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Quizzes > Quizzes for Business > Education

Master the Algebra Escape Room Quiz

Challenge Your Algebra Skills with Puzzles

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting elements of an Algebra Escape Room Quiz.

This Algebra Escape Room quiz helps you practice algebra with 15 quick, multiple-choice puzzles on equations, factoring, and more, so you can build speed and spot gaps before a test. When you want more, try the Linear Equations and Graphs quiz or mix it up with the Escape Room Puzzle quiz .

Solve for x: 2x + 3 = 11.
x = 8
x = 4
x = 7
x = 3
Subtracting 3 from both sides gives 2x = 8. Dividing both sides by 2 yields x = 4.
Solve for x: x/4 = 5.
x = -20
x = 1
x = 20
x = 9
Multiplying both sides of the equation by 4 isolates x. So x = 4 Ã- 5 = 20.
What is f(3) if f(x) = 2x + 1?
5
7
6
3
Substitute x = 3 into the function to get f(3) = 2(3) + 1 = 7. This direct substitution isolates the variable for evaluation.
Find the next term in the arithmetic sequence: 5, 8, 11, ...
15
14
12
13
The sequence increases by 3 each term, so adding 3 to the last term 11 gives 14. Recognizing the constant difference confirms 14 as the next term.
Which operation isolates x in 5x - 2 = 13 first?
Multiply by 5, then add 2
Add 2, then divide by 5
Divide by 5, then subtract 2
Subtract 5, then divide by 2
We first undo the subtraction by adding 2 to both sides, giving 5x = 15. Then dividing by 5 isolates x = 3.
Solve for x: 3(x - 2) = 9.
x = 1
x = 5
x = -5
x = 3
Expanding the expression gives 3x - 6 = 9. Adding 6 and then dividing by 3 gives x = 5.
What are the roots of the equation x^2 - 5x + 6 = 0?
x = -2 and x = -3
x = 3 and x = -2
x = 2 and x = 3
x = 1 and x = 6
The quadratic factors as (x - 2)(x - 3) = 0, so the solutions are x = 2 and x = 3. Setting each factor to zero isolates the roots.
A sequence follows the rule a_n = n^2 + 1. What is the fifth term?
20
24
25
26
Plugging n = 5 into the formula gives 5^2 + 1 = 26. This follows directly from substituting the index into the rule.
What is f(g(2)) when f(x) = x + 3 and g(x) = 2x?
4
5
8
7
First compute g(2) = 4, then substitute into f to get f(4) = 7. This nested evaluation combines both function rules.
Which method is most efficient to solve the system: 2x + 3y = 6 and x = 2y - 1?
Elimination
Graphing
Substitution
Quadratic formula
Since x is already isolated in the second equation, substituting 2y - 1 into the first equation is fastest. This avoids additional elimination steps.
If P = 2(l + w) and P = 20 when l - w = 2, what are the values of l and w?
l = 7 and w = 3
l = 6 and w = 4
l = 5 and w = 5
l = 4 and w = 6
From the perimeter equation l + w = 10 and the difference equation l - w = 2, adding them gives 2l = 12 so l = 6. Substituting back yields w = 4.
Which expression simplifies 4(x + 2) - 3x?
x - 8
x + 8
8x
x + 2
Distribute 4 to get 4x + 8, then subtract 3x to obtain x + 8. This combines like terms correctly.
The quadratic function h(x) = x^2 - 4x + 3 has its vertex at which point?
(2, -1)
(1, -2)
(4, 3)
(-2, 1)
The vertex formula x = -b/(2a) gives x = 4/2 = 2, and h(2) = 2^2 - 4·2 + 3 = -1. Therefore, the vertex is at (2, -1).
Given the sequence 3, 8, 15, 24, ..., where the differences increase by 2 each time, what is the sixth term?
35
50
48
42
Differences are 5, 7, 9, 11, 13, so the fifth term is 35 and the sixth term adds 13 to 35 giving 48. Recognizing this quadratic difference pattern leads to 48.
Which function rule models doubling the input then adding 5?
f(x) = x^2 + 5
f(x) = (x + 5)/2
f(x) = 2x + 5
f(x) = 2(x + 5)
Applying the doubling as 2x and then adding 5 yields the rule f(x) = 2x + 5. This matches the described operation order.
Solve for x: x^2 - 3x - 10 = 0.
x = -2 or x = -5
x = 5 or x = -2
x = -5 or x = 2
x = 2 or x = 5
Factoring gives (x - 5)(x + 2) = 0, so x = 5 or x = -2. This finds both roots of the equation.
Solve the system of equations x + y = 5 and x - y = 1.
x = 4 and y = 1
x = 3 and y = 2
x = 1 and y = 4
x = 2 and y = 3
Adding the two equations gives 2x = 6 so x = 3, then substituting back yields y = 2. This elimination approach quickly finds both variables.
What is the vertex form of the quadratic function f(x) = x^2 + 6x + 5?
f(x) = (x - 3)^2 + 4
f(x) = (x - 6)^2 - 5
f(x) = (x + 6)^2 + 5
f(x) = (x + 3)^2 - 4
Completing the square gives f(x) = (x + 3)^2 - 4, revealing the vertex at (-3, -4). This is the standard method to convert to vertex form.
For what value of k does the quadratic equation x^2 + kx + 9 = 0 have exactly one real root?
k = 0
k = 3
k = 9
k = 6 or k = -6
A single real root occurs when the discriminant is zero, so k^2 - 36 = 0 gives k = ±6. This condition yields a repeated root.
What is the domain of the function f(x) = 1/(x - 2)?
All real numbers
x > 2
All real numbers except x = 2
x < 2
The denominator cannot be zero, so x = 2 is excluded. Therefore, the domain is all real numbers except 2.
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Learning Outcomes

  1. Apply algebraic equations to solve escape room clues
  2. Identify patterns in linear and quadratic problems
  3. Analyse problem scenarios to choose correct operations
  4. Evaluate multiple-choice options for fastest solutions
  5. Master strategic thinking under time constraints
  6. Demonstrate command of variables and functions concept

Cheat Sheet

  1. Master linear equations - Cracking linear equations is like solving secret codes: keep both sides balanced and the mystery unfolds. With practice, transforming 2x + 3 = 7 into x = 2 will feel as natural as unlocking a treasure chest.
  2. Tackle quadratics with confidence - The quadratic formula (x = −b ± √(b²−4ac) / 2a) is your superpower for second-degree equations. Memorize it, and you'll breeze through puzzles that once felt impossible.
  3. Spot equation patterns - Recognizing recurring structures - like perfect squares or difference of squares - can save you loads of time. Once you spot a pattern, you'll know exactly which shortcut to use.
  4. Time yourself for speed - Throw yourself into timed quizzes to build that rapid-fire problem-solving reflex. Racing against the clock simulates high-stakes exams and escape-room challenges.
  5. Know your variables and functions - Variables are the actors and functions are the directors in the algebraic stage. Mastering how f(x)=x² behaves lets you predict its performance on any graph.
  6. Eliminate wrong answers fast - Multiple-choice problems reward quick elimination of outliers. Spot the outrageous options first to zero in on the right solution in record time.
  7. Analyze before you calculate - Pause and decide if substitution or elimination will be your best tool in a system of equations. A strategic move here can slash your calculation time in half.
  8. Memorize key formulas - Having formulas like a²−b²=(a−b)(a+b) at your fingertips turns tough questions into one-step wonders. No more panicking when you see that familiar pattern.
  9. Translate words into math - Converting a story problem into an equation is the bridge to the solution. Practice with narrative puzzles to sharpen your translation skills.
  10. Play interactive algebra games - Turn drills into thrill with digital escape rooms that test every algebraic skill. Team up, solve clues, and celebrate when you break free!
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