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Algebra 2 - Expressions - Check for Understanding

10 questions

10th - 10th Grade

Mathematics

Algebra 2 - Expressions - Check for Understanding is a Grade 10 mathematics worksheet that builds fluency with interpreting, evaluating, and rewriting algebraic expressions. Students determine which expressions are equivalent, evaluate an expression by substituting negative values for variables, identify an expression for the area of a rectangle with algebraic side lengths, and translate verbal descriptions involving squares, cubes, multiplication, subtraction, and constants. The worksheet includes 10 questions: 9 multiple-choice items and 1 multiple-select item. Several questions ask students to select all equivalent expressions, while others assess expression evaluation, identifying the constant in a translated expression, and recognizing factored or rewritten forms. Use this free printable worksheet as a check for understanding after instruction or as independent practice. It includes a complete answer key for efficient review and grading.

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Worksheets

Algebra 2 - Expressions - Check for Understanding

Total questions: 10

Name
Class
Date
1.

Select the correct answer. Which expression is equivalent to the given expression? (ab2)3b5\frac{\left(ab^2\right)^3}{b^5}

a)

a3ba^3b

b)

a3b\frac{a^3}{b}

c)


a3a^3

d)

a4b\frac{a^4}{b}

2.

Select the correct answer. The length of a rectangle is (x - 8) units, and its width is (x + 11) units. Which expression can represent the area of the rectangle?

a)

x2 + 3x − 88x^2\ +\ 3x\ -\ 88

b)

x2 − 3x − 88x^2\ -\ 3x\ -\ 88

c)

x2 + 3x + 88x^2\ +\ 3x\ +\ 88

d)

x2 − 3x + 88x^2\ -\ 3x\ +\ 88

3.

Select the correct answer. What is the value of this expression if a = -7 and b = -3?

a3 − b2a^3\ -\ b^2

a)

-334

b)

-352

c)

-12

d)

-30

4.

Select all the correct answers. Which expressions are equivalent to the given expression?

y−8y3x0x−2y^{-8}y^3x^0x^{-2}

a)

x2y11\frac{x^2}{y^{11}}

b)

1y24\frac{1}{y^{24}}

c)

x−2y−5x^{-2}y^{-5}

d)

1x2y5\frac{1}{x^2y^5}

e)

y−24y^{-24}

5.

Select the correct answer. Which statement correctly describes this expression?

2m3 − 112m^3\ -\ 11

a)

the difference of twice a number and 11 cubed

b)

the difference of twice the cube of a number and 11

c)

twice the cube of a number subtracted from 11

d)

the cube of twice a number decreased by 11

6.

Select the correct answer. Which expression is equivalent to the given expression?

45\sqrt[]{45}

a)

53\sqrt[3]{5}

b)

95\sqrt[5]{9}

c)

59\sqrt[9]{5}

d)

35\sqrt[5]{3}

7.

Select all the correct answers. Which expressions are equivalent to the given expression?

252\sqrt[]{252}

a)

718\sqrt[18]{7}

b)

76\sqrt[6]{7}

c)

12612126^{\frac{1}{2}}

d)

67\sqrt[7]{6}

e)

25212252^{\frac{1}{2}}

8.

Select the correct answer. Which expression is equivalent to the given expression?

68\sqrt[8]{6}

a)

96\sqrt[]{96}

b)

384\sqrt[]{384}

c)

48\sqrt[]{48}

d)

576\sqrt[]{576}

9.

Select the correct answer. Write an expression to represent the sum of three times the square of a number and -7. In your expression, what is the value of the constant?

a)

1

b)

3

c)

2

d)

-7

10.

Select the correct answer. Which expression is equivalent to the given expression?

2x2 − 11x −62x^2\ -\ 11x\ -6

a)

(2x + 3)(x - 2)

b)

2(x + 3)(x - 2)

c)

2(x - 3)(x + 1)

d)

(2x + 1)(x - 6)

Answer Key

Algebra 2 - Expressions - Check for Understanding

Total questions: 10

1.
a)

a3ba^3b

2.
a)

x2 + 3x − 88x^2\ +\ 3x\ -\ 88

3.
b)

-352

4.
c)

x−2y−5x^{-2}y^{-5}

, d)

1x2y5\frac{1}{x^2y^5}

5.
b)

the difference of twice the cube of a number and 11

6.
a)

53\sqrt[3]{5}

7.
e)

25212252^{\frac{1}{2}}

8.
b)

384\sqrt[]{384}

9.
d)

-7

10.
d)

(2x + 1)(x - 6)

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FAQs

What does this Algebra 2 expressions worksheet help students practice?

This Grade 10 worksheet helps students interpret, evaluate, and identify equivalent algebraic expressions through 10 multiple-choice and multiple-select questions. Students substitute negative values, represent a rectangle’s area with algebraic side lengths, translate verbal descriptions involving powers and operations, identify constants, and compare equivalent forms.

How can I use this worksheet to teach algebraic expressions?

Use the worksheet after modeling how to preserve operation order, evaluate powers and signs, and rewrite expressions into equivalent forms. Before students work independently, discuss how phrases such as “twice the cube of a number” differ from “the cube of twice a number,” then use the rectangle-area item to connect multiplication of binomials to a geometric context. Review the multiple-select items by asking students to justify why each selected expression has the same value.

What mistakes should I watch for on this expressions worksheet?

Watch for students applying an exponent to the wrong part of a verbal expression, confusing subtraction order, or mishandling negative values during substitution. Students may also identify only one equivalent form on a select-all item, confuse a coefficient with the constant, or overlook that an area expression comes from multiplying the rectangle’s length and width. Have students check equivalent expressions by simplifying both forms or testing a valid value.

How do I assign and grade this algebraic expressions worksheet?

On Wayground, assign this worksheet as a printable PDF or as a digital quiz. The complete answer key supports grading the equivalent-expression, substitution, verbal-translation, area, and constant-identification items, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this algebraic expressions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the equivalent-expression choices and multi-select directions are easier to scan. You can also enable a dyslexia-friendly font or translate the worksheet into another language, which may support students as they interpret the verbal expression and rectangle-area items.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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