Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Practice Star Test Quiz

Ace Your Practice Adap and AR Tests at Home

Difficulty: Moderate
Grade: Grade 10
Study OutcomesCheat Sheet
Colorful paper art promoting the Ace ADAP at Home interactive algebra quiz for high school students.

Solve for x: 2x + 3 = 7.
x = 4
x = 1
x = 2
x = 3
Subtracting 3 from both sides gives 2x = 4, and dividing by 2 leads to x = 2. This is a straightforward linear equation solution.
Evaluate: 3 * (4 + 2).
18
20
24
12
According to the order of operations, you first add 4 and 2 to get 6, and then multiply by 3 to obtain 18. Thus, 18 is the correct answer.
Simplify: 2x + 3x.
2x^2
x
6x
5x
You add like terms by summing their coefficients: 2 + 3 equals 5, producing 5x. This is the simplest form of the expression.
Solve for y: 5y = 20.
y = 4
y = 0
y = 10
y = 5
Dividing both sides of the equation by 5 isolates y, giving y = 4. This direct division yields the correct answer.
Identify the slope of the line: y = 2x + 3.
2
-2
1/2
3
In the slope-intercept form y = mx + b, the coefficient m represents the slope. Here, m is 2, which is why the slope is 2.
Solve for x: 3x - 5 = 2x + 2.
x = 2
x = -7
x = 7
x = 5
Subtracting 2x from both sides results in x - 5 = 2, and adding 5 to both sides gives x = 7. This simple manipulation confirms the correct solution.
Solve for x: 2(x - 3) = 4x + 6.
x = -3
x = -6
x = 3
x = 6
Expanding 2(x - 3) gives 2x - 6, so the equation becomes 2x - 6 = 4x + 6. Rearranging the terms leads to 2x = -12 and thus x = -6. This is the correct solution.
Factor the polynomial: x² + 5x + 6.
(x + 2)(x + 4)
(x + 3)(x + 3)
(x + 2)(x + 3)
(x + 1)(x + 6)
The numbers 2 and 3 multiply to 6 and add up to 5, which allows you to factor the quadratic as (x + 2)(x + 3). This factorization is standard for quadratics with these coefficients.
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 1 or x = 6
x = -1 or x = -6
x = 2 or x = 3
x = -2 or x = -3
Factoring the equation gives (x - 2)(x - 3) = 0, leading to the solutions x = 2 and x = 3. Both values satisfy the equation.
Simplify the radical: √18.
6
3√2
√9
9√2
The number 18 can be written as 9 multiplied by 2, so √18 becomes √9 * √2 which simplifies to 3√2. This is the simplest radical form.
Find the y-intercept of the line given by: y = 3x - 1.
y = 3
x = -1
y = -1
y = 1
In the equation y = 3x - 1, the constant term (-1) represents the y-intercept. Therefore, the line crosses the y-axis at y = -1.
Solve the system of equations: x + y = 7 and x - y = 3.
x = 3, y = 4
x = 5, y = -2
x = 5, y = 2
x = 7, y = 0
Adding the two equations eliminates y, resulting in 2x = 10 and thereby x = 5. Substituting x back into one of the equations confirms y = 2.
Evaluate the function f(x) = 2x² - 3 at x = 2.
5
7
8
1
Substituting x = 2 into the function yields 2(4) - 3 = 8 - 3 = 5. This confirms that f(2) is equal to 5.
Solve the inequality: 3x - 4 < 11.
x > 5
x < 5
x ≤ 5
x ≥ 5
Adding 4 to both sides gives 3x < 15, and dividing by 3 results in x < 5. This is the range of solutions for the inequality.
Expand the expression: (x + 3)².
x² + 3
2x + 3
x² + 6x + 9
x² + 9
Using the binomial expansion formula, (x + 3)² equals x² + 2·x·3 + 3², which simplifies to x² + 6x + 9. This is the correct expansion.
Solve the quadratic equation using the quadratic formula: 2x² - 4x - 6 = 0.
x = 2 or x = -3
x = 1 or x = -6
x = 3 or x = -1
x = 4 or x = -2
Using the quadratic formula, x = (4 ± √64) / 4 results in x = (4 ± 8)/4. This simplifies to x = 3 and x = -1, which are the correct solutions.
Simplify the rational expression: (x² - 9) / (x² - x - 12).
(x + 3) / (x + 4)
(x - 3) / (x + 4)
(x + 3) / (x - 4)
(x - 3) / (x - 4)
Factoring the numerator as (x - 3)(x + 3) and the denominator as (x - 4)(x + 3) allows you to cancel the (x + 3) factor, resulting in (x - 3)/(x - 4).
Solve the radical equation: √(2x + 3) = x - 1.
x = 2 - √6
x = 2 + √6
x = √6 - 2
x = 1 + √6
Squaring both sides gives 2x + 3 = (x - 1)², which leads to the quadratic equation x² - 4x - 2 = 0. Solving this and considering the domain restriction (x must be at least 1) eliminates one solution, leaving x = 2 + √6 as the valid answer.
A rectangle's length is twice its width. If its perimeter is 36, what is its area?
60
72
36
48
Let the width be w; then the length is 2w. The perimeter is 2(w + 2w) which equals 6w. Setting 6w = 36 gives w = 6, so the length is 12 and the area is 6 × 12 = 72.
Find the inverse of the function f(x) = 3x - 5.
(x - 5) / 3
(3x + 5) / 1
(5 - x) / 3
(x + 5) / 3
To find the inverse, swap x and y in the equation y = 3x - 5 to get x = 3y - 5, and then solve for y. The result is y = (x + 5) / 3, which is the correct inverse function.
0
{"name":"Solve for x: 2x + 3 = 7.", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Solve for x: 2x + 3 = 7., Evaluate: 3 * (4 + 2)., Simplify: 2x + 3x.","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand and analyze algebraic expressions and equations.
  2. Apply problem-solving techniques to simplify and solve linear equations.
  3. Identify key concepts in high school algebra to assess overall comprehension.
  4. Evaluate problem areas by pinpointing mistakes in practice questions.
  5. Develop confidence in executing algebraic methods for upcoming tests and exams.

At-Home STAR, AR & ADAP Practice Test Cheat Sheet

  1. Quadratic Formula - A go‑to method for solving any quadratic equation of the form ax² + bx + c = 0. Simply plug your a, b, and c into x = (-b ± √(b² - 4ac))❄(2a) and watch the magic happen. Practice with different values to see how the roots change! OpenStax Elementary Algebra Key Concepts
  2. Properties of Exponents - Master rules like the product rule (a❿ * aᵝ = a❿❺ᵝ) and power rule ((a❿)ᵝ = a❿·ᵝ) to simplify any expression with powers. These shortcuts save tons of time and keep your work neat. Start combining and breaking down exponents until it feels second nature! OpenStax Prealgebra Key Concepts
  3. Laws of Sines and Cosines - Perfect for tackling non‑right triangles by relating sides and angles in flexible ways. Use the Law of Sines when you know two angles and a side, or the Law of Cosines for two sides and the included angle. Plot a triangle on graph paper and verify your answers to build intuition! OpenStax Algebra & Trigonometry Key Concepts
  4. Inverse Functions - If f(x) maps inputs to outputs one‑to‑one, its inverse f❻¹(x) flips the process, swapping roles of x and y. To find it, rewrite y = f(x), switch x↔y, then solve for y. Test by plugging f❻¹(f(x)) to ensure you get back the original x! OpenStax Intermediate Algebra Key Concepts
  5. Logarithmic Functions - The secret weapon for solving equations where the variable hides in the exponent. Remember: log₝(b) answers "To what power must a be raised to get b?" Practice by converting between exponential and log forms to deepen understanding. OpenStax Intermediate Algebra Key Concepts
  6. Factoring Polynomials - Break down complex polynomials into products of simpler terms to solve equations and simplify expressions. Start with common factors, then tackle trinomials and difference of squares. Factoring transforms messy problems into manageable steps! OpenStax Prealgebra Key Concepts
  7. Graphing Quadratic Equations - Quadratics graph as parabolas - find the vertex, axis of symmetry, and intercepts to sketch them perfectly. The vertex formula (−b/2a, f(−b/2a)) pinpoints your turning point. Practice shifting a, b, and c to see how the parabola stretches and moves! OpenStax Elementary Algebra Key Concepts
  8. Polar Coordinates - Represent points by (r, θ) instead of (x, y), where r is the radial distance and θ the angle from the positive x‑axis. Convert back and forth using x = r cosθ, y = r sinθ to master both systems. Polar plots make circular patterns and spirals a breeze! OpenStax Algebra & Trigonometry Key Concepts
  9. Parametric Equations - Express x and y as functions of a third variable (often t), giving a dynamic description of curves and motion. Perfect for modeling projectile paths, cycloids, or any time‑dependent trajectory. Sketch each point step by step to visualize how t traces the curve! OpenStax Algebra & Trigonometry Key Concepts
  10. Key Algebra Terms - Get comfortable with vocabulary like coefficient, variable, and exponent - your secret math power tools. In 7x², 7 is the coefficient, x the variable, and 2 the exponent. A solid grasp of terms makes complex topics feel like simple puzzles! LearnTheta: Key Algebra Terms
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker