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Quizzes > High School Quizzes > Mathematics

Ace Your Wise Exam Practice Test

Access wise exam answers and boost your skills

Difficulty: Moderate
Grade: Grade 3
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz for 10th-grade algebra students to improve exam strategies.

What is the value of x in the equation 2x + 5 = 13?
6
3
5
4
Subtracting 5 from both sides gives 2x = 8, and dividing by 2 yields x = 4. This problem tests basic linear equation solving.
Simplify the expression: 3(a + 4).
3a
a + 12
3a + 4
3a + 12
Distributing 3 to both a and 4 produces 3a + 12. This utilizes the distributive property correctly.
Solve for x: x - 7 = 3.
10
3
7
-4
Adding 7 to both sides results in x = 10. This simple step demonstrates solving a basic linear equation.
Evaluate the expression 2x² when x = 3.
9
6
18
15
Substituting x = 3 into 2x² gives 2 × 9 = 18. The order of operations confirms the correct evaluation.
What is the value of y in the equation 5y = 20?
20
4
5
0
Dividing both sides of 5y = 20 by 5 results in y = 4. This illustrates solving a simple direct equation.
Solve for x: 5x - 2(x + 3) = 12.
6
5
4
8
Expanding the equation gives 5x - 2x - 6 = 12, which simplifies to 3x - 6 = 12. Adding 6 and dividing by 3 leads to x = 6.
Factor the quadratic expression: x² + 5x + 6.
(x - 2)(x + 3)
(x + 2)(x + 3)
(x + 1)(x + 6)
(x + 3)(x + 4)
The numbers 2 and 3 multiply to 6 and add to 5, so the quadratic factors as (x + 2)(x + 3). This is a standard factoring technique.
Find the solutions to the equation: x² - 5x + 6 = 0.
x = -2 or x = -3
x = 5
x = 1 or x = 6
x = 2 or x = 3
Factoring the quadratic gives (x - 2)(x - 3) = 0, so the solutions are x = 2 and x = 3. This demonstrates the zero product property.
Given f(x) = 2x + 3, what is the value of f(4)?
8
11
10
7
Substituting x = 4 into f(x) gives 2(4) + 3 = 11. This is a straightforward function evaluation.
Simplify the expression: 4x - 2(3x - 5).
-2x - 10
-2x + 10
2x - 10
6x - 10
Distributing -2 gives -6x + 10, and adding 4x results in -2x + 10. This problem applies the distributive property followed by combining like terms.
Solve for x: (2x)/3 = 8.
16
12
10
8
Multiplying both sides by 3 gives 2x = 24, and dividing by 2 leads to x = 12. This problem reinforces solving equations with fractions.
Solve the inequality: x + 4 > 9.
x > 5
x ≥ 4
x ≥ 5
x < 5
Subtracting 4 from both sides results in x > 5. The strict inequality is maintained throughout the solution.
If y = 3x - 2 and y = 4, what is the value of x?
2
4
1
-2
Setting 3x - 2 equal to 4 and solving gives 3x = 6, hence x = 2. This problem reinforces solving simple linear equations by isolation.
Factor the expression: 6x² + 9x.
3(2x² + 3x)
x(2x + 3)
6x(x + 1)
3x(2x + 3)
The greatest common factor in 6x² + 9x is 3x, and factoring it out yields 3x(2x + 3). This is a standard method for factoring out common terms.
Expand the binomial: (x + 2)².
x² + 2x
x² + 4x + 4
x² + 4
x² + 2x + 4
Using the formula (a + b)² = a² + 2ab + b², the expansion of (x + 2)² is x² + 4x + 4. This tests the application of the binomial expansion formula.
Solve the quadratic equation: 2x² - 3x - 2 = 0.
x = 2 or x = -1/2
x = -2 or x = 1/2
x = -1/2
x = 2
Factoring the equation as (2x + 1)(x - 2) = 0 gives the solutions x = -1/2 and x = 2. This problem challenges students to factor a non-monic quadratic.
Solve for x in the equation: (x - 1)/(x + 2) = 3/4.
12
10
-10
8
Cross-multiplying yields 4(x - 1) = 3(x + 2), which simplifies to x = 10. This tests the student's ability to work with rational equations.
If log₂(x) = 5, what is the value of x?
64
32
5
16
The equation log₂(x) = 5 means that 2 raised to the 5th power equals x, so x = 32. This problem introduces basic logarithmic concepts.
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 = 8/3, y = -5/3
By substituting x = y + 1 from the second equation into the first, the solution obtained is x = 8/3 and y = 5/3. This system requires combining substitution and elimination methods.
Solve for x: √(x + 6) = x - 2.
x = (5 + √33)/4
x = (√33 - 5)/2
x = (5 + √33)/2
x = (5 - √33)/2
Squaring both sides produces the quadratic x² - 5x - 2 = 0, and checking for extraneous solutions shows that only x = (5 + √33)/2 satisfies the original equation. This emphasizes the need to verify solutions when dealing with radicals.
0
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Study Outcomes

  1. Understand key algebraic concepts presented in the quiz.
  2. Analyze problem structures to identify areas for improvement.
  3. Apply effective test-taking strategies to solve targeted problems.
  4. Evaluate performance to build confidence for upcoming exams.
  5. Synthesize learned techniques to tackle a variety of algebra problems.

Wise Exam Practice Test Cheat Sheet

  1. Master the Quadratic Formula - Unleash your inner math hero by using x = (−b ± √(b² − 4ac)) / (2a) to crack any quadratic equation in ax² + bx + c = 0. With practice, each coefficient becomes a friend, and solving these puzzles feels like a quick code-break. Before you know it, quadratic villains won't stand a chance! Solve Quadratic Equations Using the Quadratic Formula
    2. Solve Quadratic Equations Using the Quadratic Formula
  2. Understand Exponential Functions - Get ready to model anything that grows or shrinks at lightning speed with f(x) = a·b^x. Tweak a and b to see dramatic curves that mirror everything from bacteria blooms to viral trends. Mastering these twists and turns gives you real-world superpowers in science and finance! Evaluate and Graph Exponential Functions
    3. Evaluate and Graph Exponential Functions
  3. Get comfortable with Logarithmic Functions - Step into the world of logs as the ultimate antidote when exponents run wild: y = log_b(x) means b^y = x. These inverses of exponentials are your key to cracking down huge or tiny values in a snap. Once you've tamed logs, solving for hidden exponents is pure victory! Evaluate and Graph Logarithmic Functions
    4. Evaluate and Graph Logarithmic Functions
  4. Learn the Properties of Logarithms - Break down complex logs into manageable chunks with the product, quotient, and power rules: log_b(xy) = log_b(x) + log_b(y), log_b(x/y) = log_b(x) − log_b(y), and log_b(x^r) = r·log_b(x). These shortcuts slice through messy expressions like a hot knife through butter. Armed with these rules, your path to simplifying any logarithmic maze is clear! Use the Properties of Logarithms
    5. Use the Properties of Logarithms
  5. Practice Solving Exponential and Logarithmic Equations - Whether you're calculating compound interest or predicting population trends, equations like a·b^x = c or log_b(x) = d pop up everywhere. Sharpen your skills by isolating the variable and switching between log and exponential forms. Soon you'll solve these real-world puzzles faster than you can say "logarithm"! Solve Exponential and Logarithmic Equations
    6. Solve Exponential and Logarithmic Equations
  6. Familiarize yourself with Polynomial Identities - Expand and factor like a boss using rules such as (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b². These identities transform gnarly polynomials into neat, solvable forms in seconds. Add them to your toolkit and watch complex expressions bow to your will! 10th Class Math Formulas and Important Formulas for Board Exams
    7. 10th Class Math Formulas and Important Formulas for Board Exams
  7. Understand the Laws of Exponents - Simplify power-packed expressions with rules like a^m·a^n = a^(m+n) and (a^m)^n = a^(mn), turning exponent chaos into clear calculations. Mastering these laws helps you tackle everything from scientific notation to algebraic proofs. Level up your simplification game and exponents will no longer scare you! 10th Class Math Formulas and Important Formulas for Board Exams
    8. 10th Class Math Formulas and Important Formulas for Board Exams
  8. Grasp the Pythagorean Theorem - In any right triangle, the squares of the legs add up to the square of the hypotenuse: a² + b² = c². This geometric gem is your go-to for distance finding, trigonometry basics, and real-world measurements. With right-angle secrets unlocked, you'll navigate math and maps with newfound confidence! Solve Applications Modeled by Quadratic Equations
    9. Solve Applications Modeled by Quadratic Equations
  9. Learn about Functions and Their Inverses - Functions turn inputs into outputs; inverses flip the process, giving you the power to rewind equations. Finding f❻¹(x) helps solve puzzles where you need to backtrack steps. Mastering this flip-flop is crucial for everything from algebra to cryptography! Finding Composite and Inverse Functions
    10. Finding Composite and Inverse Functions
  10. Explore Graphing Quadratic Equations - Plot parabolas with pizzazz by locating their vertices, axes of symmetry, and intercepts to reveal each curve's unique shape. Understanding transformations like translations and stretches lets you predict graph behavior before sketching. With these skills, quadratic curves become as simple as connect-the-dots! Graphing Quadratic Equations in Two Variables
    11. Graphing Quadratic Equations in Two Variables
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