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Quizzes > High School Quizzes > Mathematics

Ace Your NJSL A Practice Test

Sharpen algebra and math skills with targeted practice

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting NJSLA Algebra Blitz trivia quiz for middle school students.

What is the solution to the equation x + 3 = 7?
x = 4
x = 7
x = 3
x = 10
Subtracting 3 from both sides of the equation isolates x, resulting in x = 4. This simple step-by-step approach confirms the correct answer.
Simplify the expression: 3x + 4x.
7x
12x
x
x^7
By combining like terms, the coefficients 3 and 4 add up to 7, resulting in 7x. This is the correct simplified form.
Expand the expression: 2(x + 3).
2x + 6
2x + 3
2x + 5
x + 6
Distributing 2 to each term inside the parentheses gives 2x and 6. Therefore, the correct expansion is 2x + 6.
Evaluate the expression: 3(2) + 4.
10
14
8
12
Multiplying 3 by 2 gives 6, then adding 4 results in 10. This direct computation confirms that 10 is the correct answer.
Solve for x: 2x = 10.
x = 5
x = 10
x = 2
x = 8
Dividing both sides of the equation by 2 isolates x, resulting in x = 5. This is a straightforward solution using basic algebra.
Solve the equation: 2x + 3 = x + 7.
x = 4
x = 7
x = 2
x = 10
Subtracting x from both sides results in x + 3 = 7, and subtracting 3 from both sides gives x = 4. This step-by-step approach confirms the correct answer.
Solve for x: 3(x - 1) = 2x + 1.
x = 4
x = 1
x = 3
x = -4
After distributing 3 to get 3x - 3 and then isolating x by subtracting 2x and adding 3, the solution x = 4 is obtained. This confirms the proper method for solving the equation.
What is the slope of the line passing through the points (1, 2) and (3, 6)?
2
4
1/2
3
The slope is calculated using the change in y divided by the change in x, which in this case is (6 - 2) / (3 - 1). This simplifies to 4/2 = 2, which confirms the correct answer.
Factor the quadratic expression: x^2 + 5x + 6.
(x + 2)(x + 3)
(x + 1)(x + 6)
(x + 3)(x + 4)
(x + 2)(x + 4)
The numbers 2 and 3 multiply to 6 and add to 5, leading to the factorization (x + 2)(x + 3). This is the correct factorization for the quadratic expression.
Simplify the expression: 2x - 3x + 4.
-x + 4
x + 4
-x - 4
x - 4
Combining the like terms 2x and -3x results in -x, and adding 4 yields -x + 4. This is the simplified form of the expression.
Solve for x: x/3 = 4.
x = 12
x = 7
x = 3
x = 4
Multiplying both sides of the equation by 3 isolates x, resulting in x = 12. This direct method confirms the correct answer.
Solve the equation: 3x - 2 = 4x + 1.
x = -3
x = 3
x = -1
x = 1
Rearranging the equation by moving x-terms to one side and constant terms to the other gives x = -3. This proper isolation of the variable confirms the solution.
Solve for x: 4(x + 2) = 3x + 14.
x = 6
x = 7
x = 8
x = 4
After expanding 4(x + 2) to get 4x + 8 and then isolating x by subtracting 3x, the result x + 8 = 14 leads to x = 6. This step-by-step process verifies the answer.
If f(x) = 2x^2, what is the value of f(3)?
18
9
6
12
Substituting 3 into the function gives f(3) = 2*(3^2) = 18. This direct substitution confirms that the correct value is 18.
Solve the proportion: 2/3 = x/9.
x = 6
x = 9
x = 3
x = 12
Cross-multiplying the proportion yields 2*9 = 3x, which simplifies to x = 6. This systematic approach confirms the proper solution.
Factor the quadratic expression: x^2 - 5x + 6.
(x - 2)(x - 3)
(x + 2)(x + 3)
(x - 5)(x + 1)
(x - 3)(x + 2)
The factors of 6 that add up to -5 are -2 and -3, which yield the factorization (x - 2)(x - 3). This factorization accurately represents the original quadratic.
Solve the system of equations: x + y = 7 and x - y = 3.
x = 5, y = 2
x = 3, y = 4
x = 7, y = 0
x = 4, y = 3
Adding the two equations eliminates y, giving 2x = 10, and thus x = 5. Substituting back confirms that y = 2, making (5, 2) the correct solution.
Simplify the rational expression: (x^2 - 9) / (x + 3).
x - 3
x + 3
(x - 3)(x + 3)
1
By recognizing x^2 - 9 as a difference of squares, it factors into (x - 3)(x + 3). Canceling the common factor (x + 3) results in x - 3, the correct simplified expression.
Solve the absolute value equation: |2x - 4| = 6.
x = 5 and x = -1
x = 5
x = -1
x = 6
The equation |2x - 4| = 6 splits into two cases: 2x - 4 = 6 and 2x - 4 = -6. Solving these gives x = 5 and x = -1 respectively, which are both valid solutions.
Factor completely: 6x^2 - 11x - 10.
(3x + 2)(2x - 5)
(3x - 2)(2x + 5)
(6x + 5)(x - 2)
(2x + 2)(3x - 5)
Factoring by grouping reveals that the quadratic factors as (3x + 2)(2x - 5). Expanding these factors confirms they multiply to the original expression, ensuring the factorization is correct.
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Study Outcomes

  1. Apply algebraic techniques to solve linear and quadratic equations.
  2. Simplify and evaluate algebraic expressions using operations and properties.
  3. Interpret word problems and convert them into algebraic models.
  4. Analyze variable relationships to identify patterns and predict outcomes.
  5. Demonstrate improved speed and accuracy under timed testing conditions.

NJSLA Math & Algebra Practice Test Cheat Sheet

  1. Master the Order of Operations - Think of algebra like a recipe: follow PEMDAS exactly or you'll end up with a hot mess! Always start with Parentheses, then tackle Exponents, move on to Multiplication and Division (left to right), and finish with Addition and Subtraction (left to right) for a flawless result every time. OpenStax Intermediate Algebra: Key Concepts
  2. Understand Properties of Real Numbers - The Commutative, Associative, and Distributive Properties are your best friends when it comes to rearranging and simplifying expressions smoothly. Master these rules and you'll be able to shuffle numbers around without breaking a sweat! OpenStax Algebra & Trigonometry: Key Concepts
  3. Learn Exponent Rules - From the Product Rule to the Negative Exponent Rule, knowing these shortcuts turns lengthy expressions into quick calculations. For instance, a^m × a^n is just a^(m+n), so you spend less time writing and more time solving! LearnMathClass: Exponent Rules
  4. Practice Factoring Polynomials - Spot the Greatest Common Factor (GCF) first, then use grouping or special patterns to break down quadratics and higher-degree expressions. For example, x² + 5x + 6 pops right open into (x + 2)(x + 3) once you find the magic 2 and 3! OpenStax Algebra & Trigonometry: Factoring Techniques
  5. Familiarize Yourself with the Quadratic Formula - When ax² + bx + c = 0, there's no need to guess - plug into x = [-b ± √(b² - 4ac)]/(2a) and voila, instant solutions! Keep a print‑out handy or memorize the jingle to save precious minutes on exams. Sierra College: Quadratic Formula Guide
  6. Understand Radicals and Rational Exponents - The square root symbol isn't just a fancy checkmark - √9 = 3 because 3×3 = 9, and rational exponents let you express these roots with fractional powers. Master converting between radical form and exponents for ultimate flexibility in solving equations! OpenStax Algebra & Trigonometry: Radicals
  7. Learn the Binomial Theorem - Expand (a + b)^n like a pro using Σ from k=0 to n of C(n,k)a^(n-k)b^k, and you'll breeze through high‑power binomials in no time. Practice with small n first to see patterns pop before tackling the big leagues! LearnMathClass: Binomial Theorem
  8. Practice Operations with Fractions - Whether you're adding, subtracting, multiplying, or dividing, finding a common denominator or flipping and multiplying are the keys to keeping fractions friendly. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6 in a snap! Sierra College: Fraction Operations
  9. Understand Properties of Equality - If a = b, you can add, subtract, multiply, or divide both sides by the same number without breaking the balance. Use these rules to isolate variables and solve equations step by step like a true equation whisperer! Sierra College: Equality Properties
  10. Learn Special Products - Memorize (a + b)², a² - b², and the sum/difference of cubes to transform expansions and factorizations from chores into cheers. These power‑packed formulas are the ultimate time-savers on quizzes and homework! Sierra College: Special Products
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