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Quizzes > High School Quizzes > Mathematics

Semester 2 Final Exam Practice Quiz

Ace your exam with our timed quiz

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz for high school math students to evaluate their skills.

Solve for x: 2x - 5 = 9
7
8
6
5
Add 5 to both sides to get 2x = 14, then divide by 2 to isolate x. This straightforward operation leads to the correct solution, x = 7.
What is the slope of the line y = 3x + 4?
3
4
-3
1/3
In the slope-intercept form, y = mx + b, the coefficient m represents the slope. Here, m = 3, which is the correct slope.
Evaluate: 5² - 3²
16
8
18
25
First calculate 5² (which is 25) and 3² (which is 9), then subtract: 25 - 9 equals 16. This problem tests basic exponentiation and subtraction skills.
Simplify: 2(3x + 4)
6x + 8
6x + 4
5x + 8
2x + 7
Distribute 2 across the terms inside the parentheses: 2 × 3x becomes 6x and 2 × 4 becomes 8. The resulting expression 6x + 8 is the simplified form.
What is the greatest common factor (GCF) of 8 and 12?
4
2
6
8
By listing the factors of 8 (1, 2, 4, 8) and 12 (1, 2, 3, 4, 6, 12), the largest common factor is 4. This question reinforces the concept of identifying factors.
Solve for x: (x/3) + 2 = 5.
9
8
7
6
Subtract 2 from both sides to obtain x/3 = 3, then multiply by 3 to solve for x, giving x = 9. This demonstrates basic algebraic manipulation with fractions.
Factor the quadratic expression: x² - 5x + 6.
(x - 2)(x - 3)
(x + 2)(x + 3)
(x - 1)(x - 6)
(x - 3)(x + 2)
The quadratic factors into (x - 2)(x - 3) because -2 and -3 multiply to 6 and add to -5. Factoring is a key skill in solving quadratic equations.
Solve the system of equations: 2x + y = 7 and x - y = 1.
x = 8/3, y = 5/3
x = 3, y = 1
x = 2, y = 3
x = 5/3, y = 8/3
First, express y from the equation x - y = 1 as y = x - 1, then substitute into 2x + y = 7 to solve for x. Back-substitution yields the solution x = 8/3 and y = 5/3.
Simplify: 3(x - 4) + 2x.
5x - 12
5x - 4
6x - 12
3x - 4
Apply the distributive property to get 3x - 12 and then add 2x. Combining like terms yields 5x - 12, demonstrating proper handling of linear expressions.
Solve the equation: 4 - (2x + 3) = 7.
-3
3
-4
4
Distribute the negative sign inside the parentheses to obtain 4 - 2x - 3 = 7, then simplify to 1 - 2x = 7. Solving for x results in x = -3.
Expand and simplify: (x + 2)².
x² + 4x + 4
x² + 2x + 4
x² + 4
x² + 2x
Use the FOIL method to expand (x + 2)² into x² + 2x + 2x + 4, which simplifies to x² + 4x + 4. This reinforces binomial expansion skills.
Solve for x in the proportion: 7/x = 14/28.
14
7
28
4
First simplify 14/28 to 1/2, making the equation 7/x = 1/2. Cross-multiply to solve for x, resulting in x = 14.
If f(x) = 2x - 3, what is f(4)?
5
8
7
6
Substitute x = 4 into the function: f(4) = 2(4) - 3, which simplifies to 8 - 3 and results in 5. This tests function evaluation skills.
Solve for x: 1/2 (x + 4) = 3.
2
3
4
6
Multiply both sides of the equation by 2 to eliminate the fraction, resulting in x + 4 = 6. Subtract 4 from both sides to get x = 2.
Solve for x: 3x + 2 = 14.
4
3
6
5
Subtract 2 from both sides to obtain 3x = 12, then divide by 3 to isolate x. The correct solution is x = 4.
Solve the quadratic equation: x² - 3x - 10 = 0.
x = 5 or x = -2
x = 5 or x = 2
x = -5 or x = -2
x = 2 or x = -5
Factor the quadratic into (x - 5)(x + 2) = 0 and apply the zero product property. This results in the two solutions x = 5 and x = -2.
Which of the following represents the distance formula between two points (x₝, y₝) and (x₂, y₂)?
√((x₂ - x₝)² + (y₂ - y₝)²)
(x₂ - x₝) + (y₂ - y₝)
√((x₂ + x₝)² + (y₂ + y₝)²)
(x₂ - x₝)² + (y₂ - y₝)²
The distance between two points is found by taking the square root of the sum of the squared differences of their coordinates. This formula is fundamental in coordinate geometry.
Find the vertex of the parabola given by g(x) = x² - 4x + 3.
(2, -1)
(-2, -1)
(2, 1)
(-2, 1)
The x-coordinate of the vertex is found using -b/(2a), which in this case is 4/2 = 2. Substituting x = 2 into g(x) yields y = -1, giving the vertex (2, -1).
Solve for x: log₂(x) = 3.
8
3
6
9
By the definition of logarithms, log₂(x) = 3 implies that x = 2³. Calculating 2³ gives x = 8, which is the correct solution.
Solve the equation: |3x - 9| = 6.
x = 5 or x = 1
x = 5
x = 1
x = 5 and x = -1
An absolute value equation splits into two cases: 3x - 9 = 6 and 3x - 9 = -6. Solving these yields x = 5 and x = 1 respectively, covering all valid solutions.
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Study Outcomes

  1. Analyze algebraic expressions and equations to identify underlying patterns.
  2. Apply problem-solving strategies to tackle complex mathematical challenges.
  3. Evaluate geometric concepts and methods to solve related problems accurately.
  4. Synthesize multiple math skills to approach and resolve exam-level questions.

Semester 2 Final Exam Review Cheat Sheet

  1. Master the Law of Sines - The Law of Sines lets you tackle any oblique triangle by linking each angle to its opposite side with sin(A)/a = sin(B)/b = sin(C)/c. It's a lifesaver when you don't have a right angle, helping you solve missing sides or angles in no time. Get hands‑on with example problems to cement your understanding. OpenStax Algebra & Trigonometry Key Concepts
  2. Understand the Law of Cosines - Use c² = a² + b² - 2ab cos(C) to find unknown sides or angles when you've got two sides and the included angle (SAS) or all three sides (SSS). It's like the Pythagorean theorem's cooler cousin that works for every triangle shape. Practice swapping sides and angles to see this formula in action. OpenStax Algebra & Trigonometry Key Concepts
  3. Familiarize Yourself with Polar Coordinates - Polar coordinates describe points by (r, θ) instead of (x, y), where r is the distance from the origin and θ is the angle from the positive x-axis. Converting between polar and rectangular (x = r cos θ, y = r sin θ) will make mapping spirals, circles, and weird curves a breeze. Visualize both systems side by side to see how each point hops between grids. OpenStax Algebra & Trigonometry Key Concepts
  4. Learn Complex Numbers in Polar Form - Expressing z = a + bi as r(cos θ + i sin θ) (where r = √(a² + b²), θ = arctan(b/a)) makes multiplication and division as easy as adding or subtracting angles and multiplying or dividing magnitudes. It's like turning messy algebra into smooth rotations and scalings on the complex plane. Try multiplying a few sample numbers to watch the magic happen. OpenStax Algebra & Trigonometry Key Concepts
  5. Explore Parametric Equations - Parametric equations use a third variable t to define both x and y (for example, x = t², y = 2t), giving you a dynamic way to model motion, projectiles, and fancy curves. By tweaking t, you can trace out every point on the curve like a time‑lapse sketch. Plot a few examples to see how the shape evolves with t. OpenStax Algebra & Trigonometry Key Concepts
  6. Understand Vectors - Vectors pair magnitude and direction, so whether you're summing forces in physics or navigating in space, you'll use addition, subtraction, and scalar multiplication to get the job done. Graphical and component methods both work - just pick your favorite. Practice adding tip‑to‑tail or summing components to build intuition. OpenStax Algebra & Trigonometry Key Concepts
  7. Review Exponent Rules - Master rules like a❿·aᵝ = a❿❺ᵝ and (a❿)ᵝ = a❿ᵝ to simplify expressions and speed through tricky algebra. These shortcuts are your toolkit for taming large powers and roots. Drill on mixed problems to see how exponents behave under multiplication, division, and zero or negative powers. OpenStax Prealgebra Key Concepts
  8. Practice Linear Equations & Inequalities - Isolating variables, balancing both sides, and checking solutions are fundamental skills you'll use in every corner of math. From 2x - 5 = 9 to compound inequalities, getting comfortable with these steps lays a rock‑solid foundation. Challenge yourself with word problems to level up your critical‑thinking game. OpenStax Intermediate Algebra Section 2
  9. Study Exponential & Logarithmic Functions - Exponential growth and decay (f(x) = a·bˣ) plus their inverses (logarithms) pop up in everything from population models to Richter scales. Learn to switch between forms, graph key characteristics, and solve equations by "undoing" exponents with logs. Real‑world examples make these abstract ideas click. OpenStax Intermediate Algebra Key Concepts
  10. Delve into Quadratic Functions - Quadratics come in standard form (ax² + bx + c), vertex form, or factored form - and each view helps you solve, graph, and optimize parabolas. Use factoring, completing the square, or the quadratic formula x = ( - b ± √(b² - 4ac))/(2a) to find roots like a pro. Mix in graphing practice to nail vertex location and axis of symmetry. The Math Guru Grade 11 Math Exam Guide
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