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Quizzes > Mathematics > Algebra

Algebra 1 Chapter 1 Quiz - Test Your Skills

Think you can ace this intermediate algebra quiz? Dive in now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art style Algebra 1 quiz featuring fractions exponents order of operations symbols on dark blue background

Ready to boost your math confidence? Dive into our free algebra 1 chapter 1 test and tackle fractions, exponents, and order of operations. Whether you need pre algebra test prep or an intermediate algebra quiz, this algebra quiz offers targeted chapter 1 algebra practice and a quick algebra fundamentals quiz to strengthen your skills. Challenge yourself with algebra 1 questions, then review instant feedback. Ideal for homework, test prep, or review, our format adapts to your pace and highlights areas to revisit. Don't wait - start this engaging algebra 1 practice test now and see how far you'll go!

Simplify 3 + 5 * 2.
16
13
7
10
According to the order of operations, multiplication is performed before addition. First calculate 5 * 2 = 10, then add 3 to get 13. This method is often remembered by the acronym PEMDAS. Learn more about order of operations.
Simplify 6/3 + 2.
4
2
3
8
First divide 6 by 3 to get 2, then add 2 for a total of 4. Combining division and addition in this order ensures correct simplification. Review basic fraction operations.
Simplify (?3)^2.
6
-9
-6
9
When an entire negative number is squared, the result is positive because (?3)×(?3)=9. Be careful not to confuse this with ?3^2, which would be ?9. More on exponents.
Simplify 9^(1/2).
-3
81
4.5
3
An exponent of 1/2 indicates a square root. The square root of 9 is 3 (the principal root). Negative values are not chosen for the principal exponent result. Fractional exponents explained.
Combine like terms: 3x + 7x.
10x
4x
x
21x
Like terms have the same variable raised to the same power. Adding their coefficients 3 + 7 gives 10, so the sum is 10x. Learn about combining like terms.
Simplify 2(x + 3).
6x
2x + 3
2x + 6
x + 6
Use the distributive property: multiply 2 by each term inside the parentheses: 2·x = 2x and 2·3 = 6. More on the distributive law.
Solve for x: x + 5 = 12.
17
7
5
-7
Subtract 5 from both sides to isolate x: x = 12 - 5 = 7. This is a basic one?step linear equation. Solving linear equations.
Solve for x: 3x = 9.
6
3
0
-3
Divide both sides by 3 to get x = 9/3 = 3. Always perform the inverse operation to isolate the variable. Learn how to solve equations.
Evaluate 4x - 1 when x = 2.
9
8
7
6
Substitute x = 2 into the expression: 4(2) - 1 = 8 - 1 = 7. Plugging in values is key for evaluating expressions. Evaluating expressions guide.
Simplify 2x + 3 - x + 5.
3x + 2
x + 2
x + 8
x + 15
Combine like terms: 2x - x = x, and 3 + 5 = 8, giving x + 8. Be careful to group variables and constants separately. Combining like terms.
Simplify (4^3)/(2^3).
2
32
8
1
Calculate the numerator 4^3 = 64 and the denominator 2^3 = 8, then divide: 64/8 = 8. You can also use exponent rules: (4/2)^3 = 2^3 = 8. Exponent rules.
Simplify (2x^2) * (3x).
x^3
6x^3
6x^2
5x^3
Multiply coefficients: 2 * 3 = 6. Add exponents on x: 2 + 1 = 3. The product is 6x^3. Multiplying exponents.
Simplify 5 - [2 + 3*(4 - 2)].
-3
3
1
-1
First compute inside parentheses: 4 - 2 = 2, then multiply by 3 to get 6. Next add 2 for a total of 8. Finally subtract from 5 to get -3. Order of operations.
Simplify 2^3 * 2^2.
64
8
16
32
When multiplying like bases, add exponents: 2^(3 + 2) = 2^5 = 32. This rule applies to any multiplication of same-base powers. Exponent rules.
Simplify 3x^0 + 5.
8
5
3 + 5x
3x + 5
Any nonzero number to the zero power is 1. Thus 3x^0 = 3·1 = 3, and 3 + 5 = 8. Learn about zero exponents.
Combine like terms: 2x^2y - 3xy^2 + x^2y.
3x^2y - 3xy^2
3x^2y + 3xy^2
x^2y - 3xy^2
2x^2y + 3xy^2
Like terms are those with identical variable parts. Combine 2x^2y and 1x^2y to get 3x^2y; -3xy^2 remains unchanged. Combining like terms.
Solve for x: 2x + 3 = 11.
2
-4
4
7
Subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4. This is a two-step linear equation. Solving linear equations.
Solve for x: x/4 = 6.
2
24
10
12
Multiply both sides by 4 to isolate x: x = 6 × 4 = 24. Always perform the inverse operation to solve. Inverse operations.
Expand (3x - 2)^2.
9x^2 + 12x + 4
9x^2 - 4x + 4
6x^2 - 12x + 4
9x^2 - 12x + 4
Use (a - b)^2 = a^2 - 2ab + b^2: a=3x, b=2 gives 9x^2 - 12x + 4. This is a special product pattern. Square of a binomial.
Simplify (2x^2 * 4x^3) / (8x^2).
x^3
8x^3
x^2
2x
Multiply numerator: 2x^2·4x^3 = 8x^5. Then divide by 8x^2 to get x^(5?2) = x^3. Coefficients cancel and exponents subtract. Exponent division rule.
Simplify (5x - 3) + (2x + 7).
3x + 4
7x - 10
7x + 4
10x + 4
Combine like terms: 5x + 2x = 7x, and -3 + 7 = 4. This yields 7x + 4. Group variables and constants separately. Like terms.
Simplify 3(x - 2) + 4(2x + 1).
x + 2
11x + 2
11x - 2
5x - 2
Distribute: 3x -6 + 8x +4 = (3x+8x) + (-6+4) = 11x -2. Always handle each distribution separately. Distributive property.
Simplify (x^3)^2.
x^9
x^6
x^5
x
When raising a power to another power, multiply the exponents: x^(3·2) = x^6. This is a key exponent rule. Power of a power.
Simplify 27^(2/3).
3
81
9
27
27^(2/3) means take the cube root of 27 (which is 3) and square it to get 9. Fractional exponents combine root and power. Fractional exponent rules.
Solve 2(x - 3) + 4 = 16.
11
9
7
8
First distribute: 2x - 6 + 4 = 16 ? 2x - 2 = 16 ? 2x = 18 ? x = 9. Follow step?by?step isolation of x. Linear equations.
Solve for x: 1/2 x - 7 = 3.
-8
10
20
14
Add 7 to both sides: 1/2 x = 10, then multiply by 2 to get x = 20. Always reverse each operation in order. Equation solving.
Solve 3x + 2 = 2x + 9.
5
-7
7
11
Subtract 2x from both sides: x + 2 = 9, then subtract 2: x = 7. Solving for x involves collecting like terms. Learn more.
Simplify (16x^4y^2)^(3/4).
8x^3y^2
8x^4y^(3/4)
8x^3y^(3/2)
16x^3y^(3/2)
Apply exponent: 16^(3/4) = (2^4)^(3/4) = 2^3 = 8. Multiply exponents: x^(4·3/4)=x^3 and y^(2·3/4)=y^(3/2). Fractional exponents.
Simplify (x^2 - 4)/(x - 2).
x - 2
x^2 - 4
x + 2
(x + 2)/(x - 2)
Factor numerator: x^2 - 4 = (x - 2)(x + 2), then cancel (x - 2). The simplified result is x + 2, for x ? 2. Factoring techniques.
Simplify 4[2(x+1) - 3] + x.
9x + 4
8x + 4
8x - 4
9x - 4
First compute inside: 2(x+1)=2x+2, minus 3 gives 2x - 1; times 4 is 8x - 4; add x to get 9x - 4. Distributive property.
Solve (2x - 3)/5 + (x + 2)/2 = 1.
-2/3
4/9
2/3
1
Multiply both sides by 10: 2(2x-3)+5(x+2)=10 ? 4x-6+5x+10=10 ? 9x+4=10 ? 9x=6 ? x=2/3. Solving complex equations.
0
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Study Outcomes

  1. Apply Fraction Operations -

    Perform addition, subtraction, multiplication, and division of fractions and rational expressions with confidence when tackling the algebra 1 chapter 1 test.

  2. Simplify Exponent Expressions -

    Use power rules to combine like bases, evaluate zero and negative exponents, and streamline expressions in this intermediate algebra quiz.

  3. Use Order of Operations -

    Apply PEMDAS to complex numerical and algebraic expressions, ensuring accurate step-by-step solutions during chapter 1 algebra practice.

  4. Solve Linear Equations -

    Isolate variables in one-step and multi-step equations, translating word problems into algebraic solutions on this algebra fundamentals quiz.

  5. Evaluate Algebraic Expressions -

    Substitute values into expressions and simplify results to test your understanding in the free pre algebra test format.

  6. Interpret Instant Feedback -

    Analyze quiz results to pinpoint strengths and areas for review, guiding targeted study after completing the intermediate algebra quiz.

Cheat Sheet

  1. Simplifying Fractions -

    Review how to reduce fractions by dividing numerator and denominator by their greatest common divisor (GCD). For example, 18/24 becomes 3/4 after dividing both by 6 (GCD). Practice with resources like Khan Academy to build speed and accuracy.

  2. Fraction Operations -

    Master adding and subtracting fractions by finding the least common denominator (LCD); for instance, 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Multiplying and dividing fractions follows simple rules: multiply across or flip and multiply (keep - change - flip). Purplemath offers clear worked examples for each operation.

  3. Exponent Laws -

    Internalize the key rules: a^m × a^n = a^(m+n), (a^m)^n = a^(mn), and a^0 = 1 (when a≠0). Use the mnemonic "Add - Multiply - Zero" to recall sum, power of a power, and zero exponent rules. The University of Cambridge's math site provides thorough proofs and practice.

  4. Order of Operations (PEMDAS) -

    Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction, using the phrase "Please Excuse My Dear Aunt Sally." Always work inside grouping symbols first, then apply exponents, before moving left to right on M/D and A/S. This ensures consistency in solving expressions.

  5. Distributive Property & Like Terms -

    Use a(b + c) = ab + ac to expand expressions and combine like terms such as 3x + 5x = 8x. Recognizing coefficients and variables helps simplify polynomial expressions efficiently. The National Council of Teachers of Mathematics (NCTM) endorses systematic practice for mastery.

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