OutcomesCheat Sheet
Paper art depicting a trivia quiz for 10th-grade math students on chapters 8 and 11.

Solve for x: 2x + 3 = 11.
5
4
6
3
Subtracting 3 from both sides gives 2x = 8, and dividing by 2 yields x = 4. This direct approach confirms the correct solution.
Find the value of f(3) for the function f(x) = 2x + 1.
6
7
8
9
Substitute x = 3 into the function to obtain 2(3) + 1 = 7. This shows that the correct value is 7.
Simplify: 4x - 3x + 2.
x + 1
x + 2
x - 2
7x
Combine the like terms 4x and -3x to obtain x, then add 2. The simplified expression is x + 2.
Factor the expression: x² - 9.
(x + 9)(x - 1)
(x + 3)(x - 3)
(x - 3)²
(x - 9)(x + 1)
Recognize x² - 9 as a difference of squares which factors into (x + 3)(x - 3). This method directly leads to the correct factorization.
Which property allows the order of addition in an expression to be changed?
Commutative property
Associative property
Identity property
Distributive property
The commutative property states that the order of addition does not affect the result. This is the reason why changing the order is valid.
Solve the quadratic equation x² - 5x + 6 = 0.
x = -2 only
x = 2 only
x = -2 and x = -3
x = 2 and x = 3
Factoring the quadratic gives (x - 2)(x - 3) = 0, which leads to the solutions x = 2 and x = 3. This factorization method confirms the correct answers.
Simplify the expression: 2(x + 3) - 4.
2x + 4
2x + 2
x + 2
2x - 2
Apply the distributive property to get 2x + 6, then subtract 4 to obtain 2x + 2. This ordered calculation gives the correct simplified expression.
Find the x-intercept of the line y = 3x - 9.
3
9
-3
0
The x-intercept is found by setting y = 0, which results in 0 = 3x - 9 and solving for x gives x = 3. The other options do not satisfy the equation when y is zero.
What is the discriminant of the quadratic equation ax² + bx + c = 0?
b² - 4ac
4ac - b²
b² + 4ac
a² - 4bc
The discriminant in the quadratic formula is given by b² - 4ac. This component determines the nature of the roots of the quadratic equation.
Evaluate g(x) = x² - 4x + 4 at x = 5.
9
4
5
11
Substitute x = 5 into the function to get 25 - 20 + 4, which equals 9. This substitution confirms the correct result.
Factor completely: 2x² + 8x.
2(x + 4)
2x(x + 4)
2x² + 8
x(2x + 8)
The greatest common factor in 2x² + 8x is 2x, which when factored out yields 2x(x + 4). This method correctly simplifies the expression.
Solve the equation 1/(x - 2) = 2/(x - 2) + 3.
2/3
5/3
3/5
7/3
Subtracting 2/(x - 2) from both sides gives -1/(x - 2) = 3, so 1/(x - 2) = -3. Solving for x yields x = 5/3.
What is the slope of the line perpendicular to a line with slope 4?
4
-1/4
1/4
-4
Lines that are perpendicular have slopes that are negative reciprocals of each other. Thus, the negative reciprocal of 4 is -1/4.
If f(x) = 3x - 5, what is f(f(2))?
-2
-3
1
2
First, compute f(2) which equals 1, and then evaluate f(1) to get -2. This composition of function evaluation leads to the correct answer.
Solve for y in the equation 5y - 7 = 18.
5
7
4
6
Adding 7 to both sides gives 5y = 25, and dividing by 5 yields y = 5. This straightforward procedure confirms the correct solution.
Determine the vertex of the parabola given by y = -2x² + 8x - 3.
(-2, 5)
(-2, -5)
(2, 5)
(2, -5)
The vertex of a parabola is found using -b/(2a) for the x-coordinate; here, x = -8/(2×-2) = 2. Substituting x = 2 back into the equation gives y = 5, so the vertex is (2, 5).
Solve the quadratic equation 3x² - 12x + 9 = 0 using the quadratic formula.
x = 1 and x = 3
x = 1 only
x = -1 and x = -3
x = 2 and x = -2
Applying the quadratic formula to 3x² - 12x + 9 = 0 yields discriminant sqrt(144 - 108) = 6, leading to solutions x = (12 ± 6)/(6), which simplifies to x = 3 and x = 1. This confirms the correct pair of solutions.
Find the inverse of the function f(x) = (x - 4)/2.
-2x + 4
(x + 4)/2
2x + 4
2x - 4
To find the inverse, replace f(x) with y: y = (x - 4)/2, then swap x and y to get x = (y - 4)/2. Solving for y results in y = 2x + 4, which is the correct inverse.
A rectangle has a perimeter of 50 units. If the length is twice the width, what is the area of the rectangle?
1250/9
250/3
1250/3
1250/27
Let the width be w; then the length is 2w. Since the perimeter is 2(w + 2w) = 6w = 50, w equals 25/3, and the area is w × 2w = 2w², which evaluates to 1250/9 after substituting the value of w.
For the function h(x) = x³ - 3x, determine the number of turning points.
2
3
1
0
The derivative of h(x) is 3x² - 3, which factors to 3(x² - 1) and yields critical points at x = 1 and x = -1. This indicates that the function has 2 turning points, which is typical for a cubic function.
0
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Study Outcomes

  1. Apply algebraic techniques to simplify expressions and solve equations from the practice questions.
  2. Analyze problem statements to identify appropriate strategies for solving targeted mathematical questions.
  3. Evaluate and interpret problem solutions to verify understanding of core concepts.
  4. Synthesize different mathematical approaches to efficiently tackle complex test problems.
  5. Demonstrate increased confidence in solving exam-level questions through targeted practice.

Ch 8 & Ch 11 Test Review Cheat Sheet

  1. Distance Formula - Need to find the straight‑line distance between two points on the coordinate plane? Just plug into d = sqrt((x2 - x1)2 + (y2 - y1)2) and calculate. It's your go‑to shortcut for all those geometry and physics problems! Ch. 11 Key Concepts - Intermediate Algebra | OpenStax
  2. Midpoint Formula - Want the exact center of the segment connecting (x1, y1) and (x2, y2)? Average the x's and the y's to get ((x1 + x2)/2, (y1 + y2)/2). Perfect for bisecting lines or finding a segment's heart! Ch. 11 Key Concepts - Intermediate Algebra | OpenStax
  3. Standard Equation of a Circle - Graphing circles is easy when you know (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Shift h and k to move your circle, and tweak r to resize it. This keeps your curve‑drawing on point every time! Ch. 11 Key Concepts - Intermediate Algebra | OpenStax
  4. Parabolas - Parabolas are the iconic U‑shaped curves from quadratics, consisting of all points equidistant from a focus and a directrix. In vertex form you write y = a(x - h)2 + k to shift, stretch, or flip it. Mastering these tweaks makes graphing a breeze! Ch. 11 Key Concepts - Intermediate Algebra | OpenStax
  5. Ellipses - Think of an ellipse as a stretched circle: the sum of distances to two foci stays constant. Its standard form, ((x - h)2/a2) + ((y - k)2/b2) = 1, shows how wide (a) and tall (b) it is. Great for everything from planetary orbits to design art! Ch. 11 Key Concepts - Intermediate Algebra 2e | OpenStax
  6. Hyperbolas - A hyperbola features two opposite curves where the difference of distances to its foci is constant. Write it as ((x - h)2/a2) - ((y - k)2/b2) = 1 (or flipped for vertical openings). You'll spot hyperbolas in physics, architecture, and signal models! Ch. 11 Key Concepts - Intermediate Algebra 2e | OpenStax
  7. Solving Systems of Nonlinear Equations - When lines, circles, or parabolas collide, you've got a nonlinear system! Use substitution or elimination to solve algebraically, or graph to find intersection points. Practice both ways to confidently tackle these mixed‑shape puzzles. Ch. 11 Key Concepts - Intermediate Algebra 2e | OpenStax
  8. Graphs of Sine and Cosine Functions - Sine and cosine waves repeat every 2π, with amplitude (height), period (length), and phase shift (horizontal move) you can tweak. Knowing how to adjust those parameters helps you model sound waves, tides, and circular motion. Play with transformations to see the magic in action! Ch. 8 Key Concepts - Algebra and Trigonometry 2e | OpenStax
  9. Inverse Trigonometric Functions - Inverse trig functions like sin❻¹(x), cos❻¹(x), and tan❻¹(x) let you find angles from known ratios. They're essential when you know side lengths but need the angles in a triangle. Just mind the domain and range to avoid unexpected results! Ch. 8 Key Concepts - Algebra and Trigonometry 2e | OpenStax
  10. Systems of Linear Equations - Finding where two (or more) lines intersect? Use graphing for a visual, substitution to swap variables, or elimination to cancel them out. Master these methods and you'll solve economic models, circuit problems, and more in no time! Ch. 11 Key Concepts - Algebra and Trigonometry 2e | OpenStax
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