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Quizzes > High School Quizzes > Mathematics

Black Card Revoked Practice Quiz

Practice with PDF answers for exam success

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art depicting trivia for The Black Card Challenge quiz testing high school algebra skills.

This Black Card Revoked quiz helps you see how much you know about Black culture, from TV and movies to music and moments. Answer 20 quick questions, get instant answers and links to learn more, and have fun while you pick up a new fact or two.

Solve the equation 3x - 7 = 11. What is the value of x?
6
11
4
7
To isolate x, add 7 to both sides to get 3x = 18, then divide by 3 to obtain x = 6. This straightforward process demonstrates the basic method of solving linear equations.
Simplify the expression: 2(3x + 4) - 5.
6x + 3
6x + 8
3x + 3
5x + 3
Distribute 2 over (3x + 4) to get 6x + 8, and then subtract 5 to obtain 6x + 3. This problem reinforces distribution and combining like terms.
Evaluate the expression 2^3 * 2^2.
32
10
16
20
Using the exponent rule, 2^3 * 2^2 = 2^(3+2) = 2^5, which equals 32. This demonstrates the property of multiplying powers with the same base.
Factor the expression 6x + 9.
6(x + 1.5)
2(3x + 4.5)
3(2x + 3)
9(x + 2/3)
The greatest common factor of 6 and 9 is 3. Factoring 3 out of the expression gives 3(2x + 3), which is the simplest form.
Solve the equation x^2 - 9 = 0.
x = 3 or x = -3
x = 9 or x = -9
x = -3
x = 3
Recognize that x^2 - 9 is a difference of squares and factors as (x - 3)(x + 3). Setting each factor equal to zero gives the solutions x = 3 and x = -3.
Solve the equation 2(x - 3) = 4x - 10.
x = -2
x = 6
x = 2
x = 4
Expanding 2(x - 3) gives 2x - 6, and setting the equation 2x - 6 = 4x - 10 leads to 2x = 4, so x = 2. This problem emphasizes rearranging equations to isolate the variable.
Solve the quadratic equation: x^2 + 5x + 6 = 0.
x = 2 and x = 3
x = 1 and x = 6
x = -2 and x = -3
x = -1 and x = -6
The quadratic factors as (x + 2)(x + 3) = 0, which results in the solutions x = -2 or x = -3. Factoring is an efficient method for solving such quadratic equations.
For the function f(x) = 2x - 3, what is f(5)?
7
5
10
8
Substitute x = 5 into the function to get f(5) = 2(5) - 3 = 10 - 3 = 7. This question reinforces evaluation of a linear function.
Simplify the radical √50.
5√2
2√50
10√2
√25 + √2
Break 50 into 25 Ã- 2, and since √25 = 5, the expression simplifies to 5√2. This process demonstrates the simplification of radical expressions through factoring.
Simplify the expression (x^3y^2)^2.
x^2y^4
x^5y^4
x^6y^2
x^6y^4
Raise each factor to the power of 2: (x^3)^2 becomes x^6 and (y^2)^2 becomes y^4, resulting in x^6y^4. This exercise reinforces the rules of exponents in algebra.
Solve for x: (2x - 4) / 6 = 2.
8
4
6
10
Multiply both sides by 6 to eliminate the fraction, resulting in 2x - 4 = 12. Solving for x by adding 4 and then dividing by 2 yields x = 8.
Find the vertex of the quadratic function: y = 2(x - 1)^2 + 3.
(-1, 3)
(3, 1)
(1, 3)
(1, -3)
The quadratic is already in vertex form, y = a(x - h)^2 + k, where the vertex is (h, k). Here, h = 1 and k = 3, so the vertex is (1, 3).
Factor the quadratic expression: x^2 - 5x + 6.
(x - 1)(x - 6)
(x - 5)(x + 1)
(x - 2)(x - 3)
(x + 2)(x + 3)
Find two numbers that multiply to 6 and add to -5; these are -2 and -3. Thus, x^2 - 5x + 6 factors as (x - 2)(x - 3).
Solve the system of equations: x + y = 7 and x - y = 3.
(3, 4)
(-5, -2)
(5, 2)
(2, 5)
Adding the equations eliminates y, yielding 2x = 10 so that x = 5. Substituting back into one of the equations gives y = 2, solving the system.
If the sum of two numbers is 12 and their difference is 4, what are the numbers?
10 and 2
7 and 5
8 and 4
6 and 6
Setting up the system x + y = 12 and x - y = 4, adding the two equations gives 2x = 16, so x = 8 and then y = 4. This problem demonstrates solving word problems using systems of equations.
Solve the quadratic equation: 2x^2 - 3x - 2 = 0 using the quadratic formula.
x = -2 and x = -1/2
x = -2 and x = 1/2
x = 2 and x = -1/2
x = 2 and x = 1/2
Using the quadratic formula with a = 2, b = -3, and c = -2 gives a discriminant of 25. This leads to x = (3 ± 5) / 4, yielding solutions x = 2 and x = -1/2.
Simplify the expression (2x^2 - 8) / (4x) and state any restrictions on x.
(x - 2)(x + 2) / 2, where x ≠ 0
(x - 2) / (2x)
(x + 2) / (2x)
(x - 2)(x + 2) / (2x), where x ≠ 0
Factor the numerator as 2(x^2 - 4) = 2(x - 2)(x + 2) and then cancel the common factor with the denominator to obtain (x - 2)(x + 2) / (2x). The restriction x ≠ 0 is included because division by zero is undefined.
Solve the exponential equation: 2^(x + 1) = 16.
4
8
3
2
Recognize that 16 can be written as 2^4. Equate the exponents to get x + 1 = 4, which simplifies to x = 3. This problem illustrates solving exponential equations by matching bases.
Solve the inequality: 3 - 2(x - 1) < 7.
x < 1
x > 1
x > -1
x < -1
First, expand the inequality to get 3 - 2x + 2 < 7, which simplifies to 5 - 2x < 7. After subtracting 5 and dividing by -2 (remembering to flip the inequality sign), the solution is x > -1.
Solve the radical equation: √(x + 5) = x - 1.
x = -1
x = 4 and x = -1
No solution
x = 4
Square both sides of the equation to obtain x + 5 = (x - 1)^2. This simplifies to x^2 - 3x - 4 = 0, which factors as (x - 4)(x + 1) = 0. Testing the potential solutions in the original equation shows that only x = 4 is valid.
0
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Study Outcomes

  1. Analyze algebraic expressions and equations to identify underlying patterns.
  2. Apply algebraic techniques to solve exam-style problems effectively.
  3. Synthesize multiple problem-solving strategies to tackle challenging questions under test conditions.
  4. Evaluate solutions critically to detect and correct computational errors.
  5. Develop time-management skills for completing algebra sections under exam pressure.

Black Card Revoked: PDF Questions & Answers Cheat Sheet

  1. Master the Order of Operations - Put on your math cape! By mastering PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction in that snazzy left-to-right order), you'll breeze through expressions like a pro. Expressions, Equations, and Functions | High School Math
  2. Understand the Properties of Equality - Think of equality properties as the secret handshake of algebra: Reflexive, Symmetric, Transitive and Substitution. Spot how they keep equations balanced and unlock neat tricks for solving them! Expressions, Equations, and Functions | High School Math
  3. Familiarize with Basic Algebraic Identities - Gear up for shortcuts that simplify monsters of expressions! The difference of squares (a² - b² = (a - b)(a + b)) is just the start of your identity toolkit. Math Expression: Basic Algebra Formulas
  4. Grasp the Laws of Exponents - Exponents aren't scary once you know the rules: am × an = am+n, (am)n = amn, and (ab)m = am × bm. They'll help you sprint through growth and decay like a math ninja! Algebra Formulas List & All Basic Algebra Maths Formulas PDF
  5. Learn the Quadratic Formula - When equations get quadratic, call in the big guns: x = [−b ± √(b² - 4ac)]/(2a). It's your go-to move for wrestling down the roots of any ax² + bx + c = 0. Elementary Algebra Review Sheet and Common Formulas | Sierra College Mathematics Department
  6. Understand the Properties of Real Numbers - Commutative, Associative, Distributive, Identity and Inverse properties are the building blocks of every algebraic move you make. They're like the rules of the algebraic road! Elementary Algebra Review Sheet and Common Formulas | Sierra College Mathematics Department
  7. Practice Factoring Techniques - Become a pattern detective! Spot difference of squares and perfect square trinomials to factor expressions faster than you can say "x² - 9 = (x - 3)(x + 3)". Math Expression: Basic Algebra Formulas
  8. Explore Arithmetic and Geometric Progressions - Sequences aren't just for secret codes: use Tn = a + (n - 1)d for arithmetic and special formulas for geometric sums to see patterns pop! Math Expression: Basic Algebra Formulas
  9. Study Polynomial Identities - Smash through cubes with confidence using a³ + b³ = (a + b)(a² - ab + b²) and a³ - b³ = (a - b)(a² + ab + b²). These power-packed identities make simplification a snap! Elementary Algebra Review Sheet and Common Formulas | Sierra College Mathematics Department
  10. Understand the Binomial Theorem - Expand (a + b)n like a wizard with the Binomial Theorem! Master the nCr magic and watch polynomial expansions unfurl before your eyes. High School Algebra Common Core Standards
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